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Design and evaluation of adaptive redirected walking systems

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Design and evaluation of adaptive redirected walking systems

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Content Design and Evaluation of Adaptive
Redirected Walking Systems
Mahdi Azmandian
faculty of the usc graduate school
doctor of philosophy
(computer science)
May 2018
Copyright © 2018 Mahdi Azmandian
published by university of southern california
http://www.usc.edu
First Printing, May 2018
Yesterday I was clever, so I wanted to change the world.
Today I am wise, so I am changing myself.
Sell your cleverness and buy bewilderment.
– Jalaluddin Rumi
A B S T R A C T
Real walking is the most intuitive locomotion metaphor for virtual
reality applications. Despite its many benefits, real walking inher-
ently restricts users to a confined physical space. Redirected walk-
ing is a perceptual illusion introduced to overcome this limitation by
leveraging the characteristics of the human perception system. While
redirection has come a long way since its conception, a majority of
the research in the field has been focused on the perceptual aspects
of redirection. Though crucial, the human component of redirection
is just one piece of the puzzle and it does not provide us with an
application method. Harnessing the potential of redirected walking
requires acknowledging the multiple facets of the problem, and de-
signing a system that addresses its requirements methodically. This
work provides the theoretical foundation to achieve this, bridging the
gap between understanding redirection and employing it.
I begin first by providing a formal definition and hierarchical de-
sign for the envisioned redirection system. The hierarchy illustrates
how redirection techniques — as the building blocks — are used to
form heuristics, in turn forming strategies, and ultimately shaping the
structure of a complete redirection system. For a holistic conception
of a system’s performance, at each level of the hierarchy, a notion of
performance is defined that corresponds to the objectives of that level.
Measuring this nuanced understanding of performance is made pos-
sible by the evaluation methodology and platform. The methodology con-
trols for factors that affect the system’s behavior; and by simulating a
breadth of conditions allows teasing out the interaction of influential
variables.
With the theoretical foundation and methodical framework estab-
lished, I propose adaptive redirection: a novel redirection system forged
by a meta-strategy that adapts to the context in which redirection is
deployed. To develop the adaptive meta-strategy, redirection strate-
gies are first classified into three categories. Each category is closely
examined and further developed for integration with the adaptive
paradigm. Then using the evaluation platform, the performance of
each category is measured across different contexts in order to de-
velop adaptation rules for transitioning between strategies based on
the context. In addition to guiding development, the platform is also
used to measure the expected performance and space requirements
for redirected walking in the adaptive paradigm. This demonstrates
how the proposed theoretical foundation and evaluation framework
complement one another, for engineering the illusion of redirected
walking.
1
Dedicated to those who go that extra mile, just because.
A C K N O W L E D G E M E N T S
My journey started with meeting Dr. Evan Suma Rosenberg whom
I implored to be my Ph.D. advisor, long before he had an official
appointment in the Computer Science Department. Thank you for
accepting me, patiently guiding me, and always being there for me.
I send out a special thank you to my honorary co-advisor Profes-
sor Mary Whitton who helped me redesign my dissertation from the
ground up, showing me how to bring my vision to life. “Nurturing”
is the term that best describes her presence in my academic life.
Mark Bolas was the person who opened the floodgates of inspira-
tion with his authenticity and genuine care for the Mixed Reality lab.
My favorite memory of him was when in my first week of working
at the lab he walked up to me and said: “I’ve been getting some up-
dates here and there from Evan about your work. But I just wanted
to let you know that at the MxR lab we don’t f*** around, we get sh*t
done”. I also loved learning about storytelling concepts from Mark,
with his down-to-earth eccentric mannerisms.
Dr. Timofey Grechkin had me speechless on so many occasions,
from his true resolution in enlightening me, no matter the sacrifices it
entailed. Never with such reverence have I looked up to such a giving
mentor. As an often-regarded as rebellious and skeptic student, I
rarely submit to my supervisors, but Timofey’s profound knowledge
paired with his unwavering humility is why he will always have my
respect.
Rhys Yahata was the first person to show me the ropes at the MxR,
and help me implement this bizarre trick called redirected walking. We
started off as lab-mates, graduated to colleagues, evolved into friends,
and today I’m proud to call him my brother. Rhys was there for me
in my toughest times, and god only knows how plentiful they were.
But he lifted me up, and kept cheering me on. It was a thrill working
with you Rhys, and thank you for pushing me so hard because you
know I needed it.
It’s been humbling to work alongside brilliant scientists and engi-
neers who graciously shared their years of technical expertise and
always pushed me towards perfection with their invaluable feedback.
I’d be remiss not to single out Ryan Spicer whose unshakeable work
ethic always made Rhys and I feel like lollygaggers.
I’m grateful for a committee who made me truly understand what
the “Ph” — the philosophy component — of a PhD is about, with
their true commitment to the philosophy of science, and scientific
thinking. Thank you Drs. Paul Rosenbloom, Scott Fisher, Nora Aya-
nian, and Stefan Scherer.
3
4
A big thank you to David Nelson and Allison Aptaker who always
made everything flow smoothly. Their care and support is the reason
why MxR feels like family.
I’ll never find the words that would do justice, so I’ll just nod to
my mother and father, and smile, because they know.
Thank you to all who have brought light into my life with their
teachings, through different chapters of my life, from my parents, to
mentors, to friends. I bow to you all.
C O N T E N T S
i the preamble 13
1 introduction 14
1.1 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 background 22
2.1 Locomotion and Real Walking . . . . . . . . . . . . . . 22
2.2 Redirected Walking . . . . . . . . . . . . . . . . . . . . . 23
2.3 Why Redirection Works . . . . . . . . . . . . . . . . . . 23
2.4 Manipulation Techniques . . . . . . . . . . . . . . . . . 23
2.5 Perception of Redirection . . . . . . . . . . . . . . . . . 25
2.6 Drawbacks and Benefits of Redirection . . . . . . . . . 28
2.7 Approaches to Using Redirection . . . . . . . . . . . . . 29
2.8 Steering Algorithms . . . . . . . . . . . . . . . . . . . . 30
2.9 Reorientation . . . . . . . . . . . . . . . . . . . . . . . . 31
2.10 Forming a Complete Redirected Walking System . . . 32
2.11 Planned Redirection . . . . . . . . . . . . . . . . . . . . 34
2.12 Alternative Illusions . . . . . . . . . . . . . . . . . . . . 35
2.13 Terminology and Conventions . . . . . . . . . . . . . . 36
2.13.1 Redirection . . . . . . . . . . . . . . . . . . . . . 36
2.13.2 Physical Space . . . . . . . . . . . . . . . . . . . 36
2.13.3 Reorientation . . . . . . . . . . . . . . . . . . . . 36
2.13.4 System . . . . . . . . . . . . . . . . . . . . . . . . 37
2.13.5 Gain Calculation . . . . . . . . . . . . . . . . . . 37
2.13.6 User . . . . . . . . . . . . . . . . . . . . . . . . . 37
ii theoretical foundation 39
3 redirected walking systems 40
3.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Design Hierarchy of a Redirected Walking System . . . 40
3.3 Redirection Techniques . . . . . . . . . . . . . . . . . . . 41
3.3.1 Performance of Techniques . . . . . . . . . . . . 41
3.4 Redirection Heuristics . . . . . . . . . . . . . . . . . . . 42
3.4.1 Performance of Heuristics . . . . . . . . . . . . . 43
3.5 Redirection Strategies . . . . . . . . . . . . . . . . . . . . 43
3.5.1 Inputs . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5.2 Outputs . . . . . . . . . . . . . . . . . . . . . . . 45
3.5.3 Internal Components of a Redirection Strategy 45
3.5.4 Performance of Strategies . . . . . . . . . . . . . 46
3.6 Redirection System . . . . . . . . . . . . . . . . . . . . . 46
3.6.1 Performance of Redirection Systems . . . . . . . 46
5
Contents 6
4 evaluation methodology and platform 49
4.1 Simulation: The Response to Interacting Factors . . . . 50
4.2 Components of the Evaluation Platform . . . . . . . . . 50
4.2.1 Redirection Strategy . . . . . . . . . . . . . . . . 51
4.2.2 Perceptual Detection Thresholds . . . . . . . . . 51
4.2.3 Simulated User . . . . . . . . . . . . . . . . . . . 52
4.2.4 Virtual Path Generator . . . . . . . . . . . . . . . 52
4.2.5 Safety Trigger . . . . . . . . . . . . . . . . . . . . 53
4.2.6 Simulating Time & Framerate . . . . . . . . . . . 54
4.2.7 Data Logger . . . . . . . . . . . . . . . . . . . . . 54
4.3 Measuring Performance . . . . . . . . . . . . . . . . . . 56
4.4 Validating the Evaluation Platform . . . . . . . . . . . . 57
4.4.1 Micro-Scale Inspection . . . . . . . . . . . . . . . 58
4.4.2 Macro-Scale Inspection . . . . . . . . . . . . . . 62
4.4.3 Countering Deviation . . . . . . . . . . . . . . . 64
4.4.4 Gain Application Methods Robust to Locomo-
tion Behavior Variability . . . . . . . . . . . . . . 66
4.4.5 User Study and Experiment Design . . . . . . . 67
4.4.6 Task . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4.7 Results and Discussion . . . . . . . . . . . . . . 72
4.4.8 Summary . . . . . . . . . . . . . . . . . . . . . . 85
iii the adaptive paradigm 87
5 the adaptive meta-strategy 88
5.1 A Taxonomy of Redirection Strategies . . . . . . . . . . 89
5.1.1 General Strategies . . . . . . . . . . . . . . . . . 89
5.1.2 Dynamic Planning Strategies . . . . . . . . . . . 89
5.1.3 Static Planning Strategies . . . . . . . . . . . . . 90
5.2 Prediction Graph Properties . . . . . . . . . . . . . . . . 90
5.2.1 Segment Length Distribution . . . . . . . . . . . 90
5.2.2 Turn Angle Distribution . . . . . . . . . . . . . . 90
5.2.3 Branching Factor Distribution . . . . . . . . . . 91
5.3 From Prediction Graph to Most Effective Strategy . . . 91
5.3.1 Measuring Redirection Performance on a Pre-
diction Graph . . . . . . . . . . . . . . . . . . . . 91
5.3.2 Sampling the Prediction Graph Space . . . . . . 92
iv developing adaptation: the examination of redi-
rection strategies 93
6 general redirection strategies 94
6.1 Motivation and Goals . . . . . . . . . . . . . . . . . . . . 94
6.1.1 Primary Goals . . . . . . . . . . . . . . . . . . . . 94
6.1.2 Secondary Goals . . . . . . . . . . . . . . . . . . 95
6.2 Experiment1: The Interaction of Size, Strategy and Vir-
tual Path . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2.1 Experimental Setup . . . . . . . . . . . . . . . . 97
6.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . 99
Contents 7
6.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . 102
6.3 Experiment 2: The Interaction of Shape and Strategy . 104
6.3.1 Experimental setup . . . . . . . . . . . . . . . . . 104
6.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . 105
6.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . 106
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7 dynamic planning redirection strategies 108
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.2 Background on Navigation meshes . . . . . . . . . . . . 109
7.3 Path Prediction Algorithm Definition . . . . . . . . . . 111
7.4 Implementation and Performance Assessment . . . . . 114
7.4.1 Comparison to Manual Annotations . . . . . . . 114
7.4.2 Graph Generation Time . . . . . . . . . . . . . . 115
7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 116
8 static planning redirection strategies 118
8.1 Conception . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.1.1 Evolution . . . . . . . . . . . . . . . . . . . . . . 119
8.1.2 A Means to a Demonstrative End . . . . . . . . 119
8.2 From Dynamic to Static Planning . . . . . . . . . . . . . 120
8.3 COPPER’s Static Planning . . . . . . . . . . . . . . . . . 121
8.3.1 Simplifications and Assumptions . . . . . . . . 121
8.3.2 Data Structures . . . . . . . . . . . . . . . . . . . 122
8.3.3 Performing the Search . . . . . . . . . . . . . . . 122
8.3.4 Pruning . . . . . . . . . . . . . . . . . . . . . . . 123
8.3.5 Utility Function . . . . . . . . . . . . . . . . . . . 124
8.3.6 Offline Pre-Calculations . . . . . . . . . . . . . . 124
v assembling adaptation: the construction of adap-
tation rules 126
9 adaptation rules 127
9.1 Experiment: Constructing Adaptation Rules . . . . . . 128
9.1.1 User Simulation . . . . . . . . . . . . . . . . . . . 128
9.1.2 Procedure . . . . . . . . . . . . . . . . . . . . . . 128
9.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.2.1 Branching Prediction Graph . . . . . . . . . . . 129
9.2.2 Non-Branching Prediction Graph . . . . . . . . 131
9.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.4 Expected Performance of Adaptive Redirection . . . . 134
9.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 139
9.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
vi further advancements 141
10 research and development guidelines for future
work 142
10.1 Resets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.1.1 Triggering . . . . . . . . . . . . . . . . . . . . . . 143
10.1.2 Efficacy . . . . . . . . . . . . . . . . . . . . . . . . 144
Contents 8
10.1.3 Disruption . . . . . . . . . . . . . . . . . . . . . . 144
10.2 General Redirection Strategies . . . . . . . . . . . . . . 144
10.2.1 Heuristics . . . . . . . . . . . . . . . . . . . . . . 145
10.3 Dynamic Planning Redirection Strategies . . . . . . . . 145
10.3.1 Prediction Graph Integration . . . . . . . . . . . 145
10.3.2 User Intent . . . . . . . . . . . . . . . . . . . . . . 145
10.3.3 Optimization . . . . . . . . . . . . . . . . . . . . 146
10.4 Static Planning Redirection Strategies . . . . . . . . . . 146
10.4.1 Counter-Deviation . . . . . . . . . . . . . . . . . 147
10.4.2 Redirection Friendliness . . . . . . . . . . . . . . 148
10.4.3 Non-Linearity . . . . . . . . . . . . . . . . . . . . 148
10.5 Perception . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10.5.1 Calibration Procedure . . . . . . . . . . . . . . . 150
10.5.2 Gain Smoothing . . . . . . . . . . . . . . . . . . 150
10.6 Ad Hoc Redirection . . . . . . . . . . . . . . . . . . . . . 150
10.6.1 Dynamic Physical Space . . . . . . . . . . . . . . 150
10.7 Multi-User Redirection . . . . . . . . . . . . . . . . . . . 151
10.7.1 Collision Prevention . . . . . . . . . . . . . . . . 151
10.7.2 Convergence . . . . . . . . . . . . . . . . . . . . 151
G L O S S A RY O F T E R M S
2:1-turn reset an implementation of resets that uses rotation gains,
upscaling the user’s virtual motions by a factor of two,
making a 360 virtual rotation equate to a 180 rotation in the
physical space.
adaptive redirection a redirection system based on a context-aware
meta-strategy that adapts to the context in which redirection
is applied.
boundary a border designating the end of the physical space that
should be avoided by the user.
COPPER Combinatorially Optimized Pre-Planned Exploration Redirector,
a static planning redirection strategy
counter-deviation a mechanism that combats the manifestation of
deviation.
CTG shorthand for Center-based Translation Gain, a redirection
heuristic that upscales the user’s translation when moving
away from the center of the physical space.
curvature gain injecting rotations to the user’s virtual motion in
proportion to the amount of real translation.
detection threshold a critical gain value beyond which a gain is
likely to be noticed.
deviation a departure from the expected redirection applied.
dynamic planning strategy a category of redirection strategies that
require the user to be predictable in order to dynamically plan
redirection accordingly.
dynamic-gain a method of applying gains in which the rate of gains
frequently changes throughout each segment of a virtual path.
evaluation platform the proposed simulation-based platform that
allows for methodological performance evaluation or
redirection strategies/systems.
face-center reset an implementation of resets that uses rotation
gains to cause the user to face towards the center of the
physical space when the reset task is complete.
fixed-gain a method of applying gains in which the rate of gains
remains constant throughout each segment of a virtual path.
9
Contents 10
FORCE Fully Optimized Redirected Walking for Constrained
Environments, a planning redirection heuristic
FOV shorthand for Field Of View.
gain a single form of manipulating the user’s virtual motions
relative to the real motion.
general strategy the category of redirection strategies that can be
applied to any scenario.
HMD shorthand for Head/Helmet-Mounted Display.
locomotion the act of moving oneself, specifically within a virtual
reality experience.
meta-strategy a function that resides above other redirection
strategies governing how they are combined.
MPCRed Model Predictive Control Redirection, a dynamic planning
redirection strategy
Null Redirector the baseline redirection heuristic in which no
redirection techniques (gains) are applied.
perceptual threshold the category of all detection thresholds.
physical space the area within the real world in which the user
walks while exploring a virtual environment. In this work
physical space and tracked space mean the same thing.
prediction graph a graph representing the user’s short-term
navigation options within the confines of the virtual
environment.
real user a human user wearing a head-mounted display
experiencing virtual reality.
real/virtual path the simplified expression of the user’s movement
in the real/virtual world using primitives such as lines and
arcs.
real/virtual trajectory the actual trail of movement by the user in
the real/virtual world formed by the sequence of positions.
redirected walking a perceptual illusion that introduces subtle
discrepancies between real and virtual motions to keep users
within physical space boundaries.
redirected walking toolkit the open-source implementation of the
evaluation platform proposed in this work.
redirection shorthand for redirected walking
Contents 11
redirection heuristic any mechanism or algorithm that uses one or
more redirection techniques to fulfill a certain task or move
towards an objective.
redirection strategy a mechanism that uses one or more heuristics
in order to ensure users remain within the confines of the
physical space.
redirection system a complete locomotion interface that solves the
problem of exploring arbitrarily large virtual environments
within a limited physical space using one or more redirection
strategies.
redirection technique any mechanism used in redirected walking
for manipulating the user’s trajectory.
reorientation a fail-safe mechanism that is often triggered when the
user reaches a physical boundary in order to prevent the user
from leaving the physical space.
reorientation heuristic the underlying algorithm that determines
how to manipulate the relationship between the physical
space and the virtual environment to achieve a reorientation.
reorientation mechanism the underlying manipulations used to
achieve a reorientation such as rotation and/or translation
gains and also freezing the screen.
reorientation task the prompt, cues and instructions shown to the
user in order to elicit the desired actions for achieving the
reorientation.
reset a type of reorientation that involves manipulating the user’s
location in the physical space to move her out of the path of a
physical obstruction while maintaining their spatial awareness
of the virtual space.
reset buffer the area between the reset trigger and the boundary
that acts as a buffer to allow for users to react to reset cues
and safely perform the reset task.
reset trigger a safety trigger specifically designed to initiate resets.
rotation gain upscaling or downscaling a user’s virtual rotation
relative to the real rotation.
S2C shorthand for Steer-To-Center, a redirection heuristic that aims
to steer the user towards the center of the physical space.
S2O shorthand for Steer-To-Orbit, a redirection heuristic that aims
to steer the user into an orbit around the center of the
physical space.
Contents 12
safety trigger a trigger placed within the virtual representation of
the physical space in order to initiate safety mechanisms that
keep the user from harm.
search horizon the depth of a planning redirection heuristic that
determines how far in the future the user’s actions are
considered
simulated user a simulated representation of a real user.
static planning strategy a category of redirection strategies that can
only be applied when the user’s path is predetermined so that
a static redirection plan can be executed.
tracked space alternative word for physical space, specifically
referring to the physical space over which trackers are active
translation gain upscaling or downscaling a user’s virtual
translation relative to the real translation.
user a person (simulated or real) immersed in a virtual reality
experience.
VR shorthand for Virtual Reality.
Part I
T H E P R E A M B L E
1
I N T R O D U C T I O N
There is nothing more
difficult to take in hand, more
perilous to conduct, or more
uncertain in its success, than
to take the lead in the
introduction of a new order
of things.
Niccolo Machiavelli
One of the great challenges for virtual reality is locomotion: im-
parting the belief that “I am moving.” The most natural form of loco-
motion is real walking: inducing the sense of “I am moving, because
I am moving.” This seeming tautology follows the practice of us-
ing natural and intuitive metaphors while also offering an improved
sense of presence in comparison to other common locomotion inter-
faces [Usoh et al.,1999]. However, adopting a real walking metaphor
requires designating a physical space for walking, and a designated
physical space is inherently finite and bounded. This means the illu-
sion of exploring a virtual world is limited to what can be contained
in the physical space. But as with any illusion, physical limits can be
surpassed.
Redirected Walking [Razzaque, 2005] is a perceptual illusion that
plays on the idiosyncrasies of human perception to make users be-
lieve they are walking on one path, while in reality traversing another.
This is achieved by introducing subtle discrepancies between real and
virtual motions that cause virtual and real trajectories to diverge unbe-
knownst to the user. These manipulations alter the conventional one-
to-one mapping between a user’s motion in the real world and that of
the virtual. Therefore, large virtual explorations can conceivably be
mapped to real trajectories contained within the physical space. This
idea is what makes redirection a potential solution to physical space
constraints for natural locomotion in VR.
With more than a decade and half since the conception of redi-
rected walking, one must wonder what measurable impact has this
field had on the landscape of virtual reality? First off, redirection
has given us a practical reason to better understand our perception,
specifically in the manner it resolves conflicts [R¨ oßler and Hanebeck,
14
introduction 15
2006, Steinicke et al., 2010, Burns et al., 2007]. In fact, a large body
of the literature on redirection has been invested in understanding
the perceptual implications of redirected walking. This is indeed an
extremely high priority for delivering a safe and comfortable experi-
ence to end users. The knowledge obtained by extensive user studies
has established redirection’s perceptual manipulations as viable tech-
niques. Thanks to these efforts, we have now moved beyond seeing
redirection as one of the many surprising peculiarities of human per-
ception.
The much greater impact that we expect from redirection, remains
as an untapped potential, hinging on a fundamental open problem:
How exactly can redirection be utilized in practical applications? Ex-
isting incarnations of redirected walking often serve more as proof-of-
concept demonstrations often barely managing to hit the mark, rather
than widely usable solutions. This is in part due to their limited
scope, prohibitively demanding space requirements, and often dis-
comforting user experiences. The reason for this is that the practical
concerns of redirection are often an afterthought and left for specula-
tion [Azmandian et al., 2015]. I believe what has been hindering the
wide adoption of redirection is an imbalanced emphasis of research
on the key components to effectively using redirection. Research on
the technical aspects of redirection has been dwarfed by the greater
focus on the perceptual side of the problem.
The next stage of advancements involves taking the theoretical
perceptually-validated techniques and evolving them in order to as-
semble a system that enables practical application. Such a system
would examine all aspects of redirected walking to provide a com-
plete solution. The human component of redirection is just one piece
of the puzzle and it has been studied exhaustively, but it does not pro-
vide us with an application method. What is lacking is an approach
that treats redirection as a complete problem and respects both per-
ceptual and technical factors involved in solving it. We must realize
that redirected walking is a mechanism. This mindset allows us to see
it as a tool, then proceed to create a system around it that takes ad-
vantage of its properties in order to use it effectively. The answer lies
in engineering this perceptual illusion. This is the approach neces-
sary to achieve an efficacy that fosters widespread adoption, and will
make redirection an integral component of VR tracking solutions. I
present a resolution this imbalance, a foundation that can finally har-
ness the potential of redirection. This work fills the void between
understanding redirection and employing it.
This dissertation defines the concept of redirection system that
leverages the established building blocks of redirected walking in a
system that is designed to maximize salient aspects of all types of
performance. The purpose of this system is to provide the theoret-
ical and practical framework necessary for engineering redirection
1.1 goals 16
effectively. This framework both integrates previous work into its
unifying infrastructure and also serves as a roadmap for future devel-
opment of redirected walking. This work is meant to be a blueprint
upon which redirected walking is defined, designed and refined for
consumer-level deployment.
1.1 goals
The primary goal of this dissertation is to paint a clear picture of a
redirected walking system, communicating that a redirected walking
solution is not simply encapsulated in human perception and comfort
factors. For redirected walking to become usable and ubiquitous, our
attention must be shifted to all aspects that it pertains to, and uncover
the many nuances hidden deep in the interactions of this complex
system. Only with a systematic approach can we truly tap into the
potential of redirected walking.
The core goals of this dissertation can be summarized as provid-
ing a Theoretical Foundation, Methodological Framework, Empirical Per-
formance Evaluation and the System Design and Integration of a redi-
rected walking system. These ingredients are the key taking redirec-
tion from theory and putting it to practice.
1. Theoretical Foundation Establishing a clear foundation is in-
strumental in taking redirection from a mere illusion to a com-
plete solution. This is achieved by proposing the notion of a
redirection walking system. Such an infrastructure not only en-
compasses all previous efforts and identifies how they fit in the
greater picture, but it also lays out a map of avenues that de-
mand further investigation. My vision of the research trajectory
that will ultimately lead us to effective redirection is laid in the
very definitions, structures and guidelines provided.
2. Methodological Framework In my design, building upon the
infrastructure and giving substance to it is made possible with
the guidance of evaluation tools. They serve as the crucible
in which hypotheses and conjectures are matured, and forged
into robust solutions and innovative paradigms. It is impera-
tive however, to first and foremost ensure the reliability of such
tools before proceeding to rely on them for ground truths. A val-
idated methodological framework is the key to addressing both
the science of understanding the problem space and develop-
ment of new methods. The applications go beyond the context
of this work; the methodological framework is envisioned as
the de facto standard platform for future studies, analysis and
deployment.
3. Empirical Performance Evaluation The development of effec-
tive methods is only possible with scientific knowledge of the
1.2 contributions 17
problem space. By investigating various aspects of redirection,
we can understand its needs, identify principal factors of influ-
ence, and tease out deep interactions between salient proper-
ties. The knowledge obtained can help with creating useful per-
formance metrics, address practical considerations, and overall
guide the process of developing a redirection system.
4. System Design and Integration The development, and more
specifically the development of a redirection system is the end
goal of this endeavor. This is where all previous goals are tied
together, taking ideas — existing or novel — and evolving them
into deployable solutions. This is the substance we create on the
theoretical foundation, with the insight from the empirical per-
formance evaluation, and the guidance from the methodologi-
cal framework. Instances of development in this work include
automating existing methods and creating entirely new strate-
gies for redirection. An overarching development goal however,
is producing the first complete redirection system: adaptive
redirection. The driving insight of this paradigm was inspired
by the empirical performance evaluations suggesting that not
one single redirection strategy outperforms all others, but rather
the approach must adapt to the context in which it is deployed.
The process of constructing adaptive redirection also demon-
strates how the theoretical foundation in this dissertation works
in harmony with the methodological framework presented, serv-
ing as the mind and body that cultivate ideas into fully-realized
methods.
1.2 contributions
I will begin by presenting a theoretical foundation for redirected walk-
ing. This framework introduces the notion of a redirected walking
system and all its components in a hierarchical structure. Starting
with the building blocks, I will identify redirection techniques, how
they are used in heuristics, and together form redirection strategies,
and finally expand to create a redirection system. The notion of per-
formance will be defined at each in accordance with its objectives, in
order to provide a broader notion of the overall performance of an
entire redirection system.
While performance for various redirection techniques and heuris-
tics has been previously studied, the performance of a redirection
strategy and system has never been formally defined. Furthermore,
previous attempts at evaluating redirection strategies have lead to
erroneous and contradicting results in the literature. Therefore, I
propose a notion of performance that captures the essential element
to improving redirection strategies and system. I then provide a
simulation-based evaluation methodology and platform that can con-
1.2 contributions 18
structively measure this performance. Furthermore, this platform sys-
tematically controls for factors that influence the behavior of redirec-
tion, and by testing for various conditions, the framework can tease
out the interaction of influential performance factors. In order to
assess the validity of the platform, I conducted a user study that in-
vestigates the interaction between redirected walking and locomotion
behavior. The results identify the source of deviation between simu-
lated and real users, how they manifest in performance variations,
and how these variations can be contained. The overall analysis con-
firms that the evaluation methodology and platform does indeed pro-
vide us a with a valid and economical way of systematic evaluation.
This simulation platform is a breakthrough for redirected walking
in that it provides a method not only for evaluation, but rather a
tool for a wide variety of scientific studies for researchers, and also
testbed for development and creation of novel strategies and experi-
ences for scientists, developers and even content creators. To ensure
the broad of use this platform, I have made this publicly available as
the open-source Redirected Walking Toolkit
1
. To date, it has been used
by dozens of universities including MIT and Georgia Tech, and even
developers from Unity Research Labs and Google. This is the first
step towards broad outreach and the rapid development and adop-
tion of redirected walking by the virtual reality community.
With the taxonomy of a redirection system established and its eval-
uation testbed created, I dedicate the remainder of my dissertation
to developing Adaptive Redirection, a novel redirected walking system
that unifies a spectrum of redirection strategies. At the heart of this
system is a meta-strategy that accounts for the context (expressed by
the navigation properties of the virtual environment) and shifts redi-
rection strategies accordingly. The key notion behind this paradigm
is that the efficacy of a redirection strategy can be improved with bet-
ter knowledge of the user’s behavior. In essence, the answer lies in
intimately knowing your context, what it demands, and conforming
to it by adaptation. The adaptive approach utilizes this idea by hav-
ing a suite of strategies that are each designed for a specific degree of
user predictability and plan their redirection accordingly.
To develop the adaptive meta-strategy, redirection strategies are
first classified into three categories: general, dynamic planning, and
static planning strategies. Each category is closely examined and fur-
ther developed for integration with the adaptive paradigm.
For general strategies, the long-standing dispute over which strat-
egy performs is best is finally settled thanks to the concrete notion
of performance and the systematic evaluation method proposed in
this work. The performance of this strategy is then further improved
upon by introducing a heuristic for incorporating translation gains.
And lastly, the most fundamental practical question for redirected
1 http://projects.ict.usc.edu/mxr/rdwt.
1.2 contributions 19
walking is addressed: “How much space is required for general redi-
rection.”
The greatest restriction on using static planning strategies is that
they require manually annotating the virtual environment before use.
This manual initialization prevents them from automatic deployment
and integration in a redirection system. I propose automating this
manual procedure by introducing an automated prediction graph ex-
traction algorithm. This effectively serves as the key to making strate-
gies in this category readily deployable.
The category of static planning strategies is extremely effective be-
cause it leverages knowledge of user’s path. In the past, this kind
of linear approach would only be applied based on manually created
environments. So I took it upon myself to automate this process to
support arbitrary paths and allow the best choice of gains to be deter-
mined programmatically. This lead to introducing the first automated
static planning strategy: the Combinatorially Optimized Pre-Planned
Exploration Redirector (COPPER).
With each category of redirection strategies expanded upon for
integration into a redirection system I begin to assemble them into
adaptive redirection. First, using the evaluation methodology, the
performance of each category is measured across different contexts.
This data is used to develop a deeper understanding of the inter-
action between each context factor with each individual redirection
strategy. Then the sampled points in the context space are processed
by machine learning classification techniques in order to develop the
adaptation rules. This meta-strategy determines the superior strategy
based on the context, unifying existing strategies into a single solu-
tion that maximizes performance. Leveraging the evaluation plat-
form, I also measure the expected performance and space require-
ments for redirected walking with the adaptive paradigm. The re-
sults show that COPPER is the key to achieving feasible room-scale
redirection. Furthermore, in a 10 10 physical space, with COPPER
it is possible to avoid resets almost entirely. This means the typical
linear experience can be carried out seamlessly without any interrup-
tions in just an approximately 10 10 meter space. This scale can
be easily achieved with the recent introduction of inside-out tracking
solutions.
The adaptive redirection system is the first of its kind, offering a
complete solution to redirected walking that not only adheres to per-
formance requirements at various levels, but also can be deployed
seamlessly without manual intervention. The process of develop-
ing each exponent and assembling them together demonstrates how
the proposed theoretical foundation and evaluation platform comple-
ment one another. This complete framework is the solution to engi-
neering the illusion of redirected walking.
1.3 organization 20
1.3 organization
In this dissertation I present the following:
Chapter 2 survey the literature of redirected walking
Chapter 3 propose a definition and design hierarchy for redirected walk-
ing systems
Chapter 4 propose an evaluation methodology and platform for redirected
walking
– identify influential factors for redirection performance
– validate evaluation framework with user study that stud-
ies the interaction of locomotion behavior and redirected
walking
– introduce a novel counter-deviation algorithm that adjusts
gains at runtime based on user behavior to achieve robust
redirection results
Chapter 5 introduce the adaptive redirection meta-strategy design paradigm
– identify the context factors for performing adaptive redi-
rection as a quantification of prediction graph properties
– present a categorization for redirection strategies on which
adaptive redirection is constructed (general, dynamic plan-
ning, and static planning)
Chapter 6 examine the state of general redirection strategies
– evaluate and compare performance of existing general strate-
gies to determine the most effective strategy
– determine physical space requirements for general redi-
rected walking
Chapter 7 examine the state of dynamic planning redirection strategies
– introduce a novel automated path-prediction algorithm that
enables deployment of dynamic planning strategies and
enables integration with adaptive redirection with no man-
ual overhead
Chapter 8 examine the state of static planning redirection strategies
– introduce novel static planning strategy
*
develop discrete offline redirection planning algorithm
*
develop online counter deviation algorithm
– compare static planning vs dynamic planning strategies
Chapter 9 develop adaptation rules for the adaptive meta-strategy
1.3 organization 21
– present the first in-depth analysis of the interaction be-
tween prediction graph properties and redirection strate-
gies
– demonstrate the construction of adaptation rules by classi-
fying the prediction graph space using machine learning
techniques
– measure expected performance for adaptive redirection across
various physical spaces and varying environment contexts
Chapter 10 offer guidelines for future research and development of redi-
rected walking
2
B A C K G R O U N D
I invented nothing new. I
simply assembled the
discoveries of other men
behind whom were centuries
of work. Progress happens
when all the factors that make
for it are ready, and then it is
inevitable.
Henry Ford
2.1 locomotion and real walking
Locomotion meaning “action or power of motion” is derived from the
Latin loco “from a place” compounded with motio ”motion, a moving”
as “movement from place to place” [Etymology, 2017]. Locomotion
should be distinguished from navigation (or way-finding), a cognitive
task which involves finding a route from point to another. A variety
of locomotion metaphors have been introduced in the virtual real-
ity literature including flying with a joystick or other hand-controller
[Robinett et al.,1992], using a treadmill [Brooks et al.,1992], walking-
in-place (where the user makes walking motions while physically re-
maining in the same spot) [Slater et al., 1995] and leaning [Peterson
et al., 1998]. These interfaces have been compared to real walking,
where physical motions are mapped directly to movement in the vir-
tual world. The choice of locomotion metaphor has been shown to
affect the user’s experience including the sense of presence (cognitive
feeling of being in a particular scenario [Schubert, 2009]) and degree
of simulator sickness (discomfort similar to motion sickness experi-
enced in virtual environments [Kolasinski, 1995a]). Studies indicate
that real walking is superior to flying with a joystick or walking-in-
place in that it is natural and intuitive, does not require learning
a new interface, results in a greater sense of presence [Slater et al.,
1998, Usoh et al., 1999]. Furthermore, it has been reported to result
in more efficient navigation [Ruddle and Lessels,2009] and better de-
velopment of cognitive maps when exploring virtual environments
[Ruddle et al., 2011]. Despite these benefits, real walking is funda-
22
2.2 redirected walking 23
mentally limited as it restricts exploring virtual environments to the
confines of the physical space available for walking.
2.2 redirected walking
After Michael Moshell and Dan Mapes’s pioneering efforts, Sharif
Razzaue successfully introduced Redirected Walking as a potential
solution to overcoming physical space limitations [Razzaque, 2005].
Razzaque described redirection as “making the user turn herself by
interactively and imperceptibly rotating the virtual scene around her.”
From a technical standpoint, the idea is to forego the conventional
one-to-one mapping between physical and virtual motions, thus de-
coupling real and perceived (virtual) trajectories. By injecting ar-
tificial virtual motions, large virtual trajectories can be potentially
mapped to paths that would fit within a given physical space. The
most common example of this is gradually injecting rotations (about
the users position) to a user walking down a virtual corridor. These
rotations cause the user to veer physically (ideally unbeknownst to
the user), causing her to walk in circles when visually appearing to
walk along a straight path.
2.3 why redirection works
Redirection works by leveraging the characteristics of human percep-
tion. Self-motion is perceived using visual and vestibular cues, how-
ever, these spatial sensory systems are attuned to different ranges
of motion frequency [Gibson, 1933], and vision is generally used to
correct accumulated error in body-based senses [Posner et al., 1976].
More importantly, studies have shown that when there is conflict be-
tween these sensory cues, visual cues usually dominate [J ¨ urgens et al.,
1999]. Therefore, when artificial motions injected during redirection
cause a discrepancy between visual and vestibular cues, the conflict
is resolved by dominance of vision. This can be further explained by
the user’s strong expectation of a stable world and the plasticity of
our self-motion perception mechanisms [Razzaque, 2005].
2.4 manipulation techniques
Redirection can be seen as a process of taking a virtual trajectory and
manipulating it to fit in a smaller space. The manipulation though
is not arbitrary, but rather follows a specific set of rules. Three ma-
nipulation methods – referred to as gains – have been identified in
the redirected walking literature [Suma et al., 2012a]: translation, rota-
tion, and curvature gains. Translation gains involve scaling the user’s
translations, resulting in a perceived faster or slower displacement
in the virtual world (Figure 2). Rotation gains apply scaling to the
2.4 manipulation techniques 24
Figure 1: Example a user exploring a virtual environment while being
redirected within a small physical space (green rectangle).
The user’s real and virtual trajectories are shown in yellow
and blue respectively [Bolas, 2015].
2.5 perception of redirection 25
Figure 2: Illustration of translation gain scaling the user’s virtual
translation relative to her real translation.
Figure 3: Illustration of rotation gain scaling the user’s virtual rota-
tion relative to her real rotation.
user’s rotations, effectively increasing or decreasing perceived rota-
tions (Figure 3). Curvature gains also involve inducing rotations, but
instead are applied during translation. This is normally applied as a
user walks forward towards a point in the virtual world, resulting in
a curved path towards the target while perceiving a straight walking
path (Figure 4).
In the literature, researchers recently introduced the concept of
bending gains [Langbehn et al., 2017] where rotations are injected in
order to manipulate curved virtual paths. This allows increasing or
decreasing the curvature of a user’s corresponding path in the phys-
ical space. However, the same can also be achieved by combining
rotation and curvature gains. Furthermore, this phenomenon already
occurs when using algorithms such as steer-to-center for a user walk-
ing in an environment with a curved virtual path. Therefore, this
gain will not be treated as a fourth gain type, but rather a derivation
of the three primary gains.
2.5 perception of redirection
The human perceptual system has naturally evolved to perceive the
surrounding environment as stable during head movements that oc-
cur along with locomotion. Studies show that the environment can
still be perceived as stable even when there is a certain amount of
discrepancy between physical head movement and observed visual
2.5 perception of redirection 26
Figure 4: Illustration of curvature gain causing the user’s real tra-
jectory to curve when the perceived virtual trajectory is
straight.
movement [Jaekl et al., 2005]. Redirection takes advantage of this
property of perception in order to achieve a viable illusion.
The two main concerns when applying redirection are noticeabil-
ity and induced simulator sickness. Though the exact relationship
between redirection intensity and these factors factors is still unclear,
the researchers have been operating under the following two assump-
tions: a) greater redirection discrepancies increase the likelihood of
gains being noticed and inducing simulator sickness and b) if gains
are not detected, the simulator sickness induced due to redirection is
considered negligible. Therefore, a reasonable approach to applying
redirection is to ensure the manipulations remain undetected, and
thereby avoiding discomfort to the user. However, the efficacy of
redirection depends highly on the permitted intensity of applying
gains. Therefore, it is desirable to find — if at all possible — a de-
tection threshold for each gain such that if the applied gains are kept
below this threshold, they will remain undetected. A vast variety
of research efforts have been focused on identifying detection thresh-
olds and more broadly understanding what can cause redirection to
become noticeable.
The most authoritative and comprehensive study on this subject to
date was conducted by Steinicke et al. [Steinicke et al., 2010]. This
study consists of three experiments designed to estimate psychomet-
ric functions and perceptual detection thresholds for rotation, transla-
tion, and curvature gains respectively. Detection thresholds for rota-
tion gain have been estimated at 49% for positive (same direction as
real world rotation) gain and20% for negative (opposite to real world
rotation) gain. For translation gain the thresholds were estimated at
26% for up-scaling and 14% for downscaling. Finally, according to
their data for curvature gain to remain undetected, the circular walk-
ing arc needs to have a radius of at least 22m.
2.5 perception of redirection 27
Interestingly, the estimated threshold values vary significantly from
one study to another. For rotation gain, Jerald et al. [Jerald et al.,
2008] estimated detection thresholds at 11.2% for positive (same di-
rection as real world rotation) gain and at 5.2% for negative (going
opposite to real world rotation) gain. For curvature gain, Hodgson
and Bachmann [Hodgson and Bachmann, 2013] successfully used an
informally estimated curvature radius of 7.5 meters with no users
reporting noticing redirection.
While several factors might have contributed to this variation, it is
clear that the estimation methodology played a critical role. In an ear-
lier version of their study Steinicke et al. [Steinicke et al., 2009] used
a different version of the experimental task (which authors believed
might have introduced a bias in participants’ responses). This study
yielded a very different set of threshold estimates for both rotation
(41% and 10% respectively) and curvature (15 meter radius) gains.
Grechkin et al. [Grechkin et al., 2016] revisited this problem with
a deeper inspection of the methodologies for measuring detection
thresholds, and also to investigate the potential interaction of curva-
ture and translation gain thresholds. They proposed using an adap-
tive method as opposed to a method of constant stimuli [Leek, 2001].
Adaptive methods rely on previously observed responses to deter-
mine which stimulus level should be tested next. For greater effi-
ciency, the goal typically is to select the test level that is likely to
provide the most information regarding the estimated threshold. In
order to further reduce the required number of trials, most adaptive
methods focus only on estimation of detection thresholds, not the full
psychometric function. While adaptive methods are generally more
efficient compared to the method of constant stimuli, they can also
be more susceptible to bias. However, overall the adaptive procedure
is particularly suitable for use in redirected walking, because it is
specifically designed to rapidly estimate detection thresholds using a
binary yes/no task.
It is important to note that Grechkin’s estimates for curvature de-
tection thresholds were significantly smaller compared to levels pre-
viously established by Steinicke et al. [Grechkin et al.,2016, Steinicke
et al., 2010]. Based on the estimates, participants were less sensi-
tive to curvature gain than previously reported. The exact cause
of the observed differences in estimated thresholds is unclear and
can potentially be explained by several factors including hardware
setup, methodological differences and population differences. Their
data showed that detection threshold estimates are quite sensitive to
changes in estimation method and underlined the importance of fur-
ther research in this area.
Their results also suggest that when curvature gains are increas-
ing from trial to trial in very small increments as can happen in an
adaptive procedure after the initial burn-in period, participants are
2.6 drawbacks and benefits of redirection 28
less likely to detect even significant curvature gain. While this effect
introduces an undesirable bias for estimation of the true curvature
detection threshold, from the application viewpoint the fact that a
very gradual introduction of curvature gain might actually desensi-
tize participants to this perceptual manipulation can be valuable.
One of the more important findings from Grechkin et al. studies
was large between-subject variability observed in their data. This
lead to proposing a per-user calibration using an adaptive procedure
as opposed to applying a global average for all users. This would al-
low for increasing redirection efficacy (when possible) by using more
intense gains for users that are less sensitive, while preventing gain
detection for users with greater sensitivity.
Beyond redirection intensity and between-user variations, some
studies have identified other factors involved in gain detection. Neth
et al. showed that the user’s walking velocity can influence the sensi-
tivity to curvature gain [Neth et al., 2012]. The rate of changing gain
values has also been shown to result in their detection. While previ-
ously it was assumed that gains would remain unnoticed so long as
values were within detection thresholds, Zhang showed that rapidly
changing gain can also cause users to notice gain [Zhang and Kuhl,
2013b, Zhang et al., 2014]. This finding suggests using a mechanism
for smoothly varying gains to prevent detection. Other factors that
influence detection have also been hypothesized such as user engage-
ment, density of virtual objects in the environment, HMD intrinsics
(such as field-of-view) and also tracking fidelity. Though not formally
investigated, there is a possibility that any of the factors mentioned
may also interact with eachother, complicating the problem of thresh-
old detection even further.
I believe the definitive solution to the perceptual component of redi-
rection would be in the form of a calibration process gauging detec-
tion thresholds that would be done per user, per virtual experience
(including environment and user task), and per hardware setup. Fur-
thermore, during runtime, gains would need to be varied gradually
and potentially account for the user’s velocity. Additionally, a sec-
ondary custom-tailored set of detection thresholds can also be mea-
sured that would give higher priority to redirection efficacy by using
more aggressive gains, aiming less for preventing detection and more
for reducing resets. It is critical however, to always prevent inducing
simulator sickness and compromising the experience of redirected
walking altogether.
2.6 drawbacks and benefits of redirection
Employing redirection is not without side effects, the most common
of which is inducing or exacerbating simulator sickness [Pausch R.
and Conway, 1992], particularly when large gains are applied. Simu-
2.7 approaches to using redirection 29
lator sickness symptoms are similar to those of motion sickness and
include nausea, dizziness, blurred vision, disorientation, and vertigo
[Kolasinski,1995b, Kennedy et al.,2003] and these ailments are preva-
lent even in the absence of redirection. It remains an open prob-
lem how exactly redirection correlates to simulator sickness but it is
hypothesized that when gains are unnoticeable, induced simulator
sickness is the same as natural walking [Razzaque, 2005]. Another
side effect that was recently investigated was added cognitive load.
Bruder reported significant influence of redirected walking on verbal
as well as spatial working memory tasks, and also a significant effect
of cognitive tasks on walking behavior [Bruder et al., 2015].
Though redirection can have adverse effects, it still retains various
benefits of natural walking. These benefits include an enhanced sense
of presence [Usoh et al., 1999], efficient navigation [Ruddle and Les-
sels,2009, Suma et al.,2011], improved development of cognitive map
of environments [Ruddle et al., 2011] without interfering with navi-
gation and spatial cognition [Hodgson et al., 2011, Suma et al., 2011].
2.7 approaches to using redirection
With the benefits and limitations of redirection identified, the impor-
tant question to answer is how exactly redirection must be applied.
Redirection can compress a path to fit inside the boundaries of a
tracked space, but this can come at the cost of redirection being no-
ticed. Algorithms for containing the user within the tracked space
can be classified into two categories by their approach to addressing
the matter of noticeability. The first approach commonly known as
motion compression [Nitzsche et al., 2004] considers noticeability as a
soft constraint, and focuses on minimizing the overall manipulations.
As a result, when the user approaches a physical boundary, large ro-
tations are injected (the world visually spins around the user’s head)
to prevent leaving the boundary [Su, 2007]. The second approach is
to restrict gain values to guarantee redirection is unnoticeable (or tol-
erable). With this restriction, redirection alone cannot ensure users re-
maining safely within the physical boundaries. Therefore, to achieve
a complete solution, an additional mechanism is required to reori-
ent the user which can come at the price of potentially interrupting
the virtual task at hand. In this dissertation, my focus is on the gain-
restricted approach, aiming to form a redirected walking solution that
puts simulator sickness prevention before continuity of the narrative.
It should be mentioned that the imperceptible application of gains
makes for compelling experiences, but this comes at the cost of lim-
ited efficacy. Some researchers take a more pragmatic approach and
aim for creating experiences that employ higher gain values which
may be less realistic, but enable greater exploration capabilities. This
is best exemplified in Interrante’s [Interrante et al.,2007] work where
2.8 steering algorithms 30
the user’s motions (in the intended direction of travel) were up-scaled
by a factor of 10. Within the context of this work however, unnotice-
able gains are a hard constraint.
2.8 steering algorithms
The first redirection algorithms were introduced by Razzaque [Raz-
zaque, 2005]. These algorithms injected rotations (via rotation and
curvature gains and no translation gain) to steer the user away from
the tracked space boundaries, and were thus referred to as steering
algorithms. Steering algorithms redirect users with no knowledge of
the user’s intended path in the virtual world, and simply assume
the user will continue in the direction she is facing. They are essen-
tially greedy algorithms that take into account the current state of
the user in the physical space at each calculation frame to determine
the gain values to apply. Three steering algorithm were proposed
by Razzaque: Steer-To-Center (S2C), Steer-To-Orbit (S2O), and Steer-
To-Changing-Targets, each different in their steering strategy (Figure
5). S2C steers users towards the center of the space, whereas S2O
attempts to steer users into an orbital motion about the center (with
a 7.5 meter radius). Steer-To-Changing-Targets is similar to S2C but
instead of using a single point as the target, multiple points on the
physical space are marked as targets, and the active target changes
depending on the user’s position.
Steering algorithms were further developed and studied by Hodg-
son et al. [Hodgson and Bachmann, 2013]. They presented formal
implementations of steering algorithms that also incorporated damp-
ening features to avoid drastic changes of injected rotations. In their
implementation, the change in position and orientation at each frame
is calculated to determine how much rotation could be applied by ro-
tation and curvature gains. Then, the maximum of the two was taken
and adjusted using an exponential moving average to determine the
rotation to inject in that frame.
Hodgson et al. also compared steering algorithms by simulation
and live user studies [Hodgson and Bachmann, 2013]. Metrics used
for evaluation included mean rate of rotation injection, mean distance
from tracked space center and number of wall contacts. For the live
user study, users performed a collection task in a virtual forest, and
the same data was recorded for use in simulation mode. Various syn-
thetic virtual paths were also generated for use in simulations in the
shape of zigzags, figure eights, and also straight lines. When users
reached the physical boundaries of the 40 meter by 20 meter tracked
space, they were manually instructed (by the experimenter) to stop
and turn away from wall. In simulations on the other hand, this was
not enforced, and the virtual user was allowed to exceed boundary
limits which may not be an accurate simulation of reality. Their re-
2.9 reorientation 31
(a) Steer-to-Center (b) Steer-to-Orbit
Figure 5: A demonstration of the user’s path in the real world when
the steer-to-center and steer-to-orbit strategies are used.
With steer-to-center, when the user walks along a straight
line in the virtual environment, the path will curve back to
the center forming a circle that passes through the center of
the tracked space. On the other hand, for steer-to-orbit, the
path is curved such that the user orbits around the center of
the tracked space.
sults indicated that S2C outperformed all other algorithms though
in some cases S2O was a strong close second. In a follow-up study
[Hodgson et al., 2014] arguments were also made for using S2O in-
stead of S2C, leaving the S2C-S2O rivalry unsettled and inconclusive.
2.9 reorientation
Imposing limits on gains entails a restriction on the mapping capa-
bilities of redirection. This in turn means applying redirection gains
exclusively is not sufficient to ensure user containment within the
tracked space. Thus, when the user inevitably reaches a physical
boundary, a fail-safe mechanism must be triggered to prevent the
user from leaving the tracked space. Such a safety measure is known
as a reorientation technique. The purpose of a reorientation is not only
to immediately prevent the user from leaving the tracked space, but
also to manipulate the real to virtual mapping in a way that progres-
sion in the user’s desired direction is made possible. This can be
contrasted to manually stopping and turning the user at a boundary
which not only puts the user at risk, but it also prevents them from
continuing along the intended direction.
Resets were the the first form of reorientation introduced in the lit-
erature [Williams et al., 2007]. Resetting involves manipulating the
2.10 forming a complete redirected walking system 32
users location in physical space to move them out of the path of the
physical obstruction while maintaining their spatial awareness of the
virtual space. Visually, resets are presented as a prompt, instructing
the user to turn in place or walk in a specific direction. Once the
task is complete, the prompt disappears and the user can continue
walking in her original direction in the virtual world without leav-
ing the tracked space. Williams introduced three resetting methods
among which the 2:1-Turn was overall superior to the other two (Fig-
ure6). This method involves instructing the user to rotate360 degrees
in-place, then resume walking in the original direction. As the user
begins to rotate, the physical rotation is upscaled by a factor of 2
(similar to rotation gain), such that the user only physically rotates
180 degrees while visually appearing to rotate 360 degrees in the vir-
tual world. Modifications to this method have also been proposed
that cause the user to face either the center, inward perpendicular to
the nearest wall, or towards the farthest corner in the tracked space
when the resetting task is complete [Zmuda et al., 2013a].
Peck et al. [Peck et al., 2010] coined the term “reorientation tech-
niques” to encompass the class of methods that resolve boundary
collisions and expanded this notion to include distractors. Distractors
are defined as objects in the virtual environment that the user focuses
on while the virtual world rotates. In Peck’s work, users would see
and hear a hummingbird that moved side to side, attracting their at-
tention causing them to turn their heads side to side as their gaze
followed this distractor. These head rotations were used as opportu-
nities to subtly inject rotations (again similar to rotation gains). Users
ranked this method as more natural and reported higher levels of
presence compared to previous reorientation methods, even though
this method was more time-consuming than the 2:1-Turn reset.
A reorientation can be divided into two components, the reorien-
tation mechanism and the reorientation task. The reorientation mecha-
nism refers to the underlying manipulations used to achieve the de-
sired result such as rotation and/or translation gains and also freez-
ing the screen [Williams et al., 2007]. The reorientation task involves
the prompt, cues and instructions shown to the user in order to elicit
the desired action. The cues can involve displaying text, playing
sound effects, and/or spawning a 3D object, while the instruction
may be presented (implicitly or explicitly) as “go to a target location”,
“turn in-place” or “follow an object with your gaze” [Williams et al.,
2007, Peck et al., 2010].
2.10 forming a complete redirected walking system
Redirection gains offer a non-intrusive unnoticeable mechanism for
trying to keep users within the tracked space, while reorientations of-
fer a guaranteed containment technique that temporarily interrupts
2.10 forming a complete redirected walking system 33
(a) initial state
(b) mid reset
(c) end of reset
Figure 6: Illustration of how2:1-turn reset works. The user virtual ro-
tates 360 while rotating only 180 degrees in the real world.
The other 180 degree rotation is injected, causing the user
and the physical space shown in teal to rotate simultane-
ously relative to the virtual world.
2.11 planned redirection 34
users’ navigation. These two methods combined, can form a redi-
rected walking system for large-scale exploration that ensures users
remain within the tracked space, regardless of the size of the virtual
environment. This was first accomplished by Peck introducing the
“Redirected Free Exploration with Distractors (RFED)” [Peck et al.,
2012]. RFED combined S2C – as the redirection component – with
distractors – as the reorientation component – to form a large-scale
locomotion interface. Peck et al. conducted studies comparing RFED
to walking-in-place and joystick interfaces. The results suggest that
participants using RFED were significantly better at navigating and
wayfinding through virtual mazes than participants using walking-in-
place and joystick interfaces. Participants traveled shorter distances,
made fewer wrong turns, pointed to hidden targets more accurately
and more quickly, and were able to place and label targets on maps
more accurately, and more accurately estimate the virtual environ-
ment size.
Xie et al. also developed a full pipeline by combining a fixed trans-
lation gain with the 2:1-Turn reset [Xie et al., 2010]. Note that trans-
lation gain has never combined with rotation and curvature gain in a
redirected walking algorithm, but have always been deployed exclu-
sively.
Redirection when combined with reorientation may provide a fully
functional mechanism, but the outcome may not be desirable. Partici-
pants using RFED on average experienced a reorientation after every
5 meters of walking (in a 6.5 6.5 meter tracked space) reporting it
as bothersome and disruptive [Peck et al., 2012].
2.11 planned redirection
In the recent years, alternative approaches to steering algorithms have
been proposed (namely FORCE [Zmuda et al., 2013b] and MPCRed
[Nescher et al., 2014]) that leverage information of the user’s pos-
sible future path in the virtual environment to optimize redirection
parameters via planning. This approach involves investigating the
outcome of the user’s future actions under various gain choices to
determine which values perform best based on some utility function.
Preliminary studies suggest that information about the user’s future
short-term action possibilities result in improved performance.
The user’s future actions in the virtual environment are represented
as a prediction graph that expresses the user’s possible trajectory op-
tions in the near term. Constructing the graph often relies on a rep-
resentation of the virtual environment’s layout in the form of a bidi-
rectional layout graph. This annotation provides a high-level abstract
description of possible paths that a user can take. Edges of such a
graph represent the general expected direction of travel for possible
paths in a particular area of the virtual environment, while nodes cor-
2.12 alternative illusions 35
respond to decision points where potential paths diverge. The predic-
tion graph is then generated at run-time by approximating the user’s
position using the nearest point on the layout graph and a subset of
nodes that are within a fixed horizon from the user. This pruning
of the graph is done based on the fixed search horizon used by the
planning algorithm.
FORCE was shown to be more effective than steering algorithms,
and though it did not restrict users to taking a virtual path, it required
users to manually signal the beginning and end of each turn action.
Furthermore, FORCE’s search mechanism did not plan for reorienta-
tion, and instead would fail when a boundary was reached. These
matters were addressed in MPCRed [Nescher et al., 2014] which for-
mulated planned redirection as an optimal control problem. Resets
were incorporated in the search as high-cost actions, which were
preferable to leaving the boundary which incurred an infinite cost.
In MPCRed, the search horizon is defined as a function of time in-
stead of waypoints, and a discount factor is used to reduce the cost
of actions that occur farther in the future. Path prediction is achieved
by first manually assigning a bidirectional graph to the virtual envi-
ronment that represents possible trajectories. Then the user’s virtual
position was mapped to a point on this graph by factoring in the
user’s smoothed virtual orientation. MPCRed was shown to also out-
perform steering algorithms, and is expected to outperform FORCE
since it is regarded as a special case of MPCRed [Nescher et al.,2014].
The main concern with MPCRed is the computational complexity
of the search algorithm. In its current state, no pruning is performed
in the search space, and even without introducing translation gain,
the execution time can exceed 1 second in some cases. Furthermore,
generally deploying MPCRed can be troublesome, since path predic-
tion is done manually, introducing manual setup overhead.
2.12 alternative illusions
Leveraging perceptual manipulations for enabling large virtual explo-
ration is not restricted to redirected walking. A variety of techniques
have been introduced that modify the virtual environment to keep
users within tracked space bounds. Suma et al. leveraged change
blindness [Simons and Levin, 1997] applying subtle changes such as
repositioning a doorway while the user was not looking [Suma et al.,
2010b]. “Impossible Spaces” is a also a mechanic that maximizes ex-
plorable areas by using self-overlapping architectural layouts [Suma
et al., 2012b]. “Dynamic Layout Generation” takes the layout mod-
ification to a more extreme case where the layout extends and ex-
pands with respect to the tracked space constraints [Vasylevska et al.,
2013]. Non-architectural techniques such as “Self-Motion Illusions”
2.13 terminology and conventions 36
have also been proposed that manipulate optical flow to influence
users’ self-motion judgements [Bruder et al., 2012].
These manipulations enforce restrictions on or involve modifying
the environment, and are therefore, not applicable to arbitrary virtual
environments. Therefore, in the context of this dissertation, I will be
focusing strictly on the use of redirection gains to enable exploring
large virtual environments.
2.13 terminology and conventions
Considering that redirection is still in its early stages of research, the
terminology for this field is rather underdeveloped. For readers both
familiar and new to the literature, I would like to offer clarification
regarding the terms and preferred conventions in this work. These
are by no means standards of consensus but rather my personal pref-
erence for communicating concepts on this topic.
2.13.1 Redirection
The terms “redirected walking” and “redirection” are often used in-
terchangeably in the literature. For this work I also do the same,
considering redirection as an informal shorthand for redirected walk-
ing.
2.13.2 Physical Space
A variety of terms have been used for describing the space in the
real world dedicated for a user walking including: “tracked/tracking
space/area”, “physical space”, “walking space/area.” I would like
to point out that all these terms are equivalent. However, with the
emergence of inside-out tracking, I am partial to using physical space
given that the space in which a user walks is no longer necessarily
designated as a tracking area with an explicit hardware setup.
2.13.3 Reorientation
The event triggered to prevent the user from leaving the physical
space has been referred to with terms including “reset”, “reorienta-
tion”, and “wall contact resolution/prevention.” I consider the latter
two equivalent, representing the broader category of such events. Re-
sets on the other hand are a special type of reorientation, however, in
the context of this work since resets are the only type of reorientation
examined, at times resets act as a representative for the category of
interruptions that are reorientations.
2.13 terminology and conventions 37
2.13.4 System
A mechanism that uses a combination of redirection and reorienta-
tions to enable large area exploration has been described using “loco-
motion interface”, “controller” and “system.” I use the term system in
this work, and provide a formal definition for it in the next chapter.
2.13.5 Gain Calculation
Translation and rotation gains are scalar variables that represent a ra-
tio. While the more common convention used is to define them as
ratio of virtual translation/rotation to real translation/rotation [Steinicke
et al., 2010]. I personally prefer instead defining them as ratio of in-
jected translation/rotation to real translation/rotation. The latter is more
elegant with mathematical calculations, especially in that 0 is used
for the absence of gain, and negative means upscaling and positive
refers to downscaling. The previous definition suffers from the less
intuitive fitting of downscaling to the[0, 1] range and upscaling to the
[0,¥) range.
Curvature gain on the other hand is rather different than the other
two gains in that is not actually a ratio, which makes the word “gain”
less suiting to describe it. Terminology aside, curvature gain de-
scribes the ratio of “rotation injected per real distance travelled (real
translation).” First of all this definition better lines up with my pre-
ferred definition for the other two gains in that all three become a
ratio of injected motion to actual motion. Secondly, the unit for curva-
ture with this definition becomes degrees per meter or radians per meter.
In the literature this is less explicitly mentioned, and instead the cur-
vature radius R
curv
is used instead which measures the radius of the
arc-shaped real trajectory formed by a user walking in a straight line
in the virtual world. With a bit of calculation we can easily derive
that the curvature gain g
c
is equal to
1
R
curv
radians per meter. Lastly
a subtle point that can easily be overlooked is that curvature gain is
defined using real translation not virtual, and this is becomes relevant
when curvature is combined with translation gain.
2.13.6 User
Within the literature of redirected walking the terms “real user/walker”
and “virtual/simulated user/walker” are often used to describe a
person exploring a virtual environment. It is important to point out
that user and walker are essentially the same, and the word real is used
against simulated to indicate that the latter is purely simulation-based
while the formal involves real human end users. The term virtual
2.13 terminology and conventions 38
user/walker refers to the avatar — the virtual representation — of the
user in the virtual environment.
Part II
T H E O R E T I C A L F O U N D AT I O N
3
R E D I R E C T E D WA L K I N G S Y S T E M S
The beginning of wisdom is
the definition of terms.
Socrates
Before delving into specific components of a redirection system, it
is important to establish the scope and definition of redirected walk-
ing.
3.1 scope
Sharif Razzaque originally coined the term redirected walking, infor-
mally describing it in his dissertation with “... Redirected Walking
works by making the user turn herself by interactively and impercep-
tibly rotating the virtual scene around her” [Razzaque, 2005]. In his
work, “redirection” and “redirected walking” are used interchange-
ably, with redirection serving as an implicit abbreviation for redi-
rected walking. While the original definition strictly involved inject-
ing subtle rotations, unnoticeably scaling translations has also been
considered a form of redirection [Suma et al., 2012a]. Furthermore,
the term redirection has been expanded to encompass almost any
type of manipulation intended for enabling large area exploration
[Suma et al., 2012a]. However, within the context of this work, I re-
strict the term redirected walking to the imperceptible alteration of the
mapping between the physical and virtual world which strictly limits ma-
nipulations to translation, rotation, and curvature gains.
Also an important matter that can easily be overlooked is the fact
that though redirected walking is a solution applied in a 3D space,
in essence it is a problem in the horizontal two-dimensional plane.
Therefore, all calculations in this scope can be expressed in a 2D for-
mulation.
3.2 design hierarchy of a redirected walking system
The manner in which I propose structuring a redirected walking sys-
tem and simultaneously its corresponding body of knowledge is a
40
3.3 redirection techniques 41
Figure 7: The design hierarchy of a redirected walking system.
hierarchical organization (Figure 7). At the very top we have a redi-
rection system which can make use of one or more strategies. A strat-
egy would then make use of one or more heuristics which in turn
each make use of a set of techniques. I will now introduce each of
these concepts in order to build the abstract structure of a redirection
system.
3.3 redirection techniques
A redirection technique is a mechanism for manipulating the user’s
trajectory. These are essentially the atomic building blocks for redi-
rection. To this date three types of techniques have been introduced:
translation, rotation and curvature gain, which have been already de-
fined in the previous chapter.
3.3.1 Performance of Techniques
At this fundamental level, gauging the performance of these manipu-
lations would involve evaluating how they affect the user. Arguably
most of the redirected walking literature has investigated the human
aspect of redirection, which is a measure of redirection performance
at the technique level. The adverse effects of redirection techniques
identified in the literature are added cognitive load, discrepancy de-
tection (negatively impacting sense of presence or immersion), and
simulator sickness. Though the literature still has not painted a clear
image of how these effects begin to manifest, there seems to be an
3.4 redirection heuristics 42
implied consensus that these effects begin to emerge and increase as
manipulation intensities increase.
Strictly speaking, avoiding all adverse effects of redirection would
be ideal, but this would render redirection ineffective. Therefore, a
compromise must be made that balances the efficacy of redirection
(in terms of efficiently enabling large area exploration) and the bur-
den or discomfort on the user. This practical compromise has formed
approaches where researchers draw a certain line that is not to be
passed. Two common examples of this are: a) avoid detection or
b) avoid simulator sickness. The choice of restriction to impose de-
pends on the type of experience intended for the user, and ultimately
whichever is chosen, a mechanism needs to be in place to ensure the
condition is met. While avoiding detection is the more common and
arguably essential condition for creating an illusion, more research is
necessary to ensure these conditions can be satisfied for all individu-
als. This matter is discussed in length in the previous chapter along
with my suggestions to improve this area.
The ideal performance for a redirection technique would involve
allowing maximal manipulation intensities while preserving the ob-
jective restriction, essentially always aiming to be in the sweet spot,
right at the cusp of detection or inducing sickness. As future re-
search sheds more light on how the adverse effects of redirection
techniques manifest, performance metrics can be defined that gauge
these induced effects and rate the overall performance accordingly,
downrating and penalizing for each type of negative effect caused.
However, assuming accurate (detection or sickness) thresholds are
determined with a reliable procedure, I would propose using these
values as firm bounds on the intensity of manipulation techniques.
By doing so, we can guarantee the desired restriction is satisfied and
thus essentially relieving the need for improving performance at the
technique level. This would simplify the process of maximizing the
global performance of redirection system by alleviating the need to
balance between contending performance metrics. This will be fur-
ther expanded upon in this chapter when measuring a system’s per-
formance.
3.4 redirection heuristics
A heuristic is any mechanism or algorithm that uses one or more
redirection techniques to fulfill a certain task or move towards an
objective. The two most common forms of heuristics within the litera-
ture are redirection heuristics and reorientation heuristics. As the name
suggests, a redirection heuristic aims to keep users within the physi-
cal space while reorientation heuristics use techniques to reorient the
user away from the boundary. With this formulation, the steer-to-
center “steering algorithm” would be considered a redirection heuris-
3.5 redirection strategies 43
tic that uses rotation and curvature gain techniques to meet the objec-
tive of steering the user towards the center of the space. Similarly the
face-center reset is a reorientation heuristic that uses the rotation gain
technique to reorient the user away from the boundary, and have her
face the center of the space.
3.4.1 Performance of Heuristics
Arguing about the performance of a heuristic in isolation is generally
not trivial. Heuristics are often designed to perform a specific short-
term objective such as “steer the user towards the center” or “redirect
user to a specific part of the physical space”. Thus it is not easy to
argue whether or not a specific approach is superior to another at
such a scope. Researcher attempts to develop performance metrics
at a heuristic level has led to conflicting results in the literature. I
discuss these in Chapter 6.
The insight here is that in order to tease out the performance of a
specific heuristic, we must go up a level in the hierarchy and see how
it interacts with other components within a redirection strategy. Then
by systematically controlling for all other components in a strategy,
and varying the specific heuristics being compared, we can argue if
one heuristic is better than another.
The point here is that the effects of each heuristic cannot be prop-
erly evaluated until they are assembled into a working strategy. Even
when operating within a strategy, it is important to also not generalize
results beyond the specific comparison involved. For instance as we
will see in Chapter 6, S2C is shown to be superior to S2O. However,
the subtle message that can be overlooked is that these results only
hold when they are paired specifically with the face-center reset reori-
entation heuristic. One can imagine a specific reorientation heuristic
interacting more amicably with S2O, and consequently inverting the
results of this ongoing heuristic rivalry.
It should be stated that when expressions like the “S2C strategy”
are used, it is implied that the redirection strategy contains the S2C
heuristic in addition to some implied default reorientation heuristic
that is not necessarily the focus of the discussion. Similarly reori-
entation heuristics can be compared with each other by using some
default redirection heuristic and focusing on swapping out various
reorientation heuristics. There are no reports in the literature of this
having been done, but a procedure similar to the one detailed in
Chapter 6 could be used to achieve it.
3.5 redirection strategies
A strategy is a mechanism that uses one or more heuristics in order to
ensure users remain within the confines of the physical space. More
3.5 redirection strategies 44
Figure 8: The components of a redirection strategy.
specifically, a redirection strategy is a function that takes in a set of
arguments about the current state — in the broadest sense — and
returns a set of values for gains (rotations and translations) to be
applied immediately when the next frames’ calculation begin (Figure
8).
3.5.1 Inputs
The input of a redirection strategy can be grouped into either spatial
input or user input. Spatial input is comprised of all the information
describing the state of the user, physical space, and virtual environ-
ment relative at one another at a given moment. The user input on
the other hand describes the set of preferences that tailor the experi-
ence to best suit the user. Note that not all these inputs are required
for a redirection strategy to function.
3.5.1.1 Spatial Input
Constant Input:
(a) physical space dimensions: exact dimensions of the physical
space (for instance 5 5 meters for a standard Vive tracked
space).
(b) virtual environment: 3D model of the virtual environment along
with relevant auxiliary data such as specific targets or experi-
ence restrictions.
Variable Input:
(a) user real pose: the user’s position and rotation in the real world
coordinate system (and potentially additional information such
as eye-tracking data and feet position).
(b) real to virtual origin transform: the transformation matrix map-
ping the origin of the real world to the virtual world origin.
3.5 redirection strategies 45
3.5.1.2 User Input
Constant Input:
(a) detection thresholds: the extreme values for each type of gain
that could be applied without the particular user noticing redi-
rection [Steinicke et al., 2010] (conceivably a more complicated
input that would account for velocity-dependent thresholds and
other factors [Neth et al., 2012, Grechkin et al., 2016]).
(b) reorientation task preferences: specific type of reorientation
task that the user would prefer (e.g., text/voice prompt, distrac-
tor, etc.).
3.5.2 Outputs
(a) translation gain: the amount of translation to inject in the next
computation frame (as a factor of user translation in the previ-
ous computation frame).
(b) rotation gain: the amount of rotation to inject in the next com-
putation frame (as a factor of user rotation in the previous com-
putation frame).
(c) curvature gain: the amount of rotation to inject in the next com-
putation frame (as a factor of user translation in the previous
computation frame). This can also be generalized to also in-
clude injecting rotations when the user is stationary similar to
Razzaque’s proposal to inject rotations when users are standing
relatively still [Razzaque, 2005].
(d) reorientation signal: signal to trigger or disable a reorientation
task.
It is worth mentioning that the gains from the output influence the
real to virtual origin transform, which will again be fed back into the
function in the next computation frame.
3.5.3 Internal Components of a Redirection Strategy
The components of a redirection strategy may include but are not
limited to:
(a) redirection heuristic: the main component that guides the decision-
making for using gains (while user is not being reoriented).
(b) reorientation heuristic: the method for executing the reorienta-
tion task using gains.
(c) gain-smoothing mechanism: a component that ensures gain
values change gradually to prevent gain detection and user dis-
comfort.
(d) user and system state history: a summary of relevant informa-
tion from the recent computation frames.
3.6 redirection system 46
3.5.4 Performance of Strategies
The performance of a redirection strategy is tied to its efficacy in
achieving its primary goal: keeping users contained within the phys-
ical space. Failure to gradually prevent the users from leaving the
space requires an interruption to the virtual experience in the form
of a reorientation task. I posit that single most undesirable drawback
of redirection is the occurrence of these disruptions to the flow of the
narrative and that reducing them is the highest priority for improv-
ing redirection. This is why I propose defining performance metrics
for redirection strategies solely based on reorientations.
Within the context of this work, resets are the only type of reorien-
tation task considered, and the terms “reset” and “reorientation” are
almost used interchangeably. Evaluating redirection heuristics can, in
my opinion, be done at two different levels: 1) at the heuristic level,
gauging the time and efficiency of the reorientation or 2) based on
users’ subjective measures and personal preferences. However, for
this work, I treat each reorientation event similarly, focusing instead
specifically on the occurrence of a reorientation. Therefore, I use the
frequency of resets as the main factor for gauging performance and
also other functions derived based on reset frequency. It should be
noted that other derivative measures could be defined that might ex-
amine the distribution of resets throughout the experience, giving
preference to more evenly spread out reset occurrences over bursts of
back-to-back resets followed by lulls of no resets.
3.6 redirection system
A redirected walking system defines a complete locomotion interface
that solves the problem of exploring arbitrarily large virtual environ-
ments within a limited physical space by using one or more redi-
rection strategies. In its simplest form, a redirection system can be
entirely composed of a single redirection strategy, but it more cases,
multiple redirection strategies can be integrated into a meta-strategy.
A meta-strategy resides above other redirection strategies governs
how they can be integrated in order to determine the optimal output
that minimizes resets. The adaptive redirection paradigm presented
in Chapter 5 is an example of a redirection system and the first ever to
combine various redirection strategies using an adaptive meta-strategy.
3.6.1 Performance of Redirection Systems
The performance of a redirection system is essentially the sum of
the performance of its parts. This means the performance metrics
defined for various levels of the hierarchy need to be combined in
a “fair” manner to balance the potentially contending performance
3.6 redirection system 47
priorities of each level. For instance, in the proposed system, we have
the technique-level performance which focuses on the quality of the
system in the context of the user’s perception. While on the other
hand, at the heuristic and strategy levels, the focus is more on what
I like to refer to as the mechanical efficacy of the redirection, trying to
keep users away from the boundaries, for a seamless experience.
Before proposing a measure for balancing these objectives, I will
first examine commonly used evaluation methods for redirection.
3.6.1.1 Classic Performance Measures
• Minimum space required for infinite walk
In this metric the focus is on estimating the area of the small-
est physical space that enables users to walk along an infinitely
long and straight virtual path without ever reaching the bound-
aries. However, this approach relies on a special case scenario
(long straight path) which does not represent a general case.
This leads to a wide range of estimates for the minimal space
size from 30m30m [Razzaque, 2005], to 35m35m [Hodgson
and Bachmann,2013], to 40m40m [Steinicke et al.,2010], to as
much as 60m60m [Field et al., 2004]. In Chapter 6 I’ll demon-
strate how this evaluation method can be misleading and has
been the source of contradicting results in the literature.
• Number of physical space entry/exits
This metric, introduced by Hodgson et al., involved simulations
that would allow the user to artificially exceed physical space
limits [Hodgson and Bachmann, 2013]. Experimenters would
count the number of times the user entered and exited the space.
However, this metric is based on a simulation behavior that is
not representative of reality. Furthermore, there is no clear rela-
tionship between this simulated user’s trajectory and that of a
real user. The simulation method proposed in this dissertation
alleviates this problem by accurately simulating reorientation
events, and further validating the method via a user study.
• Cumulative gains applied
In this metric, the cumulative gains applied during redirection
[Hodgson and Bachmann, 2013] are measured. In the imple-
mentation, gains were kept strictly below Razzaque’s proposed
detection thresholds [Razzaque, 2005].
I argue that this metric is of limited value since the cumulative
gains don’t impact the user experience. Furthermore, this met-
ric strictly prioritizes performance at the technique level, and
can misleadingly prioritize applying no redirection at all to
other redirection strategies.
3.6 redirection system 48
3.6.1.2 Proposed Redirection System Performance Measure
There is no clear answer for how the perception-based technique-
level performance objective of minimizing awareness of redirection
should be balanced with the strategy-level performance objective of
minimizing resets. Specifically, how much awareness of redirection
is acceptable to achieve a seamless and engaging experience for the
user. I propose simplifying this problem by factoring in technique-
level performance as hard constraints for the system i.e., placing strict
limits on redirection gains that cannot be exceeded under any circum-
stances. With this approach, maximizing performance of the system
is no longer a balancing act of two performance objectives but rather
it is reduced to only maximizing performance at the redirection level.
In order for a redirection strategy within a system to be viable, it
would first need to satisfy the technique-level performance require-
ments. Once this constraint is met, the priority shifts entirely to max-
imizing the strategy-level performance based on resets. By enforc-
ing (possibly dynamic) perceptual thresholds in the form of limits
on gains, we can satisfy the technique-level requirement, and as dis-
cussed in the previous chapter, future research can aid with creating
sophisticated per-user perceptual calibration mechanisms to guaran-
tee user comfort.
With this notion of performance defined, the remainder of this dis-
sertation will strictly focus on strategy-level performance when ana-
lyzing redirection strategies and systems, assuming technique-level
requirements are already considered within the design of each strat-
egy. The evaluation platform presented in this work will therefore,
also strictly focus on this notion of performance for a methodological
assessment of redirected walking systems.
4
E VA L U AT I O N M E T H O D O L O G Y A N D P L AT F O R M
Judge yourselves before you
are judged. Evaluate
yourselves before you are
evaluated.
Umar Ibn Al Khattab
Developing effective strategies for redirected walking requires sys-
tematic evaluations across a variety of factors that influence perfor-
mance. However, in the context of redirected walking, evaluation is
by no means trivial. The standard practice of conducting user studies
as a form of evaluation can often be misleading and result in inaccu-
rate generalizations. An example of this can be seen in Hodgson’s
work [Hodgson and Bachmann,2013] which initially reported S2C to
outperform S2O, while later on (with a different choice of virtual envi-
ronment) indicated S2O as the superior choice [Hodgson et al.,2014].
This demonstrates the subtleties involved with fair performance com-
parison, and the pitfalls of overgeneralizing evaluation results.
The evaluation methodology I propose aims to overcome the lim-
itations of user studies by offering an approach that systematically
controls for influential factors and allows rigorously testing various
conditions. This is made possible using a simple human locomotion
model that replicates real user conditions with fidelity that is suffi-
cient for producing results that are reasonable approximations of real
user studies. The evaluation methodology is what gives substance
to the theoretical foundation of this work; and beyond a tool for per-
formance measurement, it is a development testbed, a platform for
analysis and the key to forming insight for what truly matters in redi-
rected walking.
In this chapter, I will first introduce the evaluation methodology
and platform and then proceed to validate it with a user study that
investigates the interaction between locomotion and redirected walk-
ing analyzing the drawbacks, margin of error, and limitations of the
platform.
49
4.1 simulation: the response to interacting factors 50
4.1 simulation: the response to interacting factors
The behavior of a system that employs redirected walking is influ-
enced by a multitude of factors such as (a) user behavior (b) phys-
ical space dimensions (c) structure of the virtual environment and
(d) perceptual thresholds in addition to the redirection strategy and
reorientation techniques applied. What complicates studying the per-
formance of such a system is how these elements interact and overall
affect performance. This makes it particularly difficult to tease out
the sheer performance of a redirection strategy, and argue about its
properties independent of these external factors.
To systematically control for factors that influence redirection, I opt
for using simulations. Simulating a walking user allows to not only
exclude between-user variability but it also enables conducting exper-
iments with large numbers of lengthy trials. By carefully varying the
parameters of interest while controlling for all relevant nuisance pa-
rameters, this approach can offer complete and fair performance com-
parisons. I posit that if a user simulation possesses sufficient fidelity, it
would yield results that are generalizable to real user situations. This
hypothesis will be put to test to validate the evaluation platform, and
gauge the error associated with it.
A word of caution that must be stated is that the use of simulations
can put us at the risk of introducing error; not only because they
are an approximation of realistic conditions, but also in that they can
permit false representations of reality. For instance, Hodgson [Hodg-
son and Bachmann, 2013] allowed simulated users to go beyond the
boundaries of the physical space limits, resulting in invalid trajecto-
ries that were not representative of nor necessarily correlative to live
user behavior. Therefore, it is not sufficient to merely advocate the
use simulations, but one must establish a standard simulation plat-
form that faithfully replicates the behavior of a redirected walking
system, as a reliable means for evaluation. And that is the purpose
of the evaluation methodology.
4.2 components of the evaluation platform
The core modules of the evaluation platform are as follows
1
:
• redirection strategy (and reorientation technique)
• perceptual detection thresholds
• simulated user
• virtual path generator
• safety triggers
1 Note that the platform components presented here have been implemented, docu-
mented and made publicly available as part of the open-source Redirected Walking
Toolkit project I developed at the USC Mixed Reality Lab (Figure 9). More informa-
tion can be found by visiting http://projects.ict.usc.edu/mxr/rdwt.
4.2 components of the evaluation platform 51
Figure 9: Snapshot of the Redirected Walking Toolkit simulating a
user being redirected in a conceptual virtual scene; shown
from various vantage points. The user’s trajectory in the
real world is shown in yellow, and virtual trajectory is
shown in blue.
• time and framerate simulator
• data logger
4.2.1 Redirection Strategy
The redirection strategy (defined in Chapter 3 in classic implementa-
tions can be divided into a redirector and a reorientation method. When
evaluating strategies, I encourage either bundling the two together
and arguing about their properties as a unit, or keeping at least one
of the two sub-components constant to prevent unintended biases.
The platform also includes a default “null redirector” which only
triggers a reorientation method of choice when necessary. This serves
as a baseline control condition to compare the performance of other
strategies against.
4.2.2 Perceptual Detection Thresholds
Perceptual detection thresholds can be interpreted as a hard limit on
how strongly redirection can be applied. Therefore, to ensure a fair
comparison of strategies, it is important to keep these values consis-
tent across conditions of an experiment, unless the objective is indeed
to compare the affect of varying these limits. Even though different
strategies presented over time have been originally conceived with
various thresholds, I encourage unifying them with empirically calcu-
lated thresholds [Steinicke et al., 2010]. Alternatively rule-of-thumb
measures can be used like [Hodgson et al., 2011] that may prioritize
4.2 components of the evaluation platform 52
redirection efficacy over the risk of user noticeability, yet have been
reported innocuous by experience.
4.2.3 Simulated User
A simulated user is essentially an abstract avatar that represents a
user navigating a virtual environment by moving in a physical space.
The user navigates from one point of interest to the next based on
a given sequence of waypoints. This is performed by moving for-
ward at a fixed speed of1 meter per second (based on [Hodgson and
Bachmann, 2013]) from one waypoint to the next. Once a waypoint
is reached, the user rotates in place at a constant rate of 90 degrees
per second (also from [Hodgson and Bachmann, 2013]) to face the
next waypoint, at which point the forward walking is resumed; until
eventually all waypoints are cleared. Also when a reorientation task
is prompted for, an override mechanism is enabled to follow the spe-
cific instructions of the applied reset. For instance, in the case of a
2:1-Turn reset, the user stops and rotates in place until the reset task
is complete. User reaction time is also simulated by including a 0.5
second delay in response to resets, followed by a 0.5 second linear
deceleration at a constant rate before coming to a complete stop.
Though this implementation of a simulated user does not capture
movement nuances of a walking human such as gait oscillations and
gaze aversions, it provides a basic representation of navigating in a
virtual environment.
4.2.4 Virtual Path Generator
A user’s trajectory in a virtual environment is implicitly dictated by
the virtual environment’s layout. Therefore, to simulate walking in
various virtual environments, instead of creating a suite of environ-
ment layouts, the platform generates various virtual trajectories that
would correspond to walking in various virtual environments. This
simplifies the design by eliminating the intermediary step of inferring
the navigability of a virtual environment in order to deduce possible
virtual trajectories.
Each virtual path is defined as a series of waypoints. In addition
to the overall length of a virtual path, the distance between consec-
utive waypoints and the angles formed by connecting them can be
controlled by adjusting the parameters of the virtual path generator:
distance sampling distribution D
d
, angle sampling distribution D
a
, and
a waypoint count N
w
. A virtual path can is generated by taking the
user’s initial pose, setting a waypoint at distance d
1
(sampled from
the distance distribution) along the user’s heading direction, then
placing the next waypoint at distance d
2
(sampled from the distance
distribution) such that the user will be required to rotate angle a
1
4.2 components of the evaluation platform 53
Category D
d
(meters) D
a
(radians) N
w
Office Building unif(2, 8) f-
p
2
,
p
2
g 200
Exploration (small) unif(2, 6) unif(-p, p) 250
Exploration (large) unif(8, 12) unif(-p, p) 100
Long Walk f1000g N/A 1
Table 1: Four categories of virtual paths.
(a) Oce Building (b) Small Exploration (c) Large Exploration
Figure 10: 3 categories of virtual paths. From left to right: Office
Building, Small Exploration, and Large Exploration.
(sampled from the angular distribution) to face the next waypoint
and so on. Therefore, in practice, the user will be required to per-
form a succession of walk and turn actions to clear all waypoints.
This implementation can also be extended to support curved paths.
I defined four categories of virtual paths representing typical vir-
tual environment scenarios used in practice (see Table 1 and Fig-
ure 10). Note that in all cases the expected length of each path is
1000 meters.
4.2.5 Safety Trigger
As the disruption of tracking or presence of physical boundaries pre-
vent real users from exceeding physical space limits, simulated users
must also be prevented from violating boundary constraints. There-
fore, when a simulated user is on the verge of leaving the physical
space, an instruction must appear to enforce this limitation (Figure
11). This is implemented by placing a safety trigger inside and within
a distance (by default0.5 meters) from each side of the physical space
boundary (Figure 12). When the user moves beyond a safety trigger,
the redirection strategy is notified in order to trigger a reorientation
that would guide the user to safety. The distance between the safety
4.2 components of the evaluation platform 54
Figure 11: Once the user is prompted with the reset task, she even-
tually reacts to the prompt and slows down until coming
to a full stop before reaching the physical space boundary.
The reset task is then performed typically within the buffer
area.
trigger and the boundary acts as a buffer to allow for users to react
to notifications before reaching a potentially dangerous hard physical
limit.
4.2.6 Simulating Time & Framerate
The evaluation platform provides a time simulation feature that al-
lows for faster calculation of a simulation’s outcome. Instead of us-
ing actual time elapsed between calculation frames, the simulation
can programmatically set this value, which enables simulating arbi-
trary framerates. For instance, to simulate a60Hz framerate, the time
elapsed between frames is artificially set to
1
60
seconds. And since the
real time elapsed is typically smaller than this value, the execution
time is reduced. Therefore, with simulated time, the platform can
run simulations at much higher speeds, and also control framerate
conditions or alternatively investigate the impact of framerate itself
on the system.
4.2.7 Data Logger
The end objective of running a simulation as with any real user study
is to gather data of the events that transpired. The platform therefore,
keeps track of the following variables in order to perform analysis
and if need be, replicate specific moments in a simulation for deeper
diagnosis and assessment.
4.2 components of the evaluation platform 55
Figure 12: Resets are initiated when a user collides with a reset trigger
(dashed-square outline) placed at safety distance d from a
hard boundary (outmost square outline). This grants the
user the opportunity to safely react to the reset prompt
within the buffer (cross-hatched area).
4.3 measuring performance 56
• total reset count
• real and virtual distance travelled between resets
• time elapsed between resets
• overall gains applied
• overall real and virtual distance travelled
• real and virtual positions at custom intervals
• applied gain at custom intervals
Additional data may be gathered depending on the demands and
specifications of an experiment.
4.3 measuring performance
Based on the performance metrics outlined in Chapter 3, measures
can be split into two categories: objective and subjective. An impor-
tant drawback of the evaluation platform to acknowledge is that as
it stands, it cannot measure nor predict subjective measures. Though
in the future psychometric models may be able to predict or esti-
mate these metrics which can be incorporated into the system. It is
timely to reiterate that an ideal redirection strategy would not incur
noticeability nor simulator sickness, and cognitive load would also
be considered a reasonable compromise for what redirection has to
offer. Therefore, it can be argued that if redirection is implemented
correctly and user-tailored preferences are indeed adopted, measur-
ing and analyzing subjective measures can be of lesser importance.
Luckily objective measures can be easily extracted from the logged
data for the purpose of evaluation.
As also stated earlier, I believe the most important objective mea-
sure is the frequency of reorientations. While in their normal state,
gains are designed to be imperceptible, reorientations are explicit in-
terruptions to the flow of the virtual experience. Even if masked
in the form of a plausible mini-game or an interaction woven into
the virtual narrative, reorientation are inherently designed as explicit
detours from the virtual progression. Therefore, I argue that reorien-
tations are crucial to be minimized; and if performance were to be
defined based on a single metric, it should be a function of reorienta-
tion count.
In addition to the raw count reorientation events, I propose using
two variations on this essential metric:
• Reorientation Regularity: Casually expressed as “reorientation
events are triggered every this many meters”, this metric is meant
to be a more tangible and intuitive metric, and a candidate for
summarizing performance in a single number. With R as over-
4.4 validating the evaluation platform 57
all reorientation count and RR as reorientation regularity of a
redirection strategy, I define:
RR
strategy
=
virtual distance travelled
R
strategy
• Relative Efficacy: To tease out the pure contribution of a redi-
rection strategy in reducing reorientation events, it is important
to compare it to the baseline NullRedirector (paired with a de-
fault reorientation method such as the 2:1-Turn reset). This is
particularly important to prevent a biased view of improved
performance when for instance, the size of a physical space is
increased (because naturally reorientation decreases when more
space is available, but the question is: “Is the strategy respon-
sible for this improvement too?”). Measuring the relative im-
provement in contrast to the baseline, relative efficacy is defined
as:
RE
strategy
=
R
NullRedirector
R
strategy
R
NullRedirector
4.4 validating the evaluation platform
To validate the platform I will investigate the interaction of user lo-
comotion behavior with redirected walking and study similarities
and differences between real and simulated users. The focus will be
specifically how locomotion characteristics cause variations in gain
outcomes at a micro scale as well as the impact on performance at
a macro scale. Towards a robust application of redirection gains that
remains agnostic to variations in locomotion behavior, we introduce a
novel counter-deviation technique that dynamically adjusts the inten-
sity of gain in order to minimize deviations from the expected effects
of redirection. The aim is to identify the specific locomotion behav-
iors that influence each of translation, curvature and rotation gains, as
well as resets, and also the degree to which each causes deviations. To
gauge the accuracy of the simulated user, I will present an experiment
that measures the contrasts between real and predicted virtual trajec-
tories along with their spatial manipulation (a micro-scale inspection)
as well as the difference in predicted versus actual performance of
the redirection strategy (macro-scale inspection). I will also attempt to
resolve the discrepancies by introducing a counter-deviation technique
which aims to prevent error caused by the “noise” of real locomotion.
This study examines both the effect real human locomotion has on the
predicted motions and overall performance of a redirection strategy
as well as the efficacy of the counter-deviation technique.
4.4 validating the evaluation platform 58
Figure 13: Snapshot of the user study setup. Participant wearing vir-
tual reality equipment is shown on the left, the user’s per-
spective in the virtual world on the right, and in the center
a top view showing the real (yellow) and virtual (blue) tra-
jectories influenced by redirection.
4.4.1 Micro-Scale Inspection
The first part of the experiment will examine what elements of hu-
man locomotion influence how gains are applied. The simulated user
abstracts a real person’s movements by making the assumption that
people walk in perfectly straight lines, only face the target direction
while walking, and rotate around their local y-axis without deviating
from the initial pivot point. While at first glance it may seem that
these postulations might not accurately model human locomotion, I
hypothesize that some of “noise” like swaying side to side will be nul-
lified over time. My goal with this part of the experiment is to isolate
what characteristics of human locomotion attribute to the deviation
from the expected results from the simulation.
In order to control and accurately study the impact locomotion
behavior has on redirection, I will test each redirection technique in
isolation. The redirection techniques that will be studied are the three
basic gains (translation, rotation, and curvature) and overt reorienta-
tions (resets).
To examine how translation gains are affected, the user will walk
along a straight path with a fixed gain applied. I will determine
if small swaying movements cause the user to deviate from the ex-
pected outcome (Figure 14). In this case I will investigate if interme-
diary motions cancel each other out, causing the overall manipulation
to only depend on the user’s net displacement.
Similar to the translation gain case, I will examine curvature gain
by having the user walk along a straight virtual path with a fixed
curvature gain applied. However, since artificial rotations will be in-
jected, I will additionally collate the effects head rotations from gazes
has on the predicted results. This data will help determine if random
head movements during locomotion cause the user to deviate from
4.4 validating the evaluation platform 59
Figure 14: Illustration of locomotion behavior causing deviations dur-
ing translation gain. The predicted user motion and its
expected effect on the target waypoint (red) is contrasted
with the actual results (black).
the predicted result. For this inspection, I will try to explain variance
in manipulations by the sum distance travelled and the user’s average
lateral distance from the virtual path.
For rotation gain, the user will traverse an L-shaped path with
gains only being applied when the users is transitioning from one
leg of the path to the other. More specifically, rotation gain will be
enabled when the user completes 2/3rds of the first leg and will be
disabled after she completes the first 1/3rd of the second leg. This
case will allow us to examine what locomotion dynamics during a
turn affect the expected outcome.
Finally, to examine the reset, the user will traverse a straight path
that triggers a reset half way through. In this case we will compare
the result from the simulated user reaction model for resets to how a
real user responds, similarly identifying the main aspects explaining
deviations.
4.4.1.1 Manipulation and Deviation Measures
To analyze the effect of redirection across users, we define two sets
of measures. Manipulation measures aim to gauge the overall effect
of gains in comparison to their absence. Deviation measures compare
how the effect of gains for a real user differ from that of a simu-
lated user. I use Figure 15 as a sample trial for illustrating how these
measure are calculated. The virtual trajectories of the simulated and
real users are shown in yellow and green respectively, as they walk
towards the square-shaped target end waypoint in the path. The cor-
responding virtual trajectories for the simulated and real users are
shown in red and blue respectively, along with the resulting pose of
the end waypoint. Since users’ end poses vary, we use the end way-
point’s pose as our reference for comparison. Our reference for no
gains applied is W
I
, which is essentially the end waypoint’s pose at
the beginning of the trial. W
A
and W
T
are the end waypoint poses
for the real an simulated users respectively. To measure the overall
manipulation, we compare W
A
and W
I
, and to measure deviation,
we compare W
A
and W
T
. The distance between poses are compared
to calculate positional manipulation/deviation and the magnitude of
4.4 validating the evaluation platform 60
Figure 15: Reference poses for calculating manipulation and devia-
tion measures. The virtual trajectories for the simulated
(yellow) and real user (green) are shown along with their
corresponding real trajectories (red and blue) and the final
pose of the target waypoints.
angular difference between the poses is calculated to obtain orienta-
tional manipulation/deviation.
4.4.1.2 Hypothesis
For the micro-scale inspection, the hypothesis is that the user’s loco-
motion behavior determines variance between overall manipulation
applied. But more importantly, I hypothesize that the variance in
manipulations among users along with the deviations from observed
redirection results can be explained away by measurable characteris-
tics of locomotion behavior. I believe for each gain, factors can be
identified that would explain variance. I suspect that for same gains,
values throughout the trajectory would matter, for some, the over-
all change would only matter (affects of intermediate values would
cancel out), and some variables would have no effect at all.
4.4.1.3 Independent and Dependent Variables
The independent variables for micro-inspection are essentially the ex-
planatory factors for the variance in redirection results. I will now
identify the variables considered for each category of trials. Note
that in orientational manipulation is only measured when relevant
(translation gain does not introduce orientational manipulation, and
a2:1-turn reset affects orientation uniformly for all users). Also since
orientational deviation can be derived from orientational manipula-
tion (by subtracting the simulated user’s orientational manipulation
from the user’s orientational deviation), the analysis would be redun-
dant and is therefore not included.
1. Translation Gain
Independent Variables
4.4 validating the evaluation platform 61
• translation gain amount of constant translation gain applied
during trial
• net translation the amount of overall displacement between
start and end of trial.
Dependent Variables
• positional manipulation
• positional deviation
2. Curvature Gain
Independent Variables
• curvature gain amount of constant curvature gain applied dur-
ing trial
• sum distance travelled the sum of the magnitude of user dis-
placement between frames from start to end of trial.
• average lateral distance from virtual path the distance between
the user and the expected virtual path, averaged throughout the
trial.
Dependent Variables
• positional manipulation
• positional deviation
• orientational manipulation
3. Rotation Gain
Independent Variables
• rotation gain amount of constant rotation gain applied during
trial
• average lateral distance from virtual path the distance between
the user and the expected virtual path,
• turn point error the distance between between the turn way-
point and users position when reaching a 45 degree angle with
the target direction, indicating how far off the user was from
the expected turn point when half of the90 degree rotation was
completed (Figure 16).
• turn radius the approximated user turn radius measured by
inspecting the two points along the path where the user’s angle
with the target direction reached 70 and 20 degrees (Figure 16).
• net turn angle the overall change in rotation before and after
the turn area (the 1-meter proximity of the turn waypoint.
Dependent Variables
• positional manipulation
• positional deviation
• orientational manipulation
4. Reset
Independent Variables
• displacement in reset the overall change in position during the
trial.
4.4 validating the evaluation platform 62
Figure 16: Illustration of key points in the user’s trajectory that are
used for estimating turn point error and turn radius. The
first time the user’s virtual angle with the target direction
reaches 70, 45, and 20 degrees is marked.
• mid-reset point error the distance between the mid-reset point
(the point where the reset tasks overall virtual rotation had
reached 180) and the simulated users reset task stopping point.
• end-reset point error the distance between the end-reset point
(the point where the reset tasks overall virtual rotation had
reached 360) and the simulated users reset task stopping point.
• mid-reset point distance to trigger the distance between the
mid-reset point and where the user was when the reset was
triggered.
• end-reset point distance to trigger the distance between the
end-reset point and where the user was when the reset was
triggered.
• reset turn diameter the approximated diameter of the circular
trajectory of the user turning in place as measured by account-
ing for the mid-reset and end-reset positions.
Dependent Variables
• positional manipulation
• positional deviation
4.4.2 Macro-Scale Inspection
The second portion of the experiment will examine how human loco-
motion dynamics influence and affect the overall performance of redi-
rection. Although our simulation may not perfectly replicate exactly
how a real person would traverse a virtual path segment while being
redirected, it may be able to provide a useful high-level performance
metric for estimating how different redirected walking approaches
4.4 validating the evaluation platform 63
can be expected to perform on a potential path or environment lay-
out. This examination will explore whether user locomotion behav-
ior causes deviations that will either ultimately impact the efficacy of
redirection or cancel out over time.
Additionally, this part of the study will compare the results of the
users to the simulation to determine two other features. First, the
comparison will identify and estimate systematic error of our simu-
lation platform. Furthermore, the juxtaposition of real and simulated
data will help us determine if relative performance trends are pre-
served. This means that if the simulation expects a specific configu-
ration to out perform another, the prediction will hold true for real
users as well.
For this examination, the user will traverse a random, procedu-
rally generated virtual path, which is made up of straight segments
connected by a randomly selected 90 degree left or right turns. The
length of the straight portions of the path are uniformly distributed
between 2 to 8 meters inclusively. Gains will be applied along the
path according to the redirection strategy chosen and resets will be
used to ensure that the user remains in the physical space. The per-
formance metric used to compare the results is the reset count as the
most crucial factor in gauging the efficacy of redirected walking. Ad-
ditionally, it captures the overall impact of locomotion manipulation
variability across users.
4.4.2.1 Hypothesis
For the macro-scale inspection, the hypothesis is that despite the vari-
ance in redirection results (due to locomotion behavior) at the micro-
scale, the average overall performance at a macro-scale for users is
similar to the simulated user. This validity of this hypothesis would
validate that the simulation fidelity in the evaluation platform is suf-
ficient for the purpose of evaluating redirection. Moreover, the eval-
uation platform can be used as an efficient and reliable metric for
offering average performance estimates for redirected walking strate-
gies and systems.
The secondary and weaker hypothesis is that performance results
from simulations preserve trends observed real user data. In this
experiment this will be investigated by testing if one strategy outper-
forms another based on real user data, this relationship also holds
true within the simulation platform.
4.4.2.2 Independent and Dependent Variables
The independent variables in this experiment are the range of circum-
stances considered and the dependent variable is our performance
factor.
Independent Variables
4.4 validating the evaluation platform 64
• user the set of real users is contrasted against a single determin-
istic simulated user.
• redirection strategy S2C and S2O both paired with a the face-
center reset form the two strategies under study.
• virtual path two procedurally generated random paths with90-
degree turns.
Dependent Variables
• reset count the number of resets triggered in each path is tallied
for each trial.
4.4.3 Countering Deviation
The objective of the final examination is to explore options to counter-
act the variability of locomotion behavior so that the actual manipu-
lation measure matches the predicted value from the simulation. Not
only is it ideal for real world results to match the simulation, but it is
also imperative when executing a planning redirection strategy. For
example, suppose a system created a sequence of gain values that
could redirect the user with little to no tolerance for error. Although
the values may work in a simulation, they would not perform as pre-
dicted because the user would deviate from the intended goal due
to real human movement dynamics. Therefore, we need to nullify
or minimize these deviations so the redirection will yield results that
are either the same as or very close to the predicted outcome. In or-
der to achieve this, the main goal when applying redirection needs to
change. Traditionally, the main goal is to adhere strictly to the rules
set by the redirection strategy. For example, in the case of greedy
algorithms like steer-to-center, the maximizing heuristic dictates that
gains should be set such that the user is redirected towards the center
of the physical space. In planned redirection, gains are typically fixed
for segments of the virtual path. Departing from these two methods,
we propose a process called counter-deviation that sets the main goal
when applying gains to be matching the expected manipulation mea-
sure. This portion of the study will test the efficacy of our proposed
counter-deviation technique.
The trials for this examination will have the user traverse a square
shaped virtual path, either clockwise or counter clockwise. Values
for translation, rotation, and curvature gain will be randomly set for
each side of the square such that the user will remain well within
the physical space, regardless of user deviation. These values will
either remain fixed for each segment or be dynamically adjusted by
the counter-deviation technique.
4.4.3.1 Instantaneous Deviation Measure
In order to negate the effects of the user’s deviation from the pre-
dicted path, we must first define a measurement to quantify the in-
4.4 validating the evaluation platform 65
stantaneous deviation. Rather than simply comparing the trajectories,
we calculate the difference in the amount of applied redirection at a
given point on the virtual path. It is important to note that a planning
algorithm does not produce a planned path, but rather a set of gain
values that result in a specific path. Therefore, in order to compare
the amount of redirection applied, the planned trajectory has to be
constructed from the gain values so that if can be sampled.
To calculate the user’s deviation, we first measure how much of the
path has been traversed by using the user’s velocity and bearing to
project her virtual pose U
V
onto the virtual path, which yields the vir-
tual progress pose P
V
(Figure 17). We then calculate where P
V
maps
to in the real world and call that pose P
R
. P
R
is then compared to the
expected target pose calculated by the simulation P
T
. The difference
between these two poses in the real world is the deviation measure.
Since users tend to round a corner by walking and turning at the
same time, measurements near a turn are not reliable because no one
point can represent where the user turned. Therefore, to track the
user’s deviation throughout the path, we only take deviation mea-
surements 1 meter before and after a turn.
4.4.3.2 Hypothesis
For the counter-deviation experiment, the hypothesis is that the counter-
deviation mechanism provided in this work is effective at reducing
the effects of locomotion behavior on redirection. Furthermore, ap-
plying counter-deviation results in unified redirection results across
all users that are within a reasonable margin of variance, ultimately
enabling redirection that is agnostic to user behavior.
4.4.3.3 Independent and Dependent Variables
The independent variables involve factors that can influence the devi-
ation and the dependent variables are our measures of this deviation.
Independent Variables
• user the set of real users is contrasted against a single determin-
istic simulated user.
• gain application method two modes of applying gains are com-
pared: the default in which gains are fixed and my proposed
approach of using dynamic gains that counter-deviation.
• virtual path two square-shaped virtual paths were considered,
one turning clockwise and the other counter-clockwise.
• checkpoint at 8 points along the virtual path the deviation is
measured, one checkpoint is placed 1 meter before each way-
point and one checkpoint is placed after each waypoint.
Dependent Variables
• positional deviation the positional deviation is measured at
each checkpoint.
4.4 validating the evaluation platform 66
• orientational deviation the orientational deviation is measured
at each checkpoint.
4.4.4 Gain Application Methods Robust to Locomotion Behavior Variabil-
ity
Our model of a simulated user coarsely expresses how a user would
move along a path in the virtual world, without incorporating nu-
anced characteristics of locomotion behavior such as gait oscillations,
lateral sway, and random gaze aversions. These locomotion charac-
teristics introduce a degree of non-determinism, which conflicts with
the predictability and deterministic assumptions made when plan-
ning redirection. Furthermore, this behavior leads to deviations from
the expected virtual path, which in turn leads to deviations from the
expected redirection mapping. Our goal is to see if we can develop a
mechanism for the gain application to adapt to the user’s locomotion
behavior, such that the redirection effect remains approximately the
same, regardless of the user’s locomotion behavior.
4.4.4.1 Fixed Gain Approach
Since users tend to round the turn at a waypoint, when to update to
the next set of gains becomes an issue. One solution to this problem
(implemented in FORCE [Zmuda et al., 2013b]) would be to have the
user explicitly stop before each turn, announce that she has stopped,
turn in place, signal when the turn is completed, and then walk to-
ward the next waypoint. A more practical alternative that we propose
is to identify a point where the waypoint is considered reached and
update all the gains when the user reaches that point. If the gains
are not updated before the user begins turning, we found that the
updated rotation gain would only be applied to a portion of the turn.
Since rotation gain strongly impacts the amount of redirection, this
can lead to large deviations. In our pilot study, we noticed that most
users began turning after a point that is 1 meter before the waypoint.
Therefore, we chose to update the gain values when users are1 meter
away from the end waypoint.
4.4.4.2 Progression-Based Alignment Counter-Deviation
The intuition behind our counter-deviation approach is to compare
the amount of currently applied redirection to the expected amount
of the simulation. To reduce the difference, we first determine the
target alignment and then apply gains that aim to align the real user
to the simulated user.
determining alignment target Determining the alignment
target is similar to the expected target pose P
T
that is calculated for
4.4 validating the evaluation platform 67
determining the instantaneous deviation (Figure 17). When the user
is further than 1 meter away from the end waypoint, the alignment
target is P
T
. However, when the user is 1 meter or less from the
waypoint, P
V
is instead set to the point on the next virtual path seg-
ment that is 1 meter away. This modified value of P
V
is used to
calculate P
T
, which is the alignment target. This modification is done
because the user’s virtual progression during a turn cannot be accu-
rately measured since they do not turn in-place but rather walk and
turn gradually along the path.
adjusting gains The objective of counter-deviation is to mini-
mize the distance and angle between P
R
and P
T
shown in Figure 17.
To accomplish this, we determine the magnitude and direction of
translation and rotation required to align the user to the target pose
and use redirection gains to apply the maximum amount based on
the detection thresholds.
The amount and direction of translation required for alignment
is determined by calculating the vector from P
R
to P
T
. Using the
change in user position DU
R
calculated in Figure 17, we inject the
maximum amount of translation allowed by the detection threshold
of translation gain.
The magnitude and direction of rotation required for alignment is
determined by calculating the angle q shown in Figure 17. Both rota-
tion and curvature gain can inject alignment rotations. For rotation
gain, we calculate the change in user orientation by finding angle be-
tween user’s previous real world pose U
R
0
and her current pose U
R
,
and use this angle to determine the gain value that minimizes q. Sim-
ilarly we measure the amount of rotation permitted using curvature
gain and set the direction to minimizeq. Since the user may walk and
rotate at the same time, rotation and curvature gain can be applied
simultaneously. However, it remains an open question as to whether
or not applying both gains simultaneously increases its noticeability.
Therefore, we decided to chose the type of gain that better minimizes
the deviation.
4.4.5 User Study and Experiment Design
Real user locomotion data for this experiment was gathered through
a user study virtual reality experience for analysis and comparison to
data generated from our simulation platform.
4.4.5.1 Participants
Thirty participants (18 male and 12 female) were recruited for our
study using online postings (Craigslist volunteers section, Facebook
posts and Twitter). Participants were between 18 and 70 years old
with a mean age of 38.8 years and a median age of 40 years and
4.4 validating the evaluation platform 68
(a) measuring virtual progression (b) measuring real world deviation
Figure 17: Calculating the instantaneous deviation for counter-
deviation.
were required to have normal or corrected normal vision. We did
not pre-screen participants for gaming or virtual reality experience.
Participant recruitment and experimental procedures were approved
by the local Institutional Review Board (IRB). Participants were paid
USD $25 for their efforts.
4.4.5.2 Apparatus
Participants wore an Oculus Rift CV1 head-mounted display (HMD)
with Ausdom wireless stereo headphones connected to a Zotac VR
GO Backpack PC that was strapped to their shoulders (Figure 18).
The CV1 HMD has a 1080 1200 per eye resolution,90Hz refresh rate,
110 degree nominal field of view (FOV), and an internal 3 degree of
freedom (3DOF) inertial sensor. The participants were tracked in an8
meter by8 meter space with a PhaseSpace Impulse X2 motion capture
system. To enable 6DOF head tracking by the Impulse X2 system,
we attached 6 non-coplanar active LEDs to the CV1. At run-time,
head orientation was tracked using the CV1’s internal inertial sensor,
while positional information was supplied by the PhaseSpace system.
We also performed periodic orientation drift correction between trials
using orientation data from the Impulse X2 system. Sound cues were
provided using a pair of wireless “over the ear” Ausdom headphones.
The virtual reality experience was designed and rendered using the
Unity game engine.
4.4.5.3 Procedure
After signing the consent form, participants completed a pre-experiment
Simulator Sickness Scale questionnaire [Kennedy et al.,1993]. Partici-
pants were then escorted to the physical space and introduced to the
hardware used for the study. After putting on the equipment (Oculus
4.4 validating the evaluation platform 69
Figure 18: Equipment used for user study: Oculus CV1 HMD with
Phasespace LEDs attached, connected to a Zotac VR GO
backpack PC.
HMD, Zotac Backpack, and Ausdom Headphones), they were loaded
into an open-ended virtual environment with beige flooring and a
blue sky. Users verbally verified they could clearly see and hear the
visuals and test music playing and then proceeded with the tutorial.
Instructions were explained through a voice-over heard on the head-
phones, guiding them through the elements of the user study includ-
ing audio and visual cues, virtual paths presented with a rope and
stanchion metaphor, the reset task (Figure 19, and boundary proxim-
ity cues (a fading in alert sound and gradual red screen tint inverse
proportional to distance from boundary). Users were also guided
through sample turn and reset trials. Participants were then asked
to verbally confirm they had understood the tutorial elements and of-
fered a chance to ask questions about the experience elements. Partici-
pants would then immediately begin the first phase of the experiment.
After the first phase, the equipment would be taken off, allowing
participants to take a 5-minute break (or longer if requested). Then
the second phase would begin with the equipment being mounted
again and resuming the virtual experience. With the second phase
completed, the equipment was taken off and users asked to com-
plete a post-experiment Simulator Sickness Scale questionnaire. At
the end, they were also asked to provide basic demographics infor-
mation, such as age and gender. Each of the two phases took 8-12
4.4 validating the evaluation platform 70
Figure 19: Illustration of the reset prompt communicating the task of
stopping and turning in place.
(a) directional (b) ground
Figure 20: Head-up display indicators used in user study that guided
the user to face the correct direction and find the target
platform on the ground.
minutes depending on the participants movement speed. On aver-
age the entire experiment took approximately 50 minutes including
breaks.
4.4.5.4 Trials
The experiment consisted of 32 trials, 24 for the micro-level inspec-
tion, 4 for the macro-level inspection and 4 belonging to the counter-
deviation assessment. These trials were randomized and split into
two 16-trial phases, each phase containing the same number trials
from each trial type.
micro-level inspection trials The 24 trials in this category
consisted of 10 walk trials, 12 turn trials, and 2 reset trials. The 10
walk trial conditions were 1) no gain 2) g
t
= 1.2 3) g
t
= 0.86 4)
4.4 validating the evaluation platform 71
g
c
= 7.63 and 5) g
c
=7.63, each being tested twice. The 12 turn
trial conditions were in the form off+90, -90g degree turns with a
rotation gain of g
r
= f0.8, 1, 1.49g, each tested twice. The 2 reset
trials were a 2:1-Turn reset tested twice.
macro-level inspection trials The 4 trials in this category
were 2 different procedurally generated, random virtual paths, each
tested once with the steer-to-center strategy and once with steer-to-
orbit. In all case, a face-center reset was set to be triggered 1 meter
from the boundary. The paths were constructed from 20 waypoints
(not including the initial point), with random 90 or -90 degree turns,
each placed between 2 to 8 meters (sampled uniformly) apart, for an
expected length of 100 meters.
4.4.6 Task
At the beginning of each trial, the participant was guided to the initial
position and orientation. This was achieved by showing a directional
visual cue pointing towards the trial’s starting platform. The plat-
form was placed on the floor, shaped as an arrow enclosed in a circle,
pointing in the trials’ starting direction. Once the user arrived at the
platform and aligned her orientation with the arrow, the platform
would be replaced with a starting line, and the first two segments
of the trial’s virtual path would be loaded. The path appeared as a
1 meter-wide walkway designated by stanchions with ropes. As the
participant would begin to walk along the path, more segments of
the path would appear, with previously cleared portions incremen-
tally disappearing. Three elements were used to help with guiding
the user along the correct direction: 1) arrows placed along the virtual
path on the floor,2) a10 meter trail indicating the user’s recent trajec-
tory and3) a “wrong way” sign appearing when the user faced more
than 135 degrees away from the correct direction of progression. In
reset trials (belonging to the micro-inspection) and path trials (belong-
ing to the macro-inspection), occasionally a reset would be triggered.
An audio cue was played, and as the scene faded to black, a stop sign
would appear with the caption “Turn in Place.” After sufficiently ro-
tating in place, the sign would disappear and the environment would
reappear allowing the user to resume progression. Resets were trig-
gered at the3 meter mark in reset trials, and for path trials, when the
user’s distance to a boundary dropped below 1 meter. As an extra
measure, to alert the user of her proximity to hard boundary limits,
an alert tone would fade in and the screen would gradually tint to red
with an audio and visual intensity proportional to boundary proxim-
ity. The end of the virtual path was delineated with a finish line on
the floor similar to the starting line. Once the end of the path was
reached, depending on the trials remaining, the user would either
4.4 validating the evaluation platform 72
(a) g
t
< 1 (b) g
t
> 1
Figure 21: End waypoint pose for translation gain trials. Simulation
results in red and user results in blue. This illustrates the
small and symmetric variance in manipulation for transla-
tion gain.
see a) a directional cue to the next platform, b) a “Break Time” sign
or a c) a “Finished” sign.
4.4.7 Results and Discussion
4.4.7.1 Experiment 1: Micro-Scale Inspection
In this section we analyze the manipulation and deviation measures
for each trial. Note that since within each condition orientational
measures are offset by a fixed value, we only perform regression on
orientational manipulation.
translation gain Figure 21 compares end waypoint poses for
translation gain trials for real and simulated users.
To examine how positional manipulation is affected by applied
translation gain and net displacement, we constructed a multiple lin-
ear regression model. The model had a good fit (R
2
= 0.99). We
treated translation gain as a two-level factor and net translation gain
as a continuous predictor variable. The model shows that both trans-
lation gain (F(1, 117) = 2256535, p < 0.001) and net displacement
(F(1, 117) = 364.31, p < 0.001) were significant predictors of posi-
tional manipulation. Positional manipulation increased by 0.19
0.01m for each meter of net displacement. On average, positional
manipulation for human participants was 0.81m (SE = 0.00016) for
g
t
= 0.86 and 1.03m (SE = 0.00024) for g
t
= 1.26.
We also constructed a multiple linear regression model to explore
how positional deviation is affected by translation gain and net dis-
placement as main effects. The model had a good fit (R
2
= 0.99).
The model shows that both gains (F(1, 117) = 136.16, p< 0.001) and
displacement (F(1, 117) = 4238.84, p < 0.001) significantly affect po-
sitional deviation. Positional deviation increased by 0.18 0.01m for
each meter of net displacement. The average positional deviation
was 0.009m (SE = 0.00069) for g
t
= 0.86 and 0.012m (SE = 0.0011) for
g
t
= 1.26.
4.4 validating the evaluation platform 73
The results indicate that effect of translation gain can be explained
by the net displacement, which implies that the shape of the virtual
trajectory is not a factor and the gains essentially cancel each other
out throughout the path. Though it can be argued that translation
gain has a small impact on deviation when applied in solitude, it can
however, play a part in increasing deviation when combined with
other gains. For instance, the user’s lateral motions along the virtual
path can cause intermediary deviations that can shift the pivot point
of applied rotations, which can in turn magnify deviations.
curvature gain Figure22 compares end waypoint poses for cur-
vature gain trials for real and simulated users.
To examine how positional manipulation is affected by sum dis-
tance travelled and average lateral distance from the virtual path we
constructed a multiple linear regression model. We treated both sum
distance travelled and average lateral distance from the virtual path
as continuous predictor variables. The model shows that both sum
distance travelled (F(1, 117) = 1523.001, p < 0.001) and average lat-
eral distance from the virtual path (F(1, 117) = 5.61, p = 0.019) were
significant predictors of positional manipulation. Positional manipu-
lation increased by 0.32 0.01m for each meter of sum distance trav-
elled and decreased by 0.17 0.01m for each meter of average lateral
distance from the virtual path. On average, positional manipulation
for human participants was 1.68m (SE = 0.011) for g
c
=7.63 and
1.69m (SE = 0.013) for g
c
= 7.63.
We constructed a multiple linear regression model to explore how
positional deviation is affected by sum distance travelled and average
lateral distance from the virtual path as main effects. The model
shows that both sum distance travelled (F(1, 117) = 1444.31, p <
0.001) and average lateral distance from the virtual path (F(1, 117) =
31.64, p < 0.001) were significant predictors of positional deviation.
Positional deviation increased by 0.32 0.01m for each meter of sum
distance travelled and decreased by 0.41 0.01m for each meter of av-
erage lateral distance from the virtual path. On average, positional de-
viation for human participants was0.078m (SE =0.011) for g
c
=7.63
and 0.082m (SE = 0.013) for g
c
= 7.63.
We also constructed a multiple linear regression model to explore
how orientational manipulation is affected by sum distance travelled
and average lateral distance from the virtual path as main effects.
The model shows that sum distance travelled (F(1, 117)= 563.35, p<
0.001) was a significant predictor of orientational manipulation, how-
ever, average lateral distance from the virtual path was not significant
(F(1, 117) = 0.003, p = 0.10). Orientational manipulation increased
by 7.65 0.01° for each meter of sum distance travelled. On average,
orientational manipulation for human participants was 39.37° (SE =
0.21) for g
c
=7.63 and 39.63° (SE = 0.33) for g
c
= 7.63. Also for ori-
4.4 validating the evaluation platform 74
(a) g
c
< 1
(b) g
c
> 1
Figure 22: End waypoint pose for curvature gain trials. Simulation
results in red and user results in blue. This illustrates the
overshooting of curvature gain for real users vs. simula-
tion.
4.4 validating the evaluation platform 75
entational deviation the average was 1.30° (SE = 0.21) for g
c
=7.63
and 1.56° (SE = 0.33) for g
c
= 7.63.
Based on the results, we can see that the sum distance travelled is
the main factor for explaining how much curvature gain is applied
Therefore, a real user’s excess lateral motions, in comparison to the
simulated user, cause an increase in injected rotation gain. The user’s
lateral distance from the virtual path, which can be caused by both
lateral motions and simply not walking along the middle of the path,
affect the pivot point for applying the rotations of curvature gain. The
variance in pivot point influences the positional measures, but since
the amount of curvature gain applied is not affected, the orientational
measures are not influenced.
rotation gain Figure23 compares end waypoint poses for rota-
tion gain trials for real and simulated users. For each trial we mea-
sured the user’s virtual position when the angle between her orien-
tation and the target turn orientation reached 70, 45 and 20 degrees.
The distance between between the turn waypoint and user’s position
at45 degrees was defined as the turn point error, indicating how far off
the user was from the expected turn point when half of the90 degree
rotation was completed. The distance between the 70 degree and 20
degree marks was also used to approximate the turn radius. The net
turn angle was also calculated as the overall change in rotation before
and after the turn area (the 1 meter proximity of the turn waypoint).
To examine how positional manipulation is affected by rotation
gain, turn point error, turn radius, net turn angle and average lat-
eral distance from the virtual path we constructed a multiple lin-
ear regression model. We treated rotation gain as a two-level factor
and all other factors as continuous predictor variables. The model
shows that rotation gain (F(1, 111) = 1211.73, p < 0.001), net turn
angle (F(1, 111) = 705.80, p < 0.001), average lateral distance from
the virtual path (F(1, 111) = 34.71, p < 0.001) and turn point error
(F(1, 111) = 4.32, p = 0.039) were significant predictors of positional
manipulation. However, turn radius was not significant (F(1, 111) =
3.31, p = 0.071). Positional manipulation increased by 0.01 0.01m
for each degree of net turn angle, decreased by 0.66 0.01m for each
meter of average lateral distance from the virtual path, and increased
by 0.08 0.01m for each meter of turn point error. On average, po-
sitional manipulation for human participants was 0.98m (SE = 0.020)
for g
r
= 0.8 and 1.26m (SE = 0.034) for g
r
= 1.49.
We also constructed a multiple linear regression model to explore
how positional deviation is affected by rotation gain, turn point er-
ror, turn radius, net turn angle and average lateral distance from the
virtual path as main effects. The model shows that rotation gain
(F(1, 111)= 10.63, p= 0.0015), net turn angle (F(1, 111)= 418.47, p<
0.001), average lateral distance from the virtual path (F(1, 111) =
4.4 validating the evaluation platform 76
30.92, p < 0.001) and turn point error (F(1, 111) = 16.97, p < 0.001)
were significant predictors of positional deviation. However, turn
radius was not significant (F(1, 111) = 0.46, p = 0.49). Positional de-
viation decreased by 0.009 0.001m for each degree of net turn angle,
increased by 0.57 0.01m for each meter of average lateral distance
from the virtual path, and increased by 0.14 0.01m for each meter
of turn point error. On average, positional deviation for human par-
ticipants was 0.23m (SE = 0.019) for g
r
= 0.8 and 0.32m (SE = 0.029)
for g
r
= 1.49.
We also constructed a multiple linear regression model to explore
how orientational manipulation is affected by rotation gain, turn point
error, turn radius, net turn angle and average lateral distance from
the virtual path as main effects. The model shows that rotation
gain (F(1, 111) = 4096.17, p < 0.001), net turn angle (F(1, 111) =
3728.88, p < 0.001), average lateral distance from the virtual path
(F(1, 111) = 5.20, p = 0.024), turn point error (F(1, 111) = 4.49, p =
0.03) and turn radius (F(1, 111) = 7.70, p = 0.006) were all signifi-
cant predictors of orientational manipulation. Orientational manip-
ulation increased by 0.31 0.01° for each degree of net turn angle,
decreased by 2.53 0.01° for each meter of average lateral distance
from the virtual path, increased by 0.81 0.01° for each meter of turn
point error and increased by 0.55 0.01° for each meter of turn ra-
dius. On average, orientational manipulation for human participants
was20.18° (SE =0.41) for g
r
= 0.8 and25.11° (SE =0.70) for g
r
= 1.49.
Also for orientational deviation the average was 2.57° (SE = 0.36) for
g
c
=7.63 and 4.57° (SE = 0.66) for g
c
= 7.63.
Overall, among the three gain types, we see that rotation gain has
the largest impact on manifesting deviations. The amount of rotation
gain applied can mostly be explained by the net turn angle. There-
fore, similar to translation gain, rotation gains can cancel each other
out when the user turns side to side, and only the overall change in
heading is what determines the amount of rotation that is injected.
For rotation gain trials, we observe that overall less rotation is in-
jected compared to simulation, which is the opposite case in contrast
to curvature gain. Upon further inspection, we noticed that this is
due to the fact that users begin slightly facing towards the waypoint
after the current target waypoint, even before reaching a 1 meter dis-
tance from their current target waypoint. Also, in some cases, users
wouldn’t fully turn towards the next waypoint. As a result, the net
turn angle would be less than expected, thus less rotation gain would
be injected.
Similar to curvature gain, how the rotation gain gets applied, specif-
ically the pivot points heavily influence positional deviations, and
this is captured by the other factors (average lateral distance from the
virtual path and turn point error). Upon further inspection, we no-
ticed users tend to cut corners, essentially completing a turn segment
4.4 validating the evaluation platform 77
(a) g
r
< 1 (b) g
r
> 1
Figure 23: End waypoint pose for rotation gain trials. Simulation re-
sults in red and user results in blue. This illustrates the
undershooting of rotation gain for real users vs. simula-
tion.
without getting very close to the turn waypoint. This causes the ro-
tation to be injected along points that differ from the turn waypoint,
which is where the simulated user performs the turn. This turning
behavior can potentially be modelled in the simulated user to better
resemble the average user, which should reduce the overall deviations
along turns.
It is important to point out the fundamental difference between in-
jecting translations (via translation gains) and rotations (via curvature
and rotation gains). Only the vector of net translation influences the
translation gain applied, regardless of the origin and where the trans-
lation took place. For rotations on the other hand, the specific place
where the rotation is injected (the pivot point) matters, and variance
in this pivot point manifests in positional deviations. Furthermore,
with injecting rotations, small variances in rotation can result in po-
sitional deviations of great magnitude. Therefore, injecting rotations
play a greater part in causing deviations. The magnitude of rotations
involved with rotation gain is substantially greater than curvature
gains, making rotation gain responsible for the majority of deviation
as well.
reset Figure 24 compares end waypoint poses for rotation gain
trials for real and simulated users. For each trial we measured the
reset displacement, which is the overall change in position during the
4.4 validating the evaluation platform 78
reset task. We also marked the user’s mid-reset and end-reset positions
in the real world, signifying when the reset task’s overall virtual ro-
tation had reached 180 and 360 respectively. These positions were
compared to the point where the reset was triggered. We also mea-
sured mid-reset and end-reset point error by measuring the distance of
these points to the simulated user’s reset task stopping point. The
reset turn diameter was also approximated by the distance between
the mid-reset and end-reset positions.
A multiple linear regression model was calculated to predict posi-
tional manipulation based on displacement in reset, mid-reset point
distance to trigger, end-reset point distance to trigger and reset turn
diameter as main effects (i.e. we did not consider any interactions).
The model shows that reset turn diameter (F(1, 54) = 37.78, p <
0.001), mid-reset point distance to trigger (F(1, 54) = 9.96, p = 0.003),
and end-reset point distance to trigger (F(1, 54) = 7.22, p = 0.001) all
significantly affected positional manipulations. However, displace-
ment in reset was not a significant factor (F(1, 54) = 0.52, p = 0.807).
The average positional manipulation was 4.92m (SE = 0.071). It in-
creased by 1.20 0.20m for every meter of reset turn diameter, de-
creased by 0.56 0.18m for every meter in mid reset point distance
to trigger, and decreased by 1.53 0.57m for every meter in end reset
point distance to trigger.
Similarly, a multiple linear regression model was calculated to pre-
dict positional deviation based on main effects of displacement in re-
set, mid-reset point error, end-reset point error and reset turn diame-
ter. The model shows that mid-reset point error (F(1, 54)= 81.22, p<
0.001) and displacement in reset (F(1, 54)= 13.23, p< 0.001) were sig-
nificant factors; reset turn diameter (F(1, 54) = 2.47, p = 0.122) and
end-reset point error (F(1, 54) = 2.17, p = 0.151) were not significant.
The average positional deviation was0.66m (SE =0.047). It increased
by 1.42 0.16m for every meter of mid reset point error and decreased
by 0.36 0.10m for every meter in displacement.
Reset trials are somewhat comparable to rotation gain trials in that
they both involve injecting rotation gains. However, in a 2:1-turn
reset, the injected rotation is always 180 degrees, meaning the orien-
tational measures are the same across users. On the other hand, the
broad variations in how users react to resets substantially influence
the pivot points for injecting the rotation, and thus results in variation
in positional measure that is much greater than rotation gain trials.
There is not a consistent overshooting or undershooting as we ob-
served with curvature and rotation gain respectively, but rather early
and late reactions can result in a decrease or increase in positional
manipulation. It is also important to note that users begin rotating
before coming to a full stop, which has a similar effect to an early
reaction to reset. This explains the majority of end poses appearing
lower than the simulated end pose in Figure 24. In general, the vari-
4.4 validating the evaluation platform 79
Figure 24: End waypoint pose for reset trials. Simulation results in
red and user results in blue. This illustrates the large vari-
ance in manipulation during resets for real users vs. simu-
lation.
ation in pivot points for injecting rotation during the reset and their
distance from the expected pivot point from the simulation explain
the positional deviation, which is captured by the explaining factors.
The measured reset displacement is an important factor in deter-
mining the appropriate reset buffer distance, which dictates at what
proximity to a boundary a reset must be triggered to keep users safe.
Though the median reset displacement for real users is 0.76m (simi-
lar to 0.78m for the simulated users), this value greatly varies across
users, which in turn explains variation in positional deviation. The
10th percentile for reset displacement was 0.46m and the 90th per-
centile was 1.21m. Based on the data, a 1.21m reset buffer distance
may be suitable. However, given the relatively high average age for
our study population, a lower value such as 1 meter would probable
be sufficient for the average user. Furthermore, the reset buffer dis-
tance can generally be adjusted for each user with a calibration pro-
cess to both ensure safety for users with slower reactions and make
better use of the physical space for those with quicker reflexes.
One subtle matter that must be addressed is a distinction in the
manner in which gains are applied. In the micro-inspection trials, the
gains were symmetric, meaning they are applied at a fixed rate, regard-
less of the direction of translation or rotation. However, in strategies
such as S2C, the direction of rotation influences the scaling factor
applied at each frame. In such an asymmetric scenario, a clockwise
rotation may be upscaled while a counter-clockwise rotation would
4.4 validating the evaluation platform 80
Figure 25: Reset counts for macro inspection trials.
be downscaled. The reason for this is to leverage gains in order to
achieve a specific goal determined by a heuristic (the user facing the
center in the case of S2C). Inspecting trials with asymmetric gain ap-
plication can potentially lead to different findings and better explain
how symmetric vs asymmetric gains can influence overall deviation.
For instance, if rotation gains are applied asymmetrically, side to side
movements would not cancel each other out and instead accumulate
and increase the overall manipulation.
4.4.7.2 Experiment 2: Macro-Scale Inspection
The reset count for each redirection strategy in each path is shown
for real users vs. the simulated user in Figure 25.
For path 1 with S2C, using a one-sample t-test comparing the ex-
pected reset count of 11 from the simulated user compared to real
users (M=11.1 , SD=1.37) we failed to reject the null hypothesis: (t(29)=
0.39, p = 0.693). For path 1 with S2O, using a one-sample t-test com-
paring the expected reset count of 15 from the simulated user com-
pared to real users (M=14.3 , SD=1.17) we reject the null hypothesis
(t(29) =3.25, p = 0.003). For path 2 with S2C, using a one-sample
t-test comparing the expected reset count of 12 from the simulated
user compared to real users (M=11.23 , SD=1.00) we reject the null
hypothesis: (t(29) =4.17, p< 0.001). For path 2 with S2O, using a
one-sample t-test comparing the expected reset count of 15 from the
simulated user compared to real users (M=15.2 , SD=1.65) we failed
to reject the null hypothesis: (t(29)= 0.88, p= 0.38).
The results from our study indicate an overall similarity between
redirection performance measured via simulation and the average
4.4 validating the evaluation platform 81
Figure 26: A sample virtual trajectory of a real user (blue) compared
to the simulated user (red). The the locations where resets
were triggered is marked with circles corresponding to the
user type.
performance for real users. Overall, we can argue that results from
simulation can provide a conservative estimate for average perfor-
mance with real users. More importantly, results from the simulation
preserve the trends present in real user data, specifically S2C outper-
forming S2O in both paths across real and simulated users.
The similarity in performance between real and simulated users
may seem to contradict our previous observations that deviations
rapidly manifest in short trials. However, deviation inherently does
not entail an increase or decrease in performance, but rather implies
that a real user’s path is becoming out of sync with the simulated
user. The diverging trajectories can potentially lead to a real user ob-
serving a reset earlier or later than the simulated user, with neither
of the two scenarios being is necessarily more likely than the other.
Redirection performing better for some users in comparison to our
simulation can potentially be explained by asymmetric gains. S2C
and S2O are greedy strategies that take the user’s motions at each
frame as an opportunity to get closer to a target objective (the user
facing the center or orbiting around the center). This means real
users who exhibit more motion than a simulated user (such as ex-
cess lateral motions and head motions) have more chances to steer
themselves, potentially improving the performance of the redirection
strategy. In contrast to using symmetric gains, an asymmetric gain
4.4 validating the evaluation platform 82
(a) xed-gain method (b) counter-deviation method
Figure 27: Resulting trajectories from counter-deviation trials. Simu-
lation trajectory in red and user trajectories in blue.
approach uses motions only to improve the user’s state, and will
stop injecting motions if necessary. Therefore, extra motions may
not necessarily be conducive to the success of a planned redirection
strategy that uses fixed gains. Furthermore, going out of sync for
a planned redirection strategy can require re-planning, which may
lead to a sub-optimal redirection plan. This emphasizes the impor-
tance of using asymmetric gains for planning strategies such as the
counter-deviation approach proposed in this work.
While the performance of redirection for some users can be better
than our simulation, in other cases we notice a decline in performance.
We believe the main reason for this is resets being triggered in situa-
tions where they may not be absolutely necessary. The most common
example of this would be a user brushing against a reset trigger due
to side-to-side lateral motions while walking virtually parallel to the
physical space boundary. Another example of this is back-to-back
resets firing when a user struggles with both performing the reset
task and resuming progression in the correct direction. These situa-
tions can be avoided by developing more advanced reset triggering
mechanisms.
4.4.7.3 Experiment 3: Countering Deviation
The contrast between user trajectories in the fixed gain vs. counter-
deviation conditions for one of the two paths can be seen in Figure27.
The positional and orientational deviations measured at each check-
point for each path contrasting fixed gains and counter-deviation are
also shown in Figure 29. For each trial, the area under the plot was
calculated as a summary of deviation for the entire trial. For each
4.4 validating the evaluation platform 83
Figure 28: End waypoint pose for last checkpoint in counter-deviation
trials for path 1.
path a paired-samples t-test was conducted to compare the effect of
using fixed-gains vs. counter-deviation.
In path 1, there was a significant difference in the positional de-
viation between using fixed gains (M=3.67, SD=0.16) and counter-
deviation (M=0.96, SD=1.14) conditions; t(30) =16.11, p < 0.001.
In path2, there was a significant difference in the positional deviation
between using fixed gains (M=3.51, SD=0.21) and counter-deviation
(M=1.75, SD=0.21) conditions; t(30) =8.30, p < 0.001. In path 1,
there was a significant difference in the orientational deviation be-
tween using fixed gains (M=59.14, SD=3.79) and counter-deviation
(M=18.02, SD=3.79) conditions; t(30) =10.83, p < 0.001. In path
2, there was a significant difference in the orientational deviation be-
tween using fixed gains (M=56.74, SD=2.89) and counter-deviation
(M=29.72, SD=2.89) conditions; t(30)=9.34, p< 0.001.
The results indicate that our counter-deviation is significantly ef-
fective at reducing both positional and orientational deviations. On
the last segment of the paths, the average positional deviation was
reduced from 0.97m to 0.28m when using counter-deviation, and sim-
ilarly from 18.09° to 5.31° for orientational deviation. The counter-
deviation ensures gain manipulation remains within a reasonable
amount from the simulation and deviation values are contained. How-
ever, a short virtual path of only 4 segments may not definitively
demonstrate how effective counter-deviation is. Using a large phys-
ical space, counter-deviation can be tested on much longer paths to
better gauge its efficacy.
The rise in deviation immediately after a turn (odd-numbered check-
points) and the fall in deviation before the subsequent turn (even-
numbered checkpoints) indicate that turns are a critical point where
deviations manifest (see Figure 29). This result is in line with re-
4.4 validating the evaluation platform 84
Figure 29: Deviation results across checkpoints for counter-deviation
trials. Error bars show standard error.
sults from the micro inspection: rotation gain trials lead to large
deviations, which hints at the vulnerability of redirection planning
for turns. Walking segments are effectively the main opportunity
for counter-deviation to recover from the deviation caused by a turn.
How well counter-deviation can manage paths with more frequent
turns and less walking in between remains an open question.
Counter-deviation is effective because it not only adjusts gains to
constantly aim for alignment, but it takes a user’s extra motions (lat-
eral movements and extra head yaw changes) and converts them into
opportunities to inject extra motion that further helps with alignment.
This approach to countering deviations converts motions that would
normally cause deviations into injected translations and rotations that
aim to realign the user with the planned trajectory. Also, deviations
can partially cancel out previous deviations, which helps with align-
ment in both fixed gain and counter-deviation cases.
Counter-deviation entails adjusting gain levels in each frame, and
although the changes between consecutive frames may often be small,
at some points along the path the changes can be more sudden. One
concern is that users may notice sudden changes in gains, even if
the gains remain within their detection thresholds. However, abrupt
changes of gain values are also present when switching gains in the
fixed-gain scenario and in redirection strategies such as S2C. One
remedy that is used to prevent sudden changes is applying smooth-
ing to the gain factor to ensure gains change more gradually between
4.4 validating the evaluation platform 85
frames [Hodgson and Bachmann, 2013]. Measuring sensitivity to
changes in gains can help with designing gain smoothing mecha-
nisms that would ensure gains remain unnoticed, and some stud-
ies have already begin to investigate this problem [Zhang and Kuhl,
2013a, Zhang et al., 2014].
4.4.8 Summary
In this study, I investigated how redirection gains interact with user
locomotion behavior to understand how the outcome of redirection
can vary across real and simulated users. By looking at the gains ap-
plied at a micro scale, we learned that the main sources of deviation
are a) lateral movements causing increased curvature gains b) prema-
ture and gradual turning along with shortcuts influencing rotation
gain pivot points and c) variations in reaction to resets, with most
deviation being caused by the latter two. Looking at gains applied
at a macro scale, we observed similar average performance between
users and the simulated model, with simulated user results offering a
conservative estimate for the average performance of real users. I ob-
served that though deviations cause real trajectories to diverge, they
do not directly decrease or increase performance. By using the pro-
posed counter-deviation mechanism, I demonstrated how deviations
can be minimized, keeping the average positional deviation below0.3
meters. This ensures a planned redirection can be executed with real
users effectively and the outcome performance would be robust to
variations in user locomotion behavior.
Overall, we learned that turns (rotation gain) and resets have a
strong impact on deviation from the simulation. While variability in
reactions to reset may not be easily accounted for in the user sim-
ulation, we may be able to improve future simulation models for
performing turns in order to mitigate deviations caused by resets.
Instead of an in-place rotation, turns can be modelled with an arc-
shaped trajectory with a radius that matches the average user (0.60m
in our dataset).
The micro scale inspection can be extended by examining how
combined gains (such as simultaneous translation and curvature) can
manifest deviations. Furthermore, trials with asymmetric gains can
help with identifying alternative locomotion behaviors that cause de-
viations, and help with better explaining the behavior of strategies
such as S2C. Another avenue also worth investigating is how the pres-
ence of gains influences the virtual trajectory. It would be helpful to
understand whether an observer in the virtual world can tell if gains
are being applied to a user or not, just by observing the user’s walk-
ing behavior.
The counter-deviation approach can be further studied by examin-
ing how deviation levels rise and fall along longer virtual paths to
4.4 validating the evaluation platform 86
better gauge its overall efficacy. The robustness of this approach can
also be further evaluated by testing how it can recover from erratic
user behavior such as exaggerated lateral movements, side-stepping
and minor detours. It would also be valuable to investigate how
counter-deviation techniques can help with recovering from the devi-
ations caused by resets.
The investigation of how deviations manifest and how they affect
performance sheds light on the differences we can expect from redi-
rection when applied with real users versus simulation. The results
affirm the validity of using the presented platform for the purpose
of evaluating the performance of redirected walking. This finding
opens the door to reliably performing simulation-based studies that
can help with understanding redirection performance factors, testing
and developing novel strategies and algorithms, and also performing
cost-benefit analyses for a custom virtual reality configuration. Al-
though the exact measurements of performance for a specific user
and virtual reality system can only be measured with live testing, a
simulated test can conservatively estimate average performance. I
envision researchers and developers performing large-scale experi-
ments and prototyping novel approaches using these simulation plat-
forms, rapidly advancing the field of redirected walking.
Part III
T H E A D A P T I V E PA R A D I G M
5
T H E A D A P T I V E M E TA - S T R AT E G Y
To improve is to change; to be
perfect is to change often.
Winston Churchill
Adaptive redirection is a context-aware meta-strategy: context-
aware in that it adapts to the context in which redirection is applied,
and a meta-strategy in that it sits above a collection of strategies and
determines which should be used depending on the context. The
central tenet of adaptive redirection is that not one single redirection
strategy outperforms all others, but rather the approach must con-
form to the context in which it is deployed, shifting from one strategy
to another to best fit to the situation. To achieve such a meta-strategy,
the specific factors that influence the effectiveness of individual redi-
rection strategies (i.e. the context) must be identified and the variance
in their performance under different conditions must be investigated.
The results from this analysis can be used to develop adaptation rules
that determine which strategy should be activated at a given point in
time given the circumstances at hand.
In the formulation that I propose, the circumstances are expressed
in the form of properties of a prediction graph that coarsely commu-
nicates the possible near term trajectories in the virtual environment.
Figure 30: Schematic for the adaptive redirection meta-strategy. This
approach adapts to the input circumstances by dynami-
cally selecting between multiple redirected walking strate-
gies.
88
5.1 a taxonomy of redirection strategies 89
The adaptive redirection meta-strategy is then defined as a function
that determines the most effective redirection strategy for a given
physical space based on the prediction graph measured at the user’s
location. In this chapter I will explore the domain, range, and map-
ping of inputs to outputs for this function.
5.1 a taxonomy of redirection strategies
Not all redirection strategies can be applied to all circumstances, but
rather their applicability is subject to the availability and properties of
the prediction graph. I can therefore, categorize redirection strategies
by grouping them by the range of circumstance in which they can
be applied. In adaptive redirection, I assume a candidate strategy
is selected from and representing each category. Ideally, the chosen
representative strategy would be determined based on one of more
factors like performance, efficiency, and/or ease of implementation.
Given the set of representatives, adaptive redirection determines a
set of rules to switch between these strategies such that the most ef-
fective of these strategies is selected based on the circumstances in
which it is applied. This does not mean a strategy is selected per
experiences, but instead within a single virtual experience, the acti-
vated strategy will not necessary stay constant and can change several
times. Since each representative strategy is essentially a placeholder,
as new techniques are developed, the meta-strategy can be reworked
to incorporate them. The purpose of this work is to introduce how
an adaptive meta-strategy can be used for a given a classification of
redirection strategies and the representative from each class.
5.1.1 General Strategies
General strategies can be applied to any scenario and do not depend
on user predictability. Therefore, they neither rely on a prediction
graph nor are able to leverage one even if available. These strategies
utilizing only current state information often follow a heuristic that
is akin to a greedy algorithm. Steering algorithms such as steer-to-
center and steer-to-orbit are examples of general strategies.
5.1.2 Dynamic Planning Strategies
Dynamic planning strategies such as FORCE [Zmuda et al., 2013b]
and MPCRed [Nescher et al., 2014] rely on the availability of a pre-
diction graph. They use the prediction graph to dynamically plan a
short-term redirection strategy. This plan is periodically updated as
the user explores the environment.
5.2 prediction graph properties 90
5.1.3 Static Planning Strategies
Static planning strategies have a very strict dependency on user pre-
dictability; they require a prediction graph that does not contain
any branches. This means the user’s virtual path is completely pre-
dictable. This feature allows the strategy to plan the entire route in
advance, thus choosing the best set of gains. Any strategy that was
designed or tailored for a specific path is considered a static planning
strategy. An examples of this is Razzaque’s zig-zag fire drill demon-
stration [Razzaque et al., 2001].
5.2 prediction graph properties
The input for an adaptive redirection meta-strategy is a prediction
graph. The prediction graph is used to first determine which strate-
gies are applicable, and are further examined to determine which
of the contending strategies would perform best. Given my classifi-
cation of strategies, three distinct scenarios can be identified: 1) no
prediction graph is available in which case the general redirection
strategy will be selected by default, 2) the prediction graph contains
branches, in which case both general and dynamic planning strate-
gies are viable, and3) the prediction graph has no branches, in which
case all three approaches are applicable. The hypothesis is that the
properties of the prediction graph are sufficient for determining the
most effective approach in scenarios2 and3. Therefore, it is essential
express the prediction graph properties with variables that capture
its characteristics. In this work we characterize prediction graphs by
the distribution of the segment length, turn angle, and branching factor.
5.2.1 Segment Length Distribution
A segment is a portion of the complete virtual path which starts at
one waypoint and ends at another. Consequently, the segment length
is the distance between the start and end waypoint. The segment
length distribution for a given prediction graph is a continuous prob-
ability distribution for the segment lengths of that graph.
5.2.2 Turn Angle Distribution
When the user finishes traversing a path segment, she turns in place
to face the next waypoint. The amount the user rotates is known as
the turn angle. Similar to the segment length distribution, the turn
angle distribution is a continuous probability distribution for the turn
angles of a given graph.
5.3 from prediction graph to most effective strategy 91
Figure 31: The components of the adaptive redirection system.
5.2.3 Branching Factor Distribution
The branching factor for a given waypoint is defined as the number
of waypoints that it connects to. For example, if a given starting way-
point only has one end point, its branching factor is 1. If waypoint
has 2 different end points then its branching factor is 2. The branch-
ing factor distribution assigns a probability value to each possible
non-zero integer branching factor.
5.3 from prediction graph to most effective strategy
The final component of the adaptive redirection meta-strategy is the
mapping from the inputted prediction graph to the most effective
redirection strategy. This problem can be formulated as a classifica-
tion of the prediction graph space: labelling regions with the strategy
that best performs within it. In order to accomplish this, I will sam-
ple the domain, label each sample with the strategy that performs the
best, and use machine learning to train a classifier that partitions the
prediction graph space based on the sample’s labels. Additionally, a
rule-based classifier will be used so that the partitioning is expressed
as a set of rules that can be easily adapted to programming logic. The
complete structure of the adaptive redirection system can be seen in
Figure 31.
5.3.1 Measuring Redirection Performance on a Prediction Graph
Measuring the performance of a strategy is often done by gauging
the frequency of resets across a lengthy virtual path. A prediction
graph on the other hand is too brief of a window to gauge how well
a strategy is performing. A potential solution could be to extend this
window further and gauge the performance throughout a broader
scope, however, it may not be fair to attribute the performance across
a longer stretch to the prediction graph which only influenced a por-
tion of the performance. Furthermore, the prediction graph at various
parts of the virtual path may have completely different characteristics
from the prediction graph under examination. MY solution to control
5.3 from prediction graph to most effective strategy 92
for this is to artificially duplicate the performance graph and extend it
into a larger graph. Therefore, I can measure the performance across
a longer virtual path that has the same performance graph properties
throughout.
5.3.2 Sampling the Prediction Graph Space
Using their defined properties, prediction graphs can be simplified
down to three sets of distributions. Therefore, a sample of the predic-
tion graph space equates to sampling the set of all possible segment
length, turn angle, and branching factor distributions. To simplify
this, the space will be truncated such that each property distribution
will have a minimum and maximum value. Additionally, the seg-
ment length and turn angle distributions will both be expressed as a
uniform distributions. The branching factor distribution is simplified
by limiting the branching to either 1 or 2. With this simplification in
place, whether or not a waypoint branches becomes binary. Therefore,
this distribution can be expressed as a single branching likelihood vari-
able, which is the probability of whether or not a waypoint branches.
Before developing the adaptation rules, each of the three categories
of redirection strategies will be closely examined in chapters6,7 and
8. Using this information I will proceed to demonstrate how to derive
the adaptation rules required for adaptive redirection in Chapter 9.
Part IV
D E V E L O P I N G A D A P TAT I O N : T H E
E X A M I N AT I O N O F R E D I R E C T I O N S T R AT E G I E S
6
G E N E R A L R E D I R E C T I O N S T R AT E G I E S
When the solution is simple,
God is answering
Albert Einstein
This chapter examines the general redirection strategy, the first of
the three sub-strategies in adaptive redirection. It must be clarified
that the general strategy (as with all sub-strategies of adaptive redi-
rection) is not a clear-cut specifically defined strategy, but rather a
categorization of redirection strategies. In my envisioning of adap-
tive redirection, each sub-strategy is simply a placeholder; and as ad-
vanced methodologies are presented in the field, each category will
be represented with a superior instance of its type.
Two carefully designed experiments are presented here that help
with better establishing this category, understanding its properties
and limitations, along with providing insight into the mechanics of
redirected walking in the most general case.
6.1 motivation and goals
Though general redirection is only one of three pillars in a broader
meta-strategy, it is particularly important for it represents the general,
or rather worst-case scenario of redirected walking. The category re-
flects a global view of redirection, in addition to a specific mode of
operation in the adaptive meta-strategy. Therefore, in addition to
serving the objectives of this dissertation (primary goals), I would
like to also address important broader matters that pertain to redi-
rected walking in general and the body of research surrounding it
(secondary goals).
6.1.1 Primary Goals
• Finding a representative for general redirection: All potential
candidates for a general redirection strategy from the literature
are gathered here for a full demonstration of their capabilities
(and the notorious standoff of S2C and S2O is meant to be set-
94
6.1 motivation and goals 95
tled once and for all). Note the objective is not necessarily to
develop the definitive general strategy, but rather to demonstrate
a means illustrating how candidates can be analyzed and com-
pared.
• Provide insight on space requirements and performance ex-
pectations: Examining the capabilities of general redirection
strategies provides an understanding of what to expect from
redirection in its most general case, offering a worst-case sce-
nario analysis of its efficacy. This leads to developing guidelines
for space requirements and other practical questions that have
been widely speculated without accurate assessment.
• Case study for using evaluation methodology and platform:
This study also serves as an opportunity to showcase the capa-
bilities of the proposed evaluation platform, and demonstrate
how to systematically control for parameters, and design effec-
tive experiments that yield reliable results.
Note that in the search for finding a suitable general strategy, the
focus will be strictly on the redirection heuristic, and not the reori-
entation heuristic, keeping the latter constant for fair comparison.
Additional studies can also be conducted to find the best suiting re-
orientation heuristic also, or even analyze how the redirection and
reorientation heuristics interact.
6.1.2 Secondary Goals
• Rectify a distorted classic metric for performance: A common
approach to defining physical space requirements for redirec-
tion is to focus on estimating the area of the smallest physical
space that enables users to walk along an infinite straight vir-
tual path without ever reaching the boundaries. However, this
approach relies on a special case scenario (long straight path)
that may not accurately represent general redirected walking
behavior. For the same type of strategies it produced a wide
range of estimates for the optimal size of physical space from
30m30m [Razzaque et al., 2001], to 35m35m [Hodgson and
Bachmann, 2013], to 40m40m [Steinicke et al., 2010], to as
much as 60m60m [Field et al., 2004]. It also does not help
with understanding the efficacy of redirected walking in phys-
ical spaces that are smaller than the optimal size or have a
non-square shape. This method of assessment will be critiqued
and proper alternatives will be offered to correct this flawed
approach.
• Demonstrate the inseparability of physical space dimensions
in general assessments: One of the most obvious external pa-
6.1 motivation and goals 96
rameters affecting the efficacy of redirection is the layout of the
physical space. This not only directly influences end users, but
also is arguably the primary practical issue in a redirected walk-
ing setup. Though when it comes to studying the performance
of redirection, each study has been undertaken in their own
pick of settings. Simulated studies considered square-shaped
physical spaces of 5m5m [Su, 2007], 20m20m Zmuda2013,
35m35m [Hodgson and Bachmann, 2013] as well as a circular
physical space of diameter 60m [Field et al., 2004]. In addi-
tion, user studies were conducted in square-shaped spaces of
4m4m [Nitzsche et al., 2004], 4.3m4.3m [Suma et al., 2010a],
5m5m [Williams et al., 2007], 6.5m6.5m [Peck et al., 2011],
9m9m [Peck et al., 2011], 11m11m [Suma et al., 2011] and
rectangular physical spaces ranging between 9.1m7.6m [Inter-
rante et al., 2007], 10m7m [Steinicke et al., 2010], 12.6m6.2m
[Nescher et al., 2014], and 45m25m [Hodgson and Bachmann,
2013]. Despite the great variety of configurations, very few stud-
ies comparing performance across multiple physical spaces of
different size. The differences in implementation details also
make it hard to generalize the results beyond a specific physical
space used in a given study. I aim to present a comprehensive
study that represents how redirection behaves with respect to
the crucial factor of physical space size.
• Advocate the combining of all gain types: None of the redirec-
tion strategies presented to date make use of all possible gains
at our disposal. In this study I aim to investigate the effects of
combining rotation, curvature, and translation gains, and posit
that including all gain types can bolster the performance of clas-
sic methods. To this end I introduce a simple strategy based on
translation gains alone to then combine with S2O and S2C and
gauge their improvement.
• Disentangle the size/strategy/performance interaction: One might
intuitively expect redirection to perform better as the physical
space becomes larger. It is important, however, to put this per-
formance improvement into context. In larger physical spaces
users can travel longer distances even when no redirected walk-
ing techniques are applied. This subtle point has been often
ignored in earlier experiments investigating the efficacy of redi-
rection strategies. By observing performance trends across var-
ious physical space types and comparing redirection strategies
to our baseline, I can better tease out the interaction, to provide
an unbiased view of a strategy’s performance.
6.2 experiment 1: the interaction of size, strategy and virtual path 97
6.2 experiment 1: the interaction of size, strategy and
virtual path
This experiment pits all general redirection strategies against each
other across various physical spaces, with varying virtual paths to
see what role each factor plays in performance, and how the strategies
compare under various circumstances.
6.2.1 Experimental Setup
6.2.1.1 Redirection Strategies
A total of six strategies are studied in this experiment, including a
baseline condition.
• Steer-To-Center (S2C) The basic heuristic used by S2C is to in-
ject small visual rotations to steer the user towards the center of
the physical space. The implementation was based on a modi-
fication to Razzaque’s original S2C implementation, introduced
in [Hodgson and Bachmann, 2013].
• Steer-To-Orbit (S2O) This strategy functions similar to S2C, but
the heuristic is to steer the user to an orbit around the center of
the physical space. S2O was also implemented as described in
[Hodgson and Bachmann, 2013].
• Center-based Translation Gain (CTG) This strategy used trans-
lation gains to slow down the user when she was moving away
from the center of the physical space (i. e. scale visual trans-
lation up relative to physical translation). If the dot product
between the direction to the center and user’s movement vector
was negative, the strategy applied a constant translation gain
factor (Figure 32).
• Combined Strategies (S2C+CTG and S2O+CTG) Since S2C
and S2O both rely exclusively on rotation and curvature gain,
and CTG only controls translation gains, it is straight forward to
combine both S2C or S2O with CTG. A subtle implementation
technicality was to isolate the effects of user’s actual movement
(caused by walking in the real world) from the user’s overall
position and orientation change influenced by injected visual
translations and rotations.
• Control condition: No Redirection The performance of these
strategies was compared to a scenario where the simulated user
travelled within the physical space without any redirection. Dur-
ing the simulation this condition was essentially treated as a
sixth strategy but then later folded into the performance mea-
sures (for relative efficacy).
6.2 experiment 1: the interaction of size, strategy and virtual path 98
(a) User moving away from center (b) User moving towards center
Figure 32: Center-based translation gain upscales virtual translations
when the user is moving away from the center of the phys-
ical space (a), otherwise no translation gains are applied
(b).
As stated earlier, each redirection strategy was internally compli-
mented with the same reorientation heuristic for fair comparison.
When the simulated user reached a boundary of the physical space,
(similar to the 2-1: Turn reset [Williams et al., 2007]) rotation gains
reoriented the to face the center of the physical space while main-
taining the same orientation in the virtual environment. Note that a
reorientation was only triggered when the user was facing towards
the boundary in contact (a 180 degree range), not merely brushing
the boundary while still heading to a direction inside the physical
space.
6.2.1.2 Perceptual Thresholds
Translations were scaled down at most by a factor of 14% (based on
[Steinicke et al., 2010]) for CTG. As for S2C and S2O, the curvature
radius was set to 7.5 meters, and rotations were scaled by factors
between 0.85 and 1.3 according to [Hodgson and Bachmann, 2013].
6.2.1.3 Virtual Paths
All four virtual path types (office building, small exploration, large
exploration, and long walk) presented from the evaluation method-
ology and platform (Chapter 4), all with an equal expected length of
1000 meters.
6.2 experiment 1: the interaction of size, strategy and virtual path 99
6.2.1.4 Simulated Walker
The simplistic implementation of a simulated walker (presented in
Chapter 4) was the only user simulation used for this experiment.
6.2.1.5 Procedure
At the start of each trial simulated user was placed in the middle
of the physical space facing “north”(parallel to one of the physical
space sides). For each physical space (squares ranging from 1 to 60
meters in one dimension) and strategy (six, including No Redirection)
pair, 10 randomized virtual paths were generated in each of the first
3 virtual path categories described above. For the Long Walk path
category (randomization was not applicable therefore) only one trial
was generated for each pair of strategy (again, including No Redirec-
tion) and area size. The reorientation counts were averaged for each
condition and used to compute relative efficacy and reorientation reg-
ularity.
6.2.2 Results
Initial examination of strategy performance across virtual path types
revealed that performance for Office Building, Small Exploration, and
Large Exploration virtual path categories was quite similar. Overall,
the relative efficacy of all strategies increased with physical space
size. In contrast, the Long Walk path resulted in qualitatively dif-
ferent step-like performance function, where the efficacy remained
relatively flat until physical space size reached a critical point. For
all physical spaces above this critical value physical paths were com-
pletely enclosed into the physical space, which correspond to 100
percent redirection efficacy. For further analysis I decided to consider
Long Walk Path separately and combine the results for the first 3
randomized path types.
6.2.2.1 Long Walk Paths
Figure 33 shows experimental results for efficacy of redirected walk-
ing relative to no redirection for Long Walk paths. The four strate-
gies using rotation and curvature gains to redirect the user (S2C,
S2C+CTG, S2O, S2O+CTG) are able to achieve 100 percent efficacy
for physical spaces sized 31 meters or larger. This happens when
redirection strategies are able to fully redirect the user onto a circle
trajectory within the physical space. In addition, S2O and S2O+CTG
strategies achieve a near-perfect efficacy of about98 percent for phys-
ical spaces sized between 22 and 30 meters. In practice this means
that a reorientation is required before the user can be redirected into
a fully circular trajectory.
6.2 experiment 1: the interaction of size, strategy and virtual path 100
Figure 33: Relative efficacy of redirected walking for Long Walk path
type.
The results indicate that both S2C and S2O strategies are not very
effective in very small physical spaces. The S2O strategy requires
physical space of at least 15 meters to achieve at least 10 percent effi-
cacy relative to no redirection (and to outperform simple CTG strat-
egy). S2C requires at least6 meters to achieve10 percent efficacy and
to outperform CTG. For intermediate size physical spaces between16
and 31 meters S2O outperforms S2C in the Long Walk path scenario.
The CTG strategy has a virtually constant efficacy of about 12 per-
cent over the full range of physical space sizes. When combined with
S2C and S2O strategies CTG improves efficacy relatively to original
versions by approximately the same amount up to physical space size
of 31 meters, where all four strategies reach 100 percent efficacy. For
S2O and S2O+CTG strategies the convergence in performance hap-
pens at 22 meters.
6.2.2.2 Randomized Path Types
To simplify the comparison between strategies I grouped physical
space sizes into three categories: up-to 20 meters, 20 to 40 meters,
40 to 60 meters (see Figure 35). I then performed a 2 way ANOVA
with grouped area size and strategy as explanatory factors and rela-
tive efficacy as response variable. The analysis revealed a significant
interaction between effects of area size and strategy type on relative
efficacy (F(8, 8985)= 209.326, p< 0.001).
Planned post-hoc comparisons revealed that combination of trans-
lation gains (CTG) with other strategies resulted in significantly higher
6.2 experiment 1: the interaction of size, strategy and virtual path 101
Figure 34: Relative efficacy of redirected walking strategies for each
tested physical space size. Error bars represent standard
error.
Figure 35: Relative efficacy of redirected walking strategies for three
aggregate groups of physical space sizes.
6.2 experiment 1: the interaction of size, strategy and virtual path 102
efficacy for all three groups of physical space sizes (all p values below
0.001). In addition, for physical spaces up-to40 meters S2C strategies
was more effective than S2O (p values less then0.001). The same was
true for the modified versions S2C+CTG and S2O+CTG. However, for
physical space sizes between 40 and 60 meters I found no significant
differences between S2C and S2O (p= 0.587) and between S2C+CTG
and S2O+CTG (p= 0.618).
6.2.3 Discussion
One very intuitive conclusion from these results is that redirected
walking strategies considered here have a minimal viable physical
space requirement. For a Long Walk scenario S2C required physical
space of at least 6m 6m to achieve10 percent relative efficacy, which
I consider minimally viable. Randomized path scenarios produced
similar results: for 5m 5m physical space relative efficacy of S2C was
8.6% (95% CI [6.5%, 10.6%]); for 6m 6m relative efficacy was 13.7%
(95% CI [11.3%, 16%]). For S2O strategy minimally viable physical
space needs to be larger. Naturally, the application of translation
gains helps to somewhat relax this requirement by effectively making
the physical space “bigger.”
The Long Walk path data suggests that a31m x31m physical space
would be sufficient to achieve infinite straight-line walking in virtual
reality for any of the strategies tested. This result is in line with earlier
estimates of 30m by Razzaque et al. [Razzaque et al., 2001] and 35m
by Hodgson and Bachmann [Hodgson and Bachmann, 2013].
However, the near perfect performance achieved by S2O in a physi-
cal space as small as22m22m indicates that these results are highly
sensible to the initial position and orientation of the user. By strate-
gically placing and orienting the user to match the desired trajectory
from the beginning we could have achieved “optimal” performance in
this smaller physical space. Conversely, an unfortunate initial config-
uration (for example, near the physical space boundary) is bound to
require at least one reorientation regardless of available space. Based
on these conclusions, I would argue that the traditional approach
of finding an “optimally sized” physical space, which enables an in-
finitely long straight-line virtual trajectory is not necessarily a good
way to define real-world space requirements for redirected walking.
The randomized paths results suggest that redirected walking effi-
cacy gradually improves as physical space area becomes larger (Fig-
ure 34). Since the rate of performance improvement slows down for
for larger physical areas, it seems that choice of physical area size
should be based cost-benefit analysis of potential performance gains
vs. expenses for enlarging the physical space further.
When comparing S2C and S2O to each other I conclude that the
choice of strategy does not seem to matter for very large physical
6.2 experiment 1: the interaction of size, strategy and virtual path 103
Figure 36: S2C+CTG average reorientation regularity for randomized
paths.
spaces (40m 40m and larger). For intermediate and small physical
spaces S2C seems to be more preferable. It is particularly true for
physical spaces smaller than approximately 15m 15m, where rela-
tive efficacy of S2O strategy is very small.
In practice most physical spaces are unlikely to exceed 10m 10m.
It is clear that under such circumstances efficacy of S2C and S2O
strategies remains limited. As a consequence the users are bound
to experience relatively large number of reorientations. Therefore, it
is critical to design reorientation mechanisms to seamlessly integrate
into overall virtual reality experience. The data also demonstrates
that for such relatively small physical spaces combining S2C and S2O
strategies with translation gains provides a significant boost in effi-
cacy. However, further research is required to fully understand the
effects of simultaneous application of curvature and translation gains
on the moving user. The primary concern here is that in combination
these two types of gains may become more noticeable.
Lastly, I’d like to provide a best possible verdict for practical con-
siderations with regard to selecting a suitable physical space size.
For this, I examine the average reorientation regularity of the best
performing redirection strategy (S2C+CTG). As shown in Figure 36,
reorientation regularity increases superlinearly with as the physical
space becomes larger. The best method I propose for determining a
suitable physical space would be to perform a cost benefit analysis
based on this metric, or setting a minimum requirement for it. For
instance if encountering a reorientation on average every 10 meters
is reasonable, an 8 8 meter physical space would suit your needs.
If that isn’t sufficient, a 12 12 meter space would increase the dis-
tance between events to20 meters, or with 20 20 we can go up to50
meters on average without getting interrupted, and with this analysis
6.3 experiment 2: the interaction of shape and strategy 104
Figure 37: Illustration of physical space shape changing with fixed
area size (ratios 1, 1.5 and 2).
one can determine the physical space is suitable for their performance
needs.
It should be noted that in this experiment a user’s reaction time was
not simulated, and the simulated user would instantly stop when a re-
set was initiated. Therefore, in practice a slightly larger space would
be needed to incorporate the reset buffer. For instance to encounter
resets every 20 meters, a 14 14 meter space would be needed in-
stead of a 12 12 meter space, allowing a 1 meter buffer past each
reset trigger.
6.3 experiment 2: the interaction of shape and strat-
egy
Physical spaces are not always square-shaped. Room layout and hard-
to-move physical obstacles may create situations where the use of a
rectangular shape may be preferable to maximize the use of available
physical space. It is, however, unclear how the shape of the physical
space may impact the performance of redirected walking strategies.
For example, when comparing8m9m vs. 6m12m physical spaces,
it is not apparent which of the two would perform best. Experiment
2 was designed to investigate the impact of physical space shape on
the efficacy of general redirection strategies.
6.3.1 Experimental setup
I compared performance of the five redirected walking strategies
(CTG, S2C, S2O, S2C+CTG, S2O+CTG) introduced in experiment 1
in square and rectangular physical spaces. The shape of the physi-
cal space was determined by the ratio of its longer side length to the
shorter side length. The shape ratios tested were 1.0, 1.5, and 2.0. To
ensure fair comparison total area was constant at 400 square meters.
The strategies were tested using three types of randomized virtual
paths: Office Building, Small Exploration and Large Exploration.
6.3 experiment 2: the interaction of shape and strategy 105
6.3.1.1 Procedure
Overall the procedure was similar to that used in experiment1. At the
start of each trial simulated user was placed in the center of the phys-
ical space. To control for possible effects of initial user orientation,
the experiment contained equal number of trials where user started
going ”North” (along the short side of the rectangle), ”East”(along
the long side of the rectangle) and ”North-East” (towards the corner).
For each path type and initial heading direction combination there
were 10 trials (90 for each strategy at each of the physical spaces for
a total of 1350 trials).
Similar to experiment 1 the primary measure was relative efficacy
of redirected walking strategies compared to no-redirection condition.
For each physical space, path type, and initial heading combination
I estimated the mean number of reorientations without redirection
(based on 10 trials) and used it to compute relative efficacy for each
of the five redirected walking strategies.
6.3.2 Results
First, I checked if initial heading of the user affected performance
of redirected walking strategies. I fitted a main effects linear model
with relative efficacy as dependent variable and strategy, shape ratio,
and initial heading as explanatory factors. The test for type III main
effects suggests that after adjusting for effects of strategy type and
sides ratio initial heading does not play significant role in explaining
variation of relative efficacy (F(2, 1341) = 0.848, p = 0.428). As a
result I did not include initial heading in further analysis.
Next I analyzed the effects of strategy and sides ratio on relative
efficacy using a 2-way ANOVA model. I found a significant two-
way interaction between strategy type and sides ratio (F(8, 1335) =
3.284, p = 0.001). This suggests that the effects of the physical space
shape on performance is different for different strategies as illustrated
by Figure 38.
As might be expected, when comparing efficacy between strategies
we found the same pattern as in experiment1 for20m20m physical
space. Therefore, I focused on comparing performance for different
area shapes within each strategy. The pairwise comparisons were
preformed using Bonferroni adjustments.
The post-hoc analysis revealed that for S2O strategy relative effi-
cacy significantly decreased for sides ratio of1.5 compared to1.0 (p=
0.019) and further decreased for sides ratio of 2.0 vs. 1.5 (p< 0.001).
Similarly, relative efficacy of S2O+CTG strategy decreased for 1.5 vs
1.0 sides ratio (p = 0.003) and for 2.0 vs. 1.5 sided ratio (p < 0.001).
In contrast, I found no evidence that S2C and S2C+CTG strategies ex-
hibit significant decrease in efficacy when switching from square to
moderately elongated rectangular physical space with sides ratio of
6.3 experiment 2: the interaction of shape and strategy 106
Figure 38: Effects of physical space shape (sides ratio) on relative effi-
cacy of redirected walking strategies. Error bars represent
standard errors.
1.5 (p = 0.788 and p = 0.757 respectively). However, relative efficacy
of these two strategies decreased for shape ratio of2.0 as compared to
1.5 (p= 0.001 and p= 0.004 respectively). I did not find a significant
change in relative efficacy of CTG strategy (p= 1.0 for shape ratio1.0
vs. 1.5; p = 0.199 for shape ratio 1.5 vs 2.0; and p = 0.887 for shape
ratio 1.0 vs. 2.0).
6.3.3 Discussion
The results of this experiment demonstrate that the sensitivity to
physical space shape differs between strategies. Both S2O and S2O+CTG
strategies perform best in square physical spaces and have a perfor-
mance penalty in rectangular spaces. By contrast, CTG strategy does
not appear to be sensitive to physical area shape. S2C was somewhat
more robust compared to S2O. Both S2C and S2C+CTG strategies
did not experienced significant performance penalty in moderately
elongated physical spaces (shape ratio 1.5), but did suffer in more
elongated rectangles (shape ratio 2.0). Taken together these observa-
tions suggest that square-shaped physical space was the best choice
across all strategies. These results also suggest that S2C is a more
robust strategy compared to S2O. Given the robustness of S2C-based
strategies in moderately elongated physical spaces we believe the first
priority in planning the layout of the physical space should be max-
imization of the total area. However, all other things being equal,
6.4 summary 107
more elongated physical spaces will likely result in higher efficacy
penalty relative to more square spaces.
6.4 summary
The results of our study outline a new way of evaluating the utility
of the physical space for redirected walking setups. There is, unfortu-
nately, no single “optimal” size of physical space that can guarantee
complete absence of user contact with the boundary, at least for gen-
eral strategies such as S2C and S2O. Furthermore, in practice the di-
mensions of most physical spaces are much smaller than previously
estimated “optimal” size of 30m 30m to 35m 35m and are unlikely
to exceed 10m 10m, where reorientation events are common. It is,
therefore, prudent to concentrate on defining and achieving an ac-
ceptable level of reorientations and developing ways for integrating
the reorientation mechanisms as an integral part of the experience.
In relatively small physical spaces the efficacy of using traditional
redirection strategies strategies that rely only on rotation and curva-
ture gains is very modest. For physical spaces smaller than 6m 6m
efficacy of original reactive strategies is unlikely to exceed 10%. The
data demonstrates, however, that a significant performance boost can
be achieved by combining these techniques with translation gains.
For example, in a 10m 10m physical space S2C reduces the num-
ber of reorientations vs. no redirection condition by 27% (95% CI
[22%,33%]); when combined with our naive translation gains imple-
mentation into S2C+CTG strategy it achieves the reduction by 46%
(95% CI [41%, 51%]).
The shape of the physical space also affects performance with square
physical spaces generally being most suitable for redirection. The
data suggests that moderately elongated rectangular shapes can also
be used without significant performance penalty.
I demonstrated how the evaluation methodology and platform of-
fers a reliable method for studying redirection strategies. This case
study demonstrate how by systematically varying the parameters of
interest while controlling for all relevant nuisance parameters we can
draw complete and fair performance comparisons. The platform can
be easily adapted to study other properties of redirection strategies
and yield results that are generalizable to real user conditions.
After all the assessments performed throughout both experiments,
the best candidate for the general redirection strategy is the combined
strategy of S2C+CTG with the classic turn-to-center reorientation.
7
D Y N A M I C P L A N N I N G R E D I R E C T I O N S T R AT E G I E S
In preparing for battle I have
always found that plans are
useless, but planning is
indispensable.
Dwight D. Eisenhower
The manual overhead of existing dynamic planning strategies (name
FORCE [Zmuda et al., 2013b] and MPCRed [Nescher et al., 2014])
deters them from being readily used and integrated with adaptive
redirection. The goal of this chapter is to address this matter and
propose a solution that would enable deploying these strategies auto-
matically. Furthermore, the proposed solution will also be used for
extracting the input required for the adaptive meta-strategy that will
be expanded on in Chapter 9.
7.1 motivation
Planning redirection strategies rely on a prediction of the user’s poten-
tial near term navigation options based on the virtual environment
layout. In current solutions, enabling path prediction requires man-
ually annotating the virtual environment with a bidirectional graph
using shaped segments or a predefined set of path primitives (straight
lines and arcs conforming to predefined specification). The process
of manual annotation is a non-standardized procedure that is both
tedious and inflexible, and requires significant preparation before an
algorithm can be deployed in a new virtual environment. To allevi-
ate these issues I propose an algorithm for automatically predicting
the user’s possible short term trajectories, which relies on navigation
meshes, a method commonly used for path planning by computer-
controlled characters in gaming applications. This algorithm can be
automatically deployed in an arbitrary virtual environment without
the need for manual layout annotation and can dynamically adjust
path predictions relative to actual user position at run-time. Instead
of imposing a fixed layout graph to the environment, the method
dynamically generates a local short-term path prediction graph with
fixed search horizon originating at user’s exact position. This path
108
7.2 background on navigation meshes 109
prediction graph can be directly passed to existing redirection strate-
gies. The proposed pipeline is efficient, standardized, and easily de-
ployable.
In this chapter I first begin by providing a brief background on nav-
igation meshes. This is followed by the design and implementation of
my proposed automatic path prediction algorithm. I then discuss the
integration of this method with planning redirection strategies such
as FORCE [Zmuda et al., 2013b] and MPCRed [Nescher et al., 2014].
7.2 background on navigation meshes
Artificial intelligence algorithms for autonomous agents in computer
games often face a similar problem of describing possible paths through
navigable areas in 3D virtual environments. This problem has been
long studied and a variety of methods have been designed to rep-
resent a navigable environment such as navigation meshes [Tozour,
2003].
Navigation meshes [Snook, 2000] represent navigable surface of
the environment as a polygonal mesh. Agents can freely navigate
across polygons with shared edges. In addition, special links can be
used to represent connectivity between polygons that do not share
an edge. For example, such links can represent adjacency when an
agent can jump from one platform to another or step vertically from
a lower lying surface to a higher ground (or vice-versa). An attractive
property of navigation meshes is their ability to represent the free
space available adjacent to a path in the environment, which enables
pathfinders to perform local obstacle avoidance.
Navigation meshes can be generated automatically. A well-known
algorithm for automatic navigation mesh generation was introduced
by Tozour [Tozour, 2002]. It first determines walkable polygons in a
3D environment by comparing their normals with the up vector, and
then iteratively merges together as many polygons as possible. Since
then, various implementations have been proposed by both academic
researchers and game engine developers extending path-finding ca-
pabilities and optimizing the performance. Navigation meshes have
been widely adopted as the standard solution to navigation in gam-
ing engines and are readily available in commercial game authoring
platforms such as Unity3D and Unreal.
I will now explore how navigation meshes can be used to generate
short-term dynamic path predictions suitable for use with planning
redirection strategies. These representations can be constructed at
run-time and can take into account both actual user position and
dynamic changes in the environment.
7.2 background on navigation meshes 110
(a) navigation graph
(b) prediction graph
Figure 39: Illustration of automated prediction graph generation start-
ing from navigation meshes and the navigation graph (a)
and using to extract short-term prediction graphs (b). In (a)
a sample virtual environment is overlayed with navigation
mesh polygons shown in green and the navigation graph
shown in red. Note that edges of the navigation graph
represent connectivity between polygons rather than the
prediction of user’s possible path. (b) shows sample short-
term path prediction graphs generated from various start-
ing points. The starting point is shown as a green dot.
7.3 path prediction algorithm definition 111
7.3 path prediction algorithm definition
The goal is to design an algorithm to automatically generate layout an-
notation graphs to be used with existing planning redirection strate-
gies. In practice such strategies operate with limited prediction hori-
zon and thus typically prune the nodes of path prediction graph be-
yond certain fixed distance d. Therefore, a partial layout annotation
representing short-term path prediction should be sufficient.
Algorithm 1 outlines the structure of the proposed procedure. The
algorithm takes as input the current user position Pos, navigation
graph of the environment NavGraph, and maximum path length d
(corresponds to fixed search horizon). Here navigation graph (see Fig-
ure 39 (left)) is a connectivity graph derived from navigation mesh.
Each navigation mesh polygon is represented as a node. Edges rep-
resent connectivity between polygons in the navigation mesh. Addi-
tionally, each node is assigned a location coinciding with the centroid
of its polygon in the virtual environment.
Algorithm 1 Generate path prediction graph
function PathPredictionGraph(Pos, NavGraph, d):
Find polygon node S in NavGraph containing Pos
S.position Pos
B, T, prevPG[] DepthLimitedDijkstra(NavGraph, S)
Define V B[ T[ S
for all vertices u and v in V do
iffu,vg2 NavGraph.edges then
addfu,vg to E
for all vertices v in V do
V V[ path(v, prevPG[v]).vertices
E E[ path(v, prevPG[v]).edges
return V , E
First, the algorithm finds node S in NavGraph corresponding to
the navigation mesh polygon currently occupied by the user. The
assigned location of this node is shifted to user position Pos. The
next step is to query navigation graph for all possible paths (in any
direction) starting from S and not exceeding length d. The process
yields a set of branching nodes B (where potential paths can split), a
set of terminal nodes T (where potential paths terminate), and the con-
nectivity function prevPG[] between the nodes in the above two sets.
This is accomplished using a modified version of Dijkstra’s algorithm
dijkstra1959note which terminates when a certain distance from the
source has been explored (see Algorithm 2).
Finally, the path prediction graph is constructed. I define the set
of vertices V as the union of starting node S, branching nodes B,
and terminal nodes T. Using connectivity information encoded in
prevPG[] we add appropriate edges to set E. To better understand
7.3 path prediction algorithm definition 112
Figure 40: Sample output of modified Dijkstra algorithm. Navigation
graph is explored up to a fixed depth. Branching nodes are
marked in red, and terminal nodes are marked in green.
Each marked node has a pointer to its previous branch
(or source) defined by prevPG[]. For illustration simplicity
only a subset of pointers is shown.
this last step it is helpful to consider the outputs generated at the
previous step in greater detail.
The Dijkstra algorithm (Algorithm 2) takes an input Graph and a
starting node S and constructs a nearest-first path search tree describ-
ing all possible paths between the nodes of the Graph. I modified
the original algorithm in two important ways. First, the depth of the
tree is limited by the maximum length of the path d. Second, the
algorithm constructs a set of branching nodes B and terminal nodes
T and keeps the track of the connectivity between these nodes within
the search tree using function prevPG[]. For each vertex u that is vis-
ited, if deg(u) > 2, we add this vertex to a set of branching nodes
B. The algorithm also maintains a set of terminal nodes T. Also at
each iteration step, in addition to updating the Dijkstra’s prev func-
tion, we define function prevPG[] that points to previous branching
node (or source S). For a vertex u being visited, prevPG[u] is set to
prevPG[prev[u]] unless prev[u] is in B, in which case it will be set to
prev[u]. The algorithm terminates when all nodes within distance d
from the source are visited (see Figure 40).
The node sets B and T, along with node S, form the initial set of
vertices V of the prediction graph. Since Dijkstra’s algorithm removes
cycles from the graph by returning a tree, we reintroduce the lost con-
nections by connecting vertices in V that are neighbors in NavGraph.
We then perform navigation mesh funneling which yields the short-
est path from a series of consecutive polygons. This is required to re-
move artifacts manifesting from the artificially inserted edges. Then
the shortest navigable path between each vertex in v and it’s predeces-
7.3 path prediction algorithm definition 113
Algorithm 2 Modified Dijkstra algorithm
function DepthLimitedDijkstra(Graph, source, d):
Define vertex sets Q, B, and T
for all vertex v in Graph do
dist[v] INFINITY
prev[v] NULL
add v to Q
dist[source] 0
while Q is not empty do
u vertex in Q with min dist[u]
remove u from Q
for all neighbor v of u do
alt dist[u] + length(u, v)
if alt< dist[v] then
dist[v] alt
prev[u] u
if deg(u)> 2 then
add u to B
if T contains prev[u] then
remove prev[u] from T
add u to T
if B contains prevPG[u] then
prevPG[u] prev[u]
else
prevPG[u] prevPG[prev[u]]
if path(source, u) is longer than d then
breakfpath() return shortest navigable pathg
return B, T, prevPG[]
7.4 implementation and performance assessment 114
Figure 41: Automatically generated prediction graph for six sample
environments.
sor (prevPG[v]) are queried. These paths are added to the prediction
graph to conclude the graph generation.
7.4 implementation and performance assessment
I implemented the proposed algorithm on the Unity3D platform. Unity
provides native support for automatic generation of navigation meshes
and path queries (e.g. finding the shortest navigable path between
two points in the environments). However, I found it more conve-
nient to use an add-on package from A* Pathfinding Project [Granberg,
2015] available in the Unity asset store. The A* Pathfinding API ex-
poses the navigation graph data structure, making implementation of
the algorithm much more straightforward.
7.4.1 Comparison to Manual Annotations
To compare our method with manual layout annotations, I relaxed
the search horizon constraint and generated a path prediction graph
covering the entire virtual environment. Figure 41 shows the path
prediction graphs generated for six test environments. In my per-
sonal judgement these results represent a reasonable replacement for
annotations that could be constructed manually. There are two types
7.4 implementation and performance assessment 115
Figure 42: Dynamic adjustment of local graph. For different place-
ments of the user (red and green), the local graph adjusts
to provide a prediction that matches the user’s position.
of artifacts present. First, extra branching nodes are created at the in-
tersections where more than three paths meet. This is due to the fact
that in the navigation graph each node can not have more than three
neighbors. Second, placement of the intersections depends on the
underlying structure of the navigation mesh and may differ from the
intuitive placement in the manual annotation. Virtual environment
authors can control this by changing the parameters of the naviga-
tion mesh. While both of these artifacts might affect planning redirec-
tion strategies, I do not believe the resulting change in performance
compared to existing methods will be significant.
In practice, the algorithm periodically generates short-term path
prediction graph (see Figure39 (right) for some examples) relative to
current location of the user. Figure 42 demonstrates how the graph
updates the trajectory prediction based on user position. In contrast,
when a manual annotation is used, path prediction is based on ap-
proximating user position by the nearest point on the annotation
graph. Given the importance of the accurate path prediction in the
near vicinity of the user, I believe our method well likely improve the
performance compared to manual annotations.
7.4.2 Graph Generation Time
From a practical standpoint, it is useful to consider time complexity
relative to maximum path length. Figure 43 shows the average exe-
cution time for creating a local graph of varying depth. Each point
has been averaged over25 random starting points in the environment
on the bottom left of Figure41. On average, our algorithm generated
path prediction graphs with search horizon up to 20 meters in 7.5
milliseconds.
7.5 discussion 116
Figure 43: Effect of search depth on execution time. Values are aver-
aged over 25 random placements of the user position in a
test environment.
This compares to 82.5 milliseconds reported by Nescher [Nescher
et al.,2014] for the average planning phase execution of the MPCRed
algorithm. I conclude that this algorithm can provide updates to the
standard planning strategies on every computation cycle.
7.5 discussion
In this section I proposed an algorithm to automate path prediction
for planning redirection strategies. This demonstrates how tedious
manual annotation of an entire environment can be replaced with au-
tomatically generated prediction graphs local to the user’s current
position. One important advantage of this approach is that it re-
lies mainly on implementation tools readily available in many game
engines, which allows for integrating planning redirection strategies
into VR applications relatively effortlessly. Furthermore, dynamically
generated path prediction graphs open the door to supporting ad-
vanced prediction techniques such as forecasting user behavior in
non-static environments and increased prediction accuracy in less
constrained architectures.
In addition to enhancing planning redirection strategies, I suggest
investigating how navigation meshes can further improve aspects of
the general redirected walking problem. Possible avenues of research
include: identifying navigation patterns for early user intent detec-
tion (e. g. knowing if the user will turn left or right at intersection)
and also developing opportunistic dynamic changes in the environ-
ment to steer users away from physical boundaries. This work has
been recently extended and further explored with clever use of ad-
vanced graph extraction techniques by [Zank and Kunz, 2017]. How-
ever, it still remains an open problem how accurate these prediction
7.5 discussion 117
graphs are, and specifically how the accuracy influences the perfor-
mance of redirection strategies.
8
S TAT I C P L A N N I N G R E D I R E C T I O N S T R AT E G I E S
Without leaps of imagination
or dreaming, we lose the
excitement of possibilities.
Dreaming, after all is a form
of planning.
Gloria Steinem
In this chapter I will introduce the Combinatorially Optimized
Path-Planned Exploration Redirector (COPPER), the first automated
instance of the static planning category. COPPER is a novel auto-
mated approach to static redirection planning that is applicable to
any deterministic virtual path. COPPER consists of two main compo-
nents, namely planning and execution. The planning component is
an offline search for the optimal mapping of the user’s virtual path
to a trajectory within the physical space. The execution component
of COPPER is ran at runtime and aims to ensure that its plan is exe-
cuted as expected by dynamically adjusting gains to minimize devi-
ations from the planned path. This counter deviation technique was
introduced and validated in Chapter 4. After a brief recount of how
this strategy was conceived, I will expand on the contrast between
dynamic and static planning strategies. Then the implementation of
COPPER’s static planning will be explained in detail. The analysis of
COPPER’s performance will be deferred to the next chapter.
8.1 conception
Thinking back on how static redirection came about, I’m reminded
of the story of how post-it glue was invented. Much in the same
way that the search for the strongest adhesive lead to discovering
an extremely weak glue with valuable properties, the pursuit of de-
veloping a general redirection strategy, yielded a highly specialized
method that showed to have many desirable characteristics.
118
8.1 conception 119
8.1.1 Evolution
As anyone with a training in mathematics and computer science would
instinctively do, I took a “divide and conquer”-inspired approach,
trying to scope down the problem and tackle one piece at a time. I
began sketching a path in the virtual environment, and then finding
ways to collapse it into a small physical space. This meant playing
around with various gains to mold the path into a shape of my liking.
After a few sketches, I thought to myself, I can automate this entire
process, letting the computer decide what choice of gains would con-
dense the virtual path into a physical space of my choosing.
Drawing inspiration from elementary Artificial Intelligence approaches
to creating a chess player, I thought a redirection strategy as a strate-
gist, carefully calculating the consequence of each future action and
ones that followed to arrive on the optimal sequence of decisions.
Therefore, the core concept of static planning is to find the optimal
mapping, among all possible mapping of the virtual path to real
world trajectories.
Chronologically, it appears that right around the year 2013, re-
searchers began devising planned redirection strategies, leading to
the introduction of FORCE, MPCRed, and my own COPPER within
month of each other; all of which at heart, adopt the same future-
thinking philosophy.
8.1.2 A Means to a Demonstrative End
The motivating end goal for developing COPPER was to assemble
some form a demonstration of redirected walking with the3D model
of my research lab. I asked myself what if I could create user expe-
rience that first involved putting on an HMD in our physical space,
only to find yourself in a graphical representation of the same envi-
ronment. But then guiding the user throughout the entire lab area,
while still remaining inside the physical space portion of the physical
lab. It would be quite compelling to virtually leave the physical space
while physically staying inside the entire time. An extra bonus to me
would be to bring the user right back to the physical space, and align-
ing the real and virtual worlds such that the same seamless transition
would happen when taking off the HMD.
Having practical objectives help with focusing the trajectory of a re-
search vector, and also lead to tangible results that illustrate progress
and indicate promise. Interestingly enough, Sharif Razzaque also
used a fire drill demonstration [Razzaque et al., 2001] to hint at the
potential for redirected walking, and we’ll soon see in this chapter,
the strategy used in the demonstration can be seen as a crude prede-
cessor or a manual approach to static planning redirection strategies.
8.2 from dynamic to static planning 120
8.2 from dynamic to static planning
By revisiting the key results from the previous chapter, we can better
understand what the downfall of dynamic planning was, and con-
versely, how we can tweak the problem to make redirection shine.
What ultimately makes the dynamic planning fall apart is the uncer-
tainty of the user’s virtual trajectory. This matter is so crucial that
is rapidly results in a degradation that renders it inferior to generic
redirection. Reversing the phrasing of the previous statement forms a
strong clue to devising a static planning strategy, which is by minimiz-
ing uncertainty, redirection efficacy can be substantially improved.
Let us reiterate the reasons for periodic re-planning in dynamic
redirection to home in on how a more effective planning approach
for redirection could work.
(a) adjusting the plan to account for deviations caused by unex-
pected user movements,
(b) (with the planned path partially consumed,) devising a new
plan with farther reaching search horizon,
(c) factoring in navigation choices made by the user at junctions.
In my interpretation, a re-planning is a sign of failure, a failing to ac-
count for something. This something is can either be one that cannot
be fundamentally accounted for (such as knowing which virtual path
the user will take) or something that is computationally prohibitive
(such as searching far in the future instead of the short term). Static
planning essentially tackles this problem by scoping it down to avoid
the impossible-to-account-for (reason (c)), and adjusting the approach
to now account for what was not before (reasons (a) and (b)), thus alle-
viating the need for re-planning redirection. Specifically the scope for
applying static planning is virtual paths with no branching options
(c). Deviations caused by unexpected user movements are combatted
using a counter deviation technique. And lastly the search horizon
is expanded to encompass the entire virtual path (b). This is how
static planning differentiates its approach with dynamic planning. In
summary, static planning adjusts both the approach and the problem
space such that a substantially more optimal path can be planned for
once, and reliably executed.
A strongly relevant open problem for dynamic planning is the opti-
mal choice of search horizon. Intuitively, looking further in the future
can only improve the search outcome, but broadening the search hori-
zon comes at an added computation cost. Since the search performed
in dynamic planning is time-sensitive, the efficiency of the search al-
gorithm heavily restricts the depth of the search horizon. Though this
would encourage developing more time-efficient search implementa-
tions, that would allow greater search horizons, Zmuda [Zmuda et al.,
2013a] argues that the return on investment for increasing the search
horizon may not be as high as might think:
8.3 copper’s static planning 121
Ideally, the path-prediction module would provide accurate
predictions of the users actions far out into the future. How-
ever, the accuracy and importance of such long-term predictions
are questionable. First, although the immediate actions can be
predicted with reasonably good accuracy, the error quickly com-
pounds for predictions made several segments in advance. There-
fore, path segments, aside from the first few, would have limited
usefulness due to prediction inaccuracies
This argument may very much hold true for how dynamic planning
is implemented, and how it lacks mechanisms to counter user devia-
tions, however, static planning aims to preserve the value of a broader
search by ensuring the user remains on the planned track, and it fol-
lows through on the original plan. In fact in this chapter, comparing
COPPER to FORCE, we can to some degree answer how useful it is
to search further in the future (provided the plan can be executed as
expected).
Ultimately when the scope is restricted to virtual paths with no
branching, static planning can be though of a variation of dynamic
planning that can perform a more exhaustive redirection plan instantly,
and has additional advanced measures that keep the user on track
such that when a re-planning is performed, the same exact path (or
the remainder of it) is found as the optimal choice.
8.3 copper’s static planning
The static planning takes a given virtual path, expressed as a series
of waypoints, and calculates the series of gains that result in the cor-
responding optimal real trajectory. The simple approach to solving
this problem is to enumerate over all possible real trajectories that are
created by combinatorially applying every possible gain value to each
virtual path segment. This brute force strategy would then pick the
gain values that yield the best trajectory. Since the set of gain values
is continuous, there are an infinite number of possible combinations
that the brute force approach would have to compare, making this
computationally unfeasible. To solve this issue, COPPER reduces the
number of compared trajectories by pruning the search space with
minimal compromise to the solution’s optimality.
8.3.1 Simplifications and Assumptions
COPPER makes two assumptions while searching for the optimal set
of gain values. The first is with regards to how the user will locomote
while traversing the virtual path. It is assumed that the user will walk
from one waypoint to the next in a straight line, while directly facing
the destination waypoint. Additionally, when the end waypoint is
reached, the user will rotate in place to face the subsequent waypoint
8.3 copper’s static planning 122
before walking towards it. This simplification allows for easy calcu-
lation of the predicted user’s real trajectory under the influence of
redirection. Furthermore, the online execution component of COP-
PER will help ensure that the user’s locomotion behavior does not
cause major deviations from the predicted outcome.
The other simplification is made to the range of gain values and
reset angles. Rather than use a continuous range, COPPER a finite
subset of discrete values. While this may cause COPPER to find a so-
lution that is sub-optimal, we can approach optimality by increasing
the set of values sampled from each range. In this work we select 3
values for each of the different types of gains, and 5 values for the
reset angle.
8.3.2 Data Structures
While searching for the optimal trajectory, COPPER uses two data
structures to keep track of candidate plans. The first is an action,
representing a decision made by the planning strategy containing pa-
rameters used at a portion of the virtual path. There are 3 types of
actions, each corresponding to a specific movement required to tra-
verse the virtual path. A turn action is selected for the portions of
the virtual path when the user reaches a waypoint and has to rotate
in place to face the next waypoint. Therefore, the turn action would
contain the rotation gain applied during the turn. Walk actions corre-
spond to the walking segments from one waypoint to another. They
contain the fixed translation and curvature gain that is applied by the
static planning redirection strategy while the user moves along the
virtual path segment. If COPPER predicts that the user is unable to
reach the end waypoint without crossing the boundary of the physi-
cal space, it will create a reset action to determine the reset angle that
the reorientation task should use when the user needs to be reset.
In order to keep track of all the decisions its made, COPPER uses
a data structure called a search node. A search node encapsulates the
information required to process virtual path segments at each search
iteration. It includes the user’s current pose (position and orientation)
in the real world, the score of the planned real trajectory, and the
sequence of actions taken up until this iteration.
8.3.3 Performing the Search
Before performing the search, the virtual path is converted from a
list of consecutive waypoints to an ordered sequence of directions. A
direction is the type of movement a user will perform when traversing
the virtual path.
A rotate-to-face direction is the movement a user has to perform
when turning in place to face the next waypoint. This direction maps
8.3 copper’s static planning 123
directly to a turn action. Therefore, when processing a rotate-to-face
direction, COPPER will generate 3 search nodes, each containing a
turn action with a unique value from the set of rotation gains.
The other movement the user will perform is walking from one
waypoint to the next in a straight line, which will be referred to as
a move-to-next direction. This direction will always map to at least
9 walk actions, one for each of the unique translation and curvature
gain value combinations. If the user’s predicted trajectory does not
fit within the physical space, reset actions will be added as needed,
thus increasing the number of created search nodes by a factor of 5;
the five-fold increase is due to the number of possible reset angles.
COPPER models the user’s reaction to a reset prompt by assuming
the user will continue to walk for 0.75 meters before coming to a
complete stop. That reaction time is factored into the remaining path
segment before creating additional walk actions. However, if it is cal-
culated that the user will reach the destination before responding to
the reset, the action is ignored. Therefore, for a virtual path segment
that requires one reset, COPPER will create up to 9 5 9 search
nodes
When processing a direction, COPPER selects an appropriate ac-
tion and applies it to all the current search nodes. As each search
node is evaluated, new child nodes are created for all the possible
values of the action. The planning strategy calculates the user’s tra-
jectory and its score for each action value. The set of produced search
nodes is then pruned before repeating the search process on the next
direction.
8.3.4 Pruning
As each direction is processed, the number of nodes at each iteration
rapidly increases. To keep the node list manageable, search nodes
that are similar need to be discarded. In order to achieve this, we
classify nodes such that they can be split into groups with similar
traits.
As directions are processed, their search nodes are assigned to a
configuration class based on its calculated user pose in the physical
space. This essentially discretizes the set of possible user poses by
creating bins. Therefore, a configuration class can be represented as
a tuple which contains a section of the physical space along with a
continuous range of user orientations. The number of configuration
classes depends on the granularity of discretization. For this experi-
ment, our 10 10 meter physical space is converted to a grid of 1 1
meter cells, and the orientation range is divided into 15 degree inter-
vals. This yields a total of 10 10 24= 2400 configuration classes.
Additionally, if the physical space shape is symmetric, further re-
duction can be applied to the search nodes. For example, a rectan-
8.3 copper’s static planning 124
gular physical space can be divided into 4 equal quadrants. Any
arbitrary configuration class in one quadrant can be transformed to
a similar one in another quadrant by rotating it around the center
of the rectangle by a multiple of 90 degrees. Therefore, in this ex-
ample, this bijective mapping allows COPPER to reduce the number
of configuration classifications by 75% (a total of 600 classes for this
experiment).
After each search node is grouped into its respective configuration
class, only the node with the best score is kept from each category.
This puts an upper bound on the total number of search nodes at
each search iteration; there can only be as many search nodes as there
are unique configuration classifications. Although it may seem like
potential optimal solutions are discarded, the rationale behind this is
that nodes belonging to the same configuration classification offer the
same spatial advantages for redirection. We assume that if an optimal
path can be found by using one of the disposed nodes, a similar
optimal path can also be obtained using the retained representative.
Since the planning component of COPPER is run offline, execution
speed is not a concern, thus the granularity for all the discretizations
can be adjusted to find possible more optimal solutions, provided
that the system has sufficient memory. Configuration classes are a
trade-off between calculation complexity/feasibility and optimality.
8.3.5 Utility Function
The utility function assigns a score to each search node based on its
current and previous actions. This score is a metric for how desirable
the planned trajectory is. In this implementation of COPPER, the
only factors that affect the score are the number of resets encountered
along the path and the number of near-reset situations experienced.
A near-reset situation is when the user’s real world end position after
a virtual segment is in one of the configuration classes that represents
a cell on the border of the physical space. The score of a search
node is defined recursively as the sum of the parent node’s score, the
number of resets encountered for this direction, and ane 1 penalty
if the planned trajectory results in a near-reset. Since a lower score
indicates a more desirable trajectory, after all the directions have been
processed, the planning strategy will select the remaining search node
with the lowest score. Although this implementation of COPPER only
scores search nodes based primarily on resets, other factors like total
amount of redirection could be factored in as well.
8.3.6 Offline Pre-Calculations
The static planning described solves the problem of finding an op-
timal redirection strategy when both the user’s starting pose in the
8.3 copper’s static planning 125
real world and also the virtual path to be traversed are known in
advance. However, COPPER can also be extended to operate in con-
ditions where either of these elements are not known. Examples of
this include: a) Designing a walkthrough without a fixed initial initial
pose (this flexibility can allow finding a more optimal path) b) Recov-
ering from excessive user deviation by redoing COPPER’s planning c)
Using COPPER in adaptive redirection which would require instantly
switching to COPPER at runtime.
The solution to dealing with this uncertainty is to pre-calculate the
optimal strategy for all possible scenarios. By having a lookup ta-
ble we can match the specific user pose and virtual path at runtime
and thus instantly access the pertinent optimal strategy. The table
will contain one entry for a representative of each configuration class,
and at runtime the user’s actual pose will be matched to the represen-
tative of its class. As for the virtual paths, the table will have entries
for all sub-sequences in the environment’s virtual path that have no
branches and at runtime the matching sequence will be used to find
the optimal strategy.
Part V
A S S E M B L I N G A D A P TAT I O N : T H E
C O N S T R U C T I O N O F A D A P TAT I O N R U L E S
9
A D A P TAT I O N R U L E S
Adapt or perish, now as ever,
is nature’s inexorable
imperative.
H. G. Wells
This chapter serves as the culmination of the work presented in this
dissertation. With the adaptive redirection meta-strategy defined and
the redirection strategy categories examined, in this chapter I will fi-
nally construct the rules that determine how exactly the adaptation
must be performed, which will complete the adaptive meta-strategy.
Achieving this requires studying the performance of each candidate
redirection strategy across the spectrum of circumstances, which not
only provides the means for constructing adaptation rules but also
offers nuanced insights as to how performance factors influence each
strategy differently. This extends the performance comparisons pre-
sented in Chapter6 by also factoring in the characteristics of the user
prediction graphs.
The comparisons performed in this chapter will be on specific in-
stances and candidates from each category, however, beyond the spe-
cific results, the purpose is to demonstrate how the evaluation method-
ology and platform can be used to develop adaptation rules for a
given set of redirection category candidates. As better candidates
from each category are introduced, superior candidates can be ex-
amined for adaptation with the procedure illustrated in this work.
For this chapter, steer-to-center (S2C) will be representing the general
category given that it outperforms its peers based on the results in
Chapter 6. I opted to use FORCE as the representative of the dynamic
planning category because of its simplicity of implementation. It
should be noted that the authors of MPCRed have stated that FORCE
is a special case of their strategy [Nescher et al., 2014]. As for static
planning, only strategies that can be used in a general context are
relevant to an adaptive redirection meta-strategy, therefore, I chose to
use COPPER as the only strategy that fulfills this requirement.
To measure the performance of each strategy across a variety of
context factors, I used the evaluation platform and extended it to
support the conditions of the experiments. The experimental results
127
9.1 experiment: constructing adaptation rules 128
are analyzed and used to shape the final structure of the adaptive
redirection meta-strategy. I conclude by demonstrating how adaptive
redirection would perform across various physical spaces with upper
and lower bounds for its expected performance, essentially provid-
ing practical guidelines for physical space requirements of redirected
walking.
9.1 experiment: constructing adaptation rules
The goal of this experiment was to determine the rules for select-
ing the best redirection strategy in adaptive redirection. This was
achieved by using machine learning to create a classifier that maps
a prediction graphs to corresponding most effective strategies. The
training data for the classifier was generated from a simulated user.
9.1.1 User Simulation
To measure the performance for each condition, I performed sim-
ulated experiments using a modified version of the simulated user
functionality included in the evaluation platform. The agent was pro-
grammed to traverse the virtual path by walking toward the next
waypoint with a constant linear velocity of 1 m/s while maintaining
its heading toward the waypoint. Upon reaching a waypoint, the sim-
ulated user would stop and turn in place with an angular velocity of
90 deg/s to face the next waypoint. When the user’s distance from a
boundary dropped below1 meter, a reset would be triggered. At this
point, the user would stop and rotate in place at 90 deg/s until the
reset task was complete.
For this experiment, I added the functionality to simulate a user’s
delayed response to a reset prompt. This was modelled as a 0.5 sec-
ond delay in reacting to a reset, and a constant linear deceleration that
caused the user to come to a full stop in 0.5 seconds. If a waypoint
contained a branch, the simulated user would randomly select one of
the possible path options. For this study, no noise was introduced to
the simulated user’s translation and rotation, thus guaranteeing that
the simulated user would walk exactly along the virtual path.
The simulation platform emulated a framerate of 60Hz and was
implemented in the Unity game engine [Unity Technologies, 2016].
9.1.2 Procedure
The redirection strategies investigated were steer-to-center (S2C), FORCE,
and COPPER, all of which were paired with the face-center reset tech-
nique. I also measured the performance for a baseline “No Redirec-
tion” strategy condition where no redirection gains were applied and
9.2 results 129
only the face-center reset would prevent exceeding the boundary lim-
its.
To generate prediction graphs, all three defining characteristics were
varied. The segment lengths (in meters) were uniformly sampled
from one of the following ranges: (0.01, 2.5), (0.01, 5), (0.01, 7.5), and
(0.01, 10). The absolute turn angle distributions were uniformly sam-
ple from ranges: (0°, 45°), (0°, 90°), (0°, 135°) and (0°, 180°). The
branching likelihood ranged from 0 to 1 in increments of 0.1.
The number of the waypoints the simulated user cleared was ad-
justed based on the segment length distribution such that the ex-
pected virtual path would be 500 meters. For instance, a segment
length distribution of [0.01, 2.5] would have the user traverse a path
of 400 waypoints.
For each trial of this experiment, the simulation began by placing
the user at the center of a 10m 10m physical space facing the positive
Z direction. The user’s prediction path would dynamically expand af-
ter each waypoint was cleared to provide a 3-waypoint-deep horizon
of navigation options. The choice of3 levels deep was selected based
on the FORCE algorithm functionality. During each trial, the number
of resets were tallied and the overall virtual distance travelled was
logged. Each condition was repeated a total of 20 times.
9.2 results
The state of the prediction graph dictates the applicability of each
strategy and in turn determines what options are available for adap-
tation. Based on this we identify three cases: a) the prediction graph
is not available, which by default S2C would be the only option, b)
the prediction graph is available but contains branches, in which case
we must select between S2C and FORCE, c) the prediction graph has
no branches where all 3 options of S2C, FORCE, and COPPER are
viable. Case a needs no adaptation rules, so I examine case b and c in
this section.
9.2.1 Branching Prediction Graph
I first examine the performance of the redirection strategies across all
prediction graph properties (Figure 44). To gauge performance we
use reset-per-distance which is calculated by dividing the reset count
by the virtual distance travelled. This is essentially the reset count
normalized by virtual path length since not all randomly generated
paths have the exact same length. Therefore, the lower the reset-per-
distance is, the higher performance is considered.
I investigated the effect of each prediction graph property on redi-
rection strategy. To simplify the analysis I modeled effects on each
redirection strategy separately. The goal was to broadly explore how
9.2 results 130
Figure 44: Performance comparison of contending redirection strate-
gies across prediction graph properties for the branching
prediction graph scenario. Error bars show standard error.
reset counts per unit distance were affected by path characteristics,
and to understand relative importance of each factor rather then de-
rive a precise functional relationship. Therefore, I modelled the re-
lationship between reset count and explanatory variables as main ef-
fects, ignoring any possible interactions.
First I constructed a linear model for the no redirection strategy
with reset per distance as a continuous response variable and max
segment length, max turn angle and branching probability as explana-
tory main factors. Max segment length (F(3, 3341) = 1183.84, p <
0.001) and max turn angle (F(3, 3341) = 1917.34, p< 0.001) were sig-
nificant predictors of reset per distance, while branching probability
was not a significant predictor (F(10, 3341) = 1.1, p = 0.361). The
general trend was for the number of resets per unit distance to de-
crease with max segment length; for example for 10m length max
segment the reset per distance decreased by 28.9% vs. 2.5m max seg-
ment length case (p < 0.0001). The reset per distance also increased
with max turn angle. For example when comparing the 45° and 180°
max turn angle situations, the number of increased by as much as
57.5% in the latter case (p< 0.0001).
For the S2C strategy a linear model with reset per distance as the re-
sponse variable and max segment length, max turn angle and branch-
ing probability as main effects explanatory variable revealed max
segment length F(3, 3344) = 11.76, p < 0.001 and max turn angle
(F(3, 3344) = 798.32, p< 0.001) as significant variables while branch-
ing probability (F(10, 3344) = 1.29, p = 0.226) was not a significant
predictor. The general trend was for the number of resets per unit
distance to increase with max segment length; for example for 10m
length max segment the reset per distance increased by2.5% vs. 2.5m
max segment length case (p < 0.0001). For the max turn angle, re-
9.2 results 131
set per distance decreased by 4.4% from the 45° to 90° (p < 0.0001)
but from 90° to 180° it consistently increased up to a factor of 24.4%
(p< 0.0001).
Finally, for the FORCE strategy a linear model with reset per dis-
tance as the response variable and max segment length, max turn
angle and branching probability as main effects explanatory variable
revealed that max segment length F(3, 3344) = 279.33, p < 0.001,
max turn angle F(3, 3344) = 46.22, pv, and branching probability
F(10, 3344) = 213.66, p< 0.001) were all significant predictors. Reset
per distance measure increased by 19.5% with max segment length
changing from 2.5 to 10 (p< 0.0001). The reset per distance decrease
with max turn angle. For example when comparing the 45° and 180°
max turn angle situations, the number of decreased by as much as
6.3% in the latter case (p < 0.0001). For branching factor, reset per
distance increased by 47.6% as branching probability increased from
0 to 1 (p< 0.0001).
In order to determine adaptation rules for the branching prediction
graph case, I labeled each condition by the strategy that performed
best. This was achieved by we measuring the mean of reset-per-
distance for each strategy for each triple of branching factor, segment
length and turn angle, and labeling the triple with the strategy with
the lowest mean reset-per-distance. I then used a PARTS rule-based
classifier with a 10-fold cross-validation to train and assess the accu-
racy of our model. PARTS outperformed other rule-based classifiers
with an accuracy of 98.9%. However, using a Random Tree classifier
can also fully fit the model and achieve a 100% accuracy using a tree
with 47 nodes. The rules derived by PARTS can be seen in Figure45,
identifying in for each region of the prediction graph space what strat-
egy should be used. These rules are well in line with the intersection
points between performance graphs in Figure44.
9.2.2 Non-Branching Prediction Graph
I now focus on cases where the prediction graph has no branches
where all strategies are applicable. The performance of each strategy
for this case can be seen in Figure46.
Similar to the previous analysis, I first investigated the effect of
each prediction graph property on COPPER. To achieve this I con-
structed a linear model with reset per distance as a continuous re-
sponse variable and max segment length and max turn angle as ex-
planatory main factors. Max segment length (F(3, 304) = 299.93, p<
0.001) and max turn angle (F(3, 304) = 1450.77, p < 0.001) were
both significant predictors of reset per distance. The general trend
was for the number of resets per unit distance to increase with max
segment length; for example for 10m length max segment the reset
per distance increased by 155.0% vs. 2.5m max segment length case
9.2 results 132
Figure 45: Derived adaptation rules for determining the most effec-
tive strategy in the branching prediction graph scenario.
(p< 0.0001). The reset per distance also increased with max turn an-
gle. For example when comparing the 45° and 180° max turn angle
situations, the number of decreased by as much as88.2% in the latter
case (p< 0.0001).
To directly compare redirection strategies while accounting for the
properties of the path, I constructed a linear model with reset per dis-
tance as an explanatory variable. The model included max turn angle,
max segment length, and redirection strategy as predictors; I consid-
ered only main effects, interaction terms were suppressed. The model
revealed that redirection strategy was the most powerful predictor of
reset count per unit distance (F(3, 1215) = 1170.25, p < 0.001), fol-
lowed by max segment length (F(3, 1215) = 2.99, p = 0.029); max
turn angle was not a significant predictor of performance (F(3, 1215)=
2.09, p = 0.1). The post-hoc analysis using Tukey’s HSD shows that
after accounting for the effects of max turn angle and max segment
length the number of resets per unit distance for COPPER strategy
(0.026 0.001) was significantly lower compared to that for FORCE
(0.075 0.001, t(1269)= 25.42, p< 0.001), S2C (0.096 0.001, t(1269)=
36.38, p < 0.001), and control condition of no redirection (0.138
0.001, t(1269) = 58.17, p< 0.001). Therefore, the rule for this case is
simply to use COPPER when the branching likelihood is 0.
9.3 discussion 133
9.3 discussion
When inspecting how a specific prediction graph property influences
a specific strategy, it is important to develop an objective sense of how
difficult it would be to contain a virtual path created from a predic-
tion graph with such properties. The performance of our baseline of
no redirection strategy helps with understanding if a given strategy’s
improved performance can be attributed to the interaction between
it and a specific factor, or if the factor alone inherently makes a path
more containable. For instance, a circle-shaped virtual path that fits
within a physical space without any need for redirection is objectively
easier to contain in the physical space in comparison to a long straight
path. This is due to the nature of the virtual path, regardless of the
redirection strategy that is to be applied.
With regards to the max segment length property, our baseline in-
dicates that larger segment lengths result in improved performance.
However, in the presence of redirection, performance declines as the
segment length becomes larger, and the magnitude of this effect is be-
comes greater as we go from S2C, to FORCE, to COPPER. However,
this can conversely be explained as the more advanced a redirection
strategy is, the more it can make use of smaller path segments by
using redirection to contain the path. The reduced performance of
our baseline with smaller segments can also be explained by the lack
of redirection causing smaller segments to get stuck near a bound-
ary and experience frequent resets, whereas longer path segments
increase the odds of escaping a near-boundary region.
As for the max turn angle property, we see that the baseline and
S2C mostly experience a reduction in performance, while for the plan-
ning strategies FORCE and COPPER, performance improves with in-
creased turn angles (especially for COPPER). This can be explained
by the fact that increasing the turn angles allows for planning strate-
gies to have more flexibility with the range of directions they can steer
the user to in order to effectively keep the path contained within the
physical space. As for our baseline, the reduced performance can sim-
ilarly be explained by the fact that larger turn angles can cause the
user to keep turning back towards the physical space boundary after
a reset, effectively undoing the reset task. And similarly, when the
turn angles are smaller, the user is more likely to escape the bound-
ary area after a reset. With regards to S2C, the greedy approach for
steering can potentially cause overshooting when the turn angles are
large, which can negatively impact the performance. However, over-
shooting is less likely at smaller angles, which can also explain the
slight performance improvement when going from a max turn an-
gle of 45° to 90°. In this range, the performance is improved since
greater turn angles help with achieving the greedy goal of steering to
9.4 expected performance of adaptive redirection 134
center. However, past 90°, the excess turn angles cause a decline in
performance.
As expected, the branching likelihood has no significant effect on
non-planning strategies. However, for FORCE, the performance de-
creases with increased branching likelihood. This is in line with our
expectation of dynamic planning strategies, where virtual path un-
certainty (i.e. user unpredictability) heavily reduces the efficacy of
our planned redirection. This hints at the need for developing better
mechanisms for dealing with uncertainty to substantially improve the
performance of dynamic planning strategies. A complementary im-
provement can also be derived from developing techniques for prun-
ing the prediction graph based on understanding the user’s intent
in order to reduce the uncertainty of the input prediction graph for
dynamic planning strategies.
In the case of a fixed virtual path, COPPER’s dominance can be
explained by how its planning differs from FORCE. FORCE searches
within a limited search horizon while COPPER continues searching
along the virtual path until it branches. This farther reach in the fu-
ture can help with developing a better plan for redirection. What
particularly makes this large-scale plan useful in practice is that it
fully commits to executing this path and ensures it with by using
counter deviation. This can be contrasted to FORCE, where the gains
are not adjusted base on the user’s locomotion behavior and thus
the redirection may not go exactly as planned. This was also stated
by Zmuda et al. [Zmuda et al., 2013b] when developing FORCE: a
greater search horizon may not be useful since the deviation incurred
at each step would make executing a larger plan impossible. Lastly,
COPPER makes use of translation gains while FORCE and S2C do
not. Based on the results in Chapter6, including translation gain with
a simple heuristic can boost performance of general redirection strate-
gies on average by 1. This value may even be greater for COPPER
because translation gain is applied using a more advanced planning
approach.
9.4 expected performance of adaptive redirection
In the previous section, I shed light on how the performance of var-
ious strategies would change based on the prediction graph, and
specifically how to construct a rule-set for using the right strategy
at the right time. However, this example was restricted to a given
physical space, and though this is exactly the approach we propose
for tailoring adaptive redirection to fit one’s specific virtual reality
configuration, it does not give a sense of performance across various
physical spaces.
As we learned in the previous chapter, similar to how the predic-
tion graph is a critical performance factor, physical space restrictions
9.4 expected performance of adaptive redirection 135
Figure 46: Performance comparison of contending redirection strate-
gies across prediction graph properties for non-branching
prediction graphs. Error bars show standard error.
is also undeniably a critical factor. In fact, a complete examination
of adaptive redirection would involve investigating the performance
of all strategies across all space requirements, first training a rule set
that determines the best choice redirection strategy, and then gauges
how well adaptive redirection would perform across all conditions.
This is, however, beyond the scope of this work, but I wish to develop
some insight into the performance we can expect from adaptive redi-
rection across various physical spaces by providing upper and lower
bounds for expected performance in a reasonable approximation of
the average virtual walking experience.
Based on our understanding of strategy performances from the pre-
vious section, we know that S2C marks our lower bound for perfor-
mance (naturally being part of the category of general strategies), and
from there, we can only do better, provided the circumstances al-
low improvement by other strategies. For cases where the prediction
graph has no branches, our best performance comes from using COP-
PER, providing the upper bound for the average scenario in this case.
The moment a branch becomes present, the only alternative we have
to our baseline of S2C is using FORCE. FORCE begins to break down
as the branching likelihood increases. Therefore, to provide a best-
case scenario for such a case, we want to keep the branching factor
to a minimum. We can imagine this to be a case where branching the
branching factors is extremely (though non-zero, otherwise COPPER
would be used). So FORCE with a branching likelihood of effectively
zero would give us an upper bound for how well we can do (if at
9.4 expected performance of adaptive redirection 136
all) compared to S2C. We use this reasoning to give upper and lower
bounds for expected performance across physical space sizes.
For determining what segment length and turn values to examine,
though using extreme cases can help with developing a theoretical
range for expected performance, we instead opt for a range that we
feel reasonably represents a somewhat typical environment’s charac-
teristics. I use a uniform distribution of (2, 8) meters for segment
length, and uniform distribution of (45°, 90°) for the absolute turn
angle values. We believe these estimates reasonably represent the
average scenario of walking in an environment.
With this setup, I can now provide upper and lower bounds for per-
formance we can expect from adaptive redirection. The most tangible
metric for communicating performance in our experience is virtual
distance between resets (calculated by dividing overall virtual distance
travelled by total reset count) which communicates how often a reset
is expected to occur relative to the progression in the real world. This
metric was proposed to provide a guidelines for redirection space
requirements when using a general redirection strategy. I adopt the
same metric to communicate a more intuitive sense of performance
expectations for adaptive redirection. Figure 47 shows the perfor-
mance for the strategies across square-shaped physical space sizes of
varying side length.
For cases where the virtual path is defined a priori, we can get the
best performance from redirection, with resets on average occurring
only for instance every 20.2 meters for a 7 7 meter physical space
and every130.2 meters for a 10 10 space. Furthermore, we see once
the physical space reaches 12 12 meters we have a less than 50%
change of having a reset within a 500 meter path. This a great refer-
ence point for designing a space dedicated to variety of virtual tours
and demonstrations. A subtle point worth noting with that is if a
reset is never triggered, we can deduce that all the walking happened
within the area of reset triggers, which means we can potentially re-
move the extra buffer and cut down on the side length by1 meter on
each side for a space of 10 10 meters.
For when the virtual path is not strictly pre-defined, in the best case
we can assume minimal branching in the environment which would
help FORCE perform the best. As our lower bound, we can refer
to S2C’s performance since it is immune to the effects of branching
factor. Using this information, we can make claims such as expecting
performance of adaptive redirection to be at worst 1 reset every 9.8
meters, and at best, every 16.8 meters in a 10 10 physical space. If
we consider a 14 14 meter space, at worst1 reset will happen every
18 meters, and at best, every 82 meters.
This information serves as practical guidelines for determining space
requirements for redirected walking. One would first consider the na-
ture of the environments that would be targeted for use in the phys-
9.4 expected performance of adaptive redirection 137
Figure 47: Expected performance of adaptive redirection across phys-
ical spaces.
9.4 expected performance of adaptive redirection 138
ical space, set preferences on what degree of performance is abso-
lutely necessary, then based on budget and other constraints one can
determine the optimal choice of physical space for redirected walking.
Furthermore, using the simulation platform, any specific conditions
or additional constraints can be incorporated, yielding a performance
analysis that is tailored to the intended use cases.
Both making arguments about performance and measuring it are
nuanced matters with redirected walking. Our prime indicator of
performance is resets, which happen with a relatively low frequency,
demanding measurement over a long period to derive accurate esti-
mates of performance with reasonable confidence intervals. On the
other hand the prediction graph, as a significant influencer of perfor-
mance, is a factor that is defined locally and can drastically change
shape and properties with relatively small movements. The artifi-
cial construction of a branching virtual path based on a local mea-
surement of prediction graph and it’s extracted characteristics was in
observance to this very fact. As the measured prediction graph go-
ing from one region of an environment to another can substantially
change properties, the performance can substantially very. In fact,
given the prediction graphs for each part of an environment, one can
associate degrees of difficulty to each region based on the performance.
With these matters considered, it is important to bear in mind that
general claims about redirection performance are not only difficult
but perhaps the incorrect approach to thinking about performance.
Ultimately, performance depends on the specific layout redirection is
applied, and the performance estimates provided are best attempts at
providing an average global value for a local measure.
An important open question for dynamic planning strategies is
finding the optimal search horizon. In theory, increasing the search
horizon can potentially lead to better redirection planning at the cost
of increasing calculation time. However, calculation time must be
brief enough for the user’s state to not change significantly during
the search, otherwise, the result would become obsolete. Using the
evaluation platform’s simulation feature, this trade-off can be evalu-
ated to potentially increase the overall performance of strategies in
this category. Based on results that COPPER’s deeper search horizon
drastically improves performance, we suspect that the optimal search
horizon can be a key factor in performance. Furthermore, including
counter deviation with dynamic planning strategies can potentially
further improve this category by ensuring the redirection plan exe-
cutes as expected, which can in turn increase the merit of performing
searches with deeper search horizons.
9.5 limitations 139
9.5 limitations
One of the main challenges in this work has been defining measur-
able attributes that describe a prediction graph, and subsequently
generating graphs that cover the spectrum they describe. To train
the adaptation rules, I only focused on segment length, turn angles
and branching factor and for each of these I assumed primitive mod-
els to simplify the analysis. A by-product of these assumptions was
that not all of the variance in performance seen in our measurements
could be explained and accounted for. This work can be substantially
improved by defining more nuanced prediction graph properties that
could capture the essence of what makes a path objectively difficult
to contain in the physical space, and potentially quantify the notion
of “redirection friendliness” for a virtual path and environment. This
can not only help with better understanding performance factors, but
also give insight into the weaknesses of each strategy, which can be
used to develop more refined strategies. Ultimately, a richer set of
adaptation rules can be extracted that account for prediction graph
properties and physical space dimensions across a broad spectrum
for optimal adaptation.
9.6 summary
In this work, I presented the adaptive redirection meta-strategy. This
paradigm posits that there is no one redirection strategy that out-
performs all in the general case, but rather circumstances in which
redirection is applied dictate the superior strategy. I proposed a for-
mal definition and design for redirection strategies, serving as the
skeleton for adaptive redirection. More broadly, this theoretical foun-
dation can aid with better understanding how previous work in the
field fits in the entire scope, and also function as a blueprint for future
advancements in the redirected walking landscape.
In order to develop an approach for selecting the appropriate strat-
egy, I proposed a variety of performance factors, identifying a spec-
trum of conditions that can influence strategies in different manners.
I then investigated the performance of each strategy throughout this
spectrum by simulating various samples of conditions and studying
the interaction of each factor with each strategy. I demonstrated how
this data could be used to develop adaptation rules, which in essence
equates to partitioning the spectrum of condition to regions in which
one strategy prevails in performance. With adaptive redirection de-
fined, I investigated different level of performance that can be ex-
pected across various physical space sizes. Using an intuitive mea-
sure, I provided upper and lower bounds for expected performance
that provide practical guidelines for determining space requirements
9.6 summary 140
and can inform the design of virtual reality experiences using redi-
rected walking.
In this work, I also examined the COPPER strategy. Although lim-
ited to predetermined paths, this approach outperforms other redi-
rected walking strategies across all tested conditions. I suggest that
the most successful approach for creating redirected walking experi-
ences with single room-scale tracking spaces (e.g. 5m 5m) would be
to focus on strategies like COPPER that provide a reasonably low re-
set frequency. COPPER’s planning strategy can also be used as a tool
for content creators to plan virtual walkthroughs of large environ-
ments with little to no resets, thereby potentially delivering a more
compelling experience than controller-based locomotion.
Despite COPPER’s relatively high redirection efficacy, (reflected in
the upper bound for adaptive redirection’s expected performance),
not all cases can benefit from using COPPER. In scenarios where
an increased sense of user freedom and agency is desired, we are
left choosing between dynamic planning and general strategies. This
emphasizes the importance of also developing and improving these
classes of strategies in future work. In summary, this chapter demon-
strated that the best strategy for redirected walking is context-dependent.
Adaptive redirection serves as a platform that brings together candi-
dates for optimizing redirection, identifies their strengths, and forms
a hybrid strategy that is superior to each individual strategy in iso-
lation. Therefore, the adaptive redirection meta-strategy provides a
foundation for making redirected walking truly work in practice and
can be extended to improve performance in the future as new redi-
rection strategies are introduced and integrated into the platform.
Part VI
F U RT H E R A D VA N C E M E N T S
10
R E S E A R C H A N D D E V E L O P M E N T G U I D E L I N E S F O R
F U T U R E W O R K
To explain all nature is too
difficult a task for any one
man or even for any one age.
‘Tis much better to do a little
with certainty & leave the rest
for others that come after you.
Isaac Newton
The main objective of this dissertation has been to develop a solid
foundation for redirected walking, articulating my vision of how a
system should be defined, designed and refined. As such, setting
clear guidelines for future endeavors both in research and develop-
ment has been at the forefront of this first articulation of a formal
theoretical foundation. I firmly believe that the theoretical founda-
tion presented in this work will aid communication and understand-
ing among research endeavors, helping research efforts come together
and fit in the larger picture of successfully applying redirection in the
future.
Broadly speaking, the next steps for improving redirection involve
targeting the elemental components within the architecture of a redi-
rected walking system and improving upon them incrementally. This
work in essence is the blueprint for future work, and an abstract skele-
ton with components that can and should be replaced with more ad-
vanced instances with new developments in the field.
To facilitate the process of expanding upon this framework, I de-
veloped the open-source Redirected Walking Toolkit
1
. This codebase is
meant to be a practical and applied foundation for redirection, com-
plementing this dissertation which aims to be the scientific and theo-
retical foundation.
The toolkit is the product of a half-decade of continuous improve-
ment through iterations of program design and engineering to meet
goals of accurate code and flexible deployment.
My hope is that this publicly available tool, along with its tutorials
and documentation, will not only serve as the standard entry point
1 http://projects.ict.usc.edu/mxr/rdwt.
142
10.1 resets 143
for newcomers, but also foster collaboration between academic re-
searchers and industry developers. Perhaps this can be another small
step towards closing the gap between academics, expert developers,
and content creators. Furthermore, the intention has been to make a
tool that is so deployment-ready that even content creators with min-
imal experience can benefit from the potential of redirected walking.
I close this dissertation by enumerating future research opportuni-
ties I have identified that can substantially improve the experience
of using redirected walking for end users, content creators and also
researchers. These research vectors are avenues for improvements
in the redirected walking system architecture that I consider of high
priority and I look forward to participating in the research commu-
nity that will address these and other topics to improve redirected
walking.
10.1 resets
As established within this work, resets are one of the main draw-
backs of using redirected walking because they disrupt the flow of
the virtual experience. Therefore, a way to improve the quality of
redirection would be to ensure that resets are triggered only in the
following conditions: 1) when they are absolutely necessary, 2) they
are used effectively and 3) are the least jarring to the user.
10.1.1 Triggering
The most common rule for triggering a reset is simply to detect the
user’s proximity to physical space boundaries. Once the distance
drops below a threshold, a reset is activated. In my experience, this
can lead to both initiating resets when it is not absolutely necessary,
and at times not firing resets soon enough. Better approaches can
involve taking into account the user’s velocity (both speed and direc-
tion of movement) to measure how much time the user has before
reaching a hard physical limit. Then a reset can be triggered based
on reaction time.
Furthermore, in my personal observations, real users tend to ex-
perience back-to-back resets, especially novice users who lose their
bearing after the reset task is complete and wobble side to side before
confidently resuming the experience. This can potentially be avoided
by adding more sophisticated rules that are a bit more lenient with
triggering resets after one was just completed, unless the user’s safety
is at risk.
10.2 general redirection strategies 144
10.1.2 Efficacy
The efficacy of existing reorientation heuristics — specifically reset
types — was not explicitly evaluated in this work. I have consis-
tently used the face-center reset throughout this work but it would
be worthwhile to see if other techniques such as Zmuda’s “face far-
thest corner” [Zmuda et al.,2013a] heuristic could potentially outper-
form face-center. This could be evaluated using the platform by, for
instance, varying reset heuristics while keeping the redirection heuris-
tic fixed. The importance of the reorientation heuristic is particularly
crucial for use in general redirection strategies.
10.1.3 Disruption
In its most basic form, a reset prompt could be presented using text
visibly displayed to the user along with a complementary audio cue
to better grab the user’s attention. However, more effective interfaces
can be used to elicit the desired behavior from the user. For instance,
Tabitha Peck [Peck et al., 2010] introduced novel ideas such as show-
ing a butterfly or hummingbird that would more naturally catch the
user’s attention and elicit head motions. As engaging as this alter-
native to plain text may be, one of its main flaws is the efficiency of
the approach. The added engagement and amusement of the user
potentially comes at the cost of reorientation sequences with longer
durations.
Grechkin [Grechkin et al., 2015] introduced the broader notion of
context-sensitive reorientations that integrate into the virtual world nar-
rative to draw users’ attention. Their main thesis was to trigger events
that were more organic and germane to the context of the virtual ex-
perience to allow a more seamless transition between reset and non-
reset states. I believe this is a direction that is worth pursuing, so
we can develop reorientation techniques that are both efficient and
seamless. One way I can imagine this playing out would be for the
content creator to define specific optional events that are relevant to
and plausible within the environment which could be called upon by
the redirection heuristic when the need arises. For instance, points of
interest in an environment could light up as target for taking snap-
shots, similar to the example provided by Grechkin’s work [Grechkin
et al., 2015].
10.2 general redirection strategies
Improving the state of general strategies is crucial in that it would
not only help raise the lower bound of performance, but it would
also allow redirection to be used effectively in applications that give
10.3 dynamic planning redirection strategies 145
complete agency to the user, i.e., freedom to walk or roam at will
within the environment.
10.2.1 Heuristics
This dissertation demonstrated how just by pairing previous heuris-
tics with a basic translation-gain redirection heuristic, we achieve a
consistent 14% performance improvement. This can potentially be
increased by adopting more sophisticated translation gain heuristics
such as ones which account for the overlap of the environment with
the physical space. Furthermore, a variety of ideas can be explored
that take into account all three redirection techniques — translation,
rotation, and curvature gains — simultaneously. And now, with the
evaluation platform presented in this work, fresh ideas can be effi-
ciently and reliably tested for rapid development. More advanced ap-
proaches can even developed that are a hybrid of multiple heuristics
combined. One factor that could lead to improved strategies would
be to account for amount of walkable space in the virtual world and
its overlap with the physical space.
10.3 dynamic planning redirection strategies
This category of strategies is particularly important in that it balances
user agency and redirection efficacy while also supporting dynamic
environments. For these strategies I identify the following three av-
enues of improvement.
10.3.1 Prediction Graph Integration
In this dissertation I introduced the concept of automatically gener-
ating prediction graphs. More recently Zank [Zank and Kunz, 2017]
introduced a more advanced approach to this problem. However,
dynamic planning strategies have not yet been integrated with auto-
matically generated prediction graphs.
By doing this integration we can better understand how effective
automatically generated prediction graphs are, what advantages they
offer over manual methods, and also determine how their potential
flaws can be resolved. Additionally, with the integration of these
techniques into the open-source toolkit, dynamic planning strategies
could be readily deployed in new applications.
10.3.2 User Intent
The uncertainty resulting from not knowing the user’s intended tra-
jectory and navigation choices manifests itself as branches in the pre-
10.4 static planning redirection strategies 146
diction graph. As we have seen in this work, the prediction graph’s
branching factor heavily influences the performance of dynamic plan-
ning strategies, and reducing them to any degree can substantially
improve performance. One way to go about this would be to develop
new methods for intent detection. Using information about the vir-
tual experience, the user’s history of movement, the context of her
actions and even body cues we can potentially improve the predic-
tion of the user’s behavior. This can result in pruning the prediction
graph and thus reducing the branching factor. Nescher [Nescher and
Kunz, 2013] and Zank [Zank and Kunz, 2016] have both shown evi-
dence of head-tracking and eye-tracking information being useful for
improving our prediction of the user’s near-term actions.
10.3.3 Optimization
The two dynamic planning strategies presented in the literature, namely
FORCE [Zmuda et al., 2013b] and MPCRed [Nescher et al., 2014] are
arguably a bit underdeveloped and serve as novel prototypes rather
than complete solutions to the problem. These strategies have a num-
ber of potential avenues for improvement. For instance, we can de-
sign more sophisticated ways to deal with uncertainty. Currently, the
approach in both strategies is based on a weighted comparison at
branching points. A potentially much more advantageous approach
would be to find a choice of gain that would work well for all possible
path options instead of selecting only the optimal choice for one of
the paths.
Reiterating a previous statement for general strategies, with the
availability of the evaluation platform, we can easily tweak and tune
the parameters for dynamic planning strategies. One of the impor-
tant open questions, for instance, is the optimal choice of search hori-
zon. In order to find the sweet spot for the search horizon, with the
platform we can understand the added performance improvement of
increasing the search horizon, and how it incurs computational costs.
Both strategies can also further be investigated and compared to un-
derstand the implications of using a waypoint-based search horizon
(FORCE) vs. a time-based horizon (MPCRed). Such research could
lead to expanding upon both approaches, possibly creating a hybrid
of the two paradigms or even design more effective solutions.
10.4 static planning redirection strategies
In the near-term, static planning strategies have the greatest poten-
tial for enabling effective applications that can reach a wide audience.
The primary reason for this is that only static planning strategies can
be feasibly deployed within room-scale tracking configurations. For-
tunately, a wide range of virtual reality applications are — or can be
10.4 static planning redirection strategies 147
— presented with a linear narrative. This means despite the restric-
tive scope of static planning, many applications can benefit from its
high performance, warranting further development of this category.
I present three areas in which improvements can be achieved.
10.4.1 Counter-Deviation
This dissertation presented the proof-of-concept for applying counter-
deviation, which is the critical factor in successfully executing a pre-
planned linear experience. For typical user behavior this implementa-
tion of counter-deviation is sufficient, allowing redirection to operate
effectively. However, there are still potential cases where the plan
and execution substantially diverge, especially for irregular walking
behavior and users curious to the point of being detrimental to the ex-
ecution. We need approaches that are more robust to a wide variety
of user deviation or unexpected behavior. An important step would
be to enumerate types of behavior that cause redirection to fail such
as strafing and cutting corners. Once enumerated, methodical testing
can be done in order to create a more methodical way of testing these
approaches.
For researchers who wish to proceed in this direction, I would like
to point out several interesting ways in which users can engage in
unusual behavior that violates the assumptions of redirected walking.
• Have a waypoint in front of you, face it, and start moving to-
wards it. Look to your left while youre walking, without turn-
ing your body and take a few steps and look back at your way-
point. If curvature gain was applied, you’ll see the waypoint is
not where you expected it to be anymore.
• Act like a first-person shooter character by turning before reach-
ing a turn, essentially strafing towards the turn so you are facing
the next target direction ahead of time. The redirection plan can
easily fall apart since the expected rotation didn’t happen near
the turn.
• Stand in place and just look left and right. If asymmetric gains
are applied you’ll notice the world keeps drifting and spinning
around you.
• Have a waypoint in front of you but don’t walk towards it.
Strafe to the left or right. In the presence of curvature gain, you
may notice the the waypoint is coming towards you or moving
away.
10.4 static planning redirection strategies 148
10.4.2 Redirection Friendliness
Examining prediction graph properties and how they interact with
different strategies was a key component in developing adaptive redi-
rection. However, this interaction also highlighted the impact of a vir-
tual environment’s shape on redirection efficacy. While redirection
strategies aim to minimize reorientations for a given virtual environ-
ment, a complementary problem is determining what makes one en-
vironment or path more conducive to redirection than another. I refer
to this as “redirection friendliness”, expressing the degree to which
a given path or environment is conducive to redirection in a target
physical space.
Identifying the defining characteristics of a redirection-friendly en-
vironment or path require further investigation. However, intuitively
long walking segments would be less desirable, and turns of greater
angles would be advantageous since rotation gain is one of our great-
est tools in redirection, giving us more opportunities of exercising
control over the trajectory shape. Part of why segment length and
turn angles were used in defining prediction graph properties for
adaptation were based on this intuition. More research in this direc-
tion can help us with better extracting these properties.
The ultimate application that can emerge from this research vector
would be a tool that gives clear guidelines to a content creator for
creating an application that would work well with redirection. One
instance that comes to mind is for to tool to guide the design process
of incrementally adding waypoints to construct a virtual path that
can avoid resets. We can imagine at each step, an area surrounding
the last placed waypoint would be highlighted, showing where the
next new waypoint can be placed without incurring a reset. A crude
solution to this would be to exhaustively run COPPER in the back-
ground that samples different next point candidates to see which ones
would lead to a path that can be explored without resets. A similar
mentality was in mind when I proposed the idea of soft and hard
waypoints in one of my earliest prototypes [Azmandian et al., 2014].
Alternatively we can imagine a diagnostic tool that gives suggestions
for “fixing” a path or environment that causes too many resets by
offering methods to slightly modify certain parts to make it more
redirection-friendly. It should be noted that the notion of redirection-
friendliness and a tool that measures it, is a factor of the specific
redirection system/strategy and physical space being used.
10.4.3 Non-Linearity
While static planning strategies offer great efficacy, they they reduce
the user’s freedom of movement. But I think between the domain
of static planning strategies and dynamic planning strategies, there
10.5 perception 149
may exist a middle ground that gives a bit more agency to the users
but can still be very effective with redirection. The idea is to have an
experience that is not explicitly linear, but rather explicitly in the form
of a small graph. Users can walk directly from one point of interest to
another based on the connectivity of these points in the graph. This
way we can exercise control over what kind of decisions the user can
make and we have already planned ways to redirect them safely from
one point to another.
Though graph-based environments are somewhat comparable to
a standard dynamic planning scenario, the core difference is that a
graph-based environment is controlled and designed with redirec-
tion in mind, but dynamic planning scenarios aren’t. The idea is that
we are trying to give the illusion of control: we show an environment
and allow the user to go from one point to another with any arbi-
trary order, but all these possibilities and how to deal with them have
already been taken into account. Whereas in a typical dynamic plan-
ning scenario, we take an environment, extract the prediction graph
and do our best to plan within the restrictions given to us, in a much
more passive manner. Here I propose giving more freedom to the
user by enforcing control on the layout of the environment.
Assuming control over the environment, we can think of more in-
teresting ways for the environment to interact with the redirection
system, informing and assisting each other. Similar to the idea of dy-
namic layout generation [Vasylevska et al.,2013] we can dynamically
adjust the shape of the environment, either explicitly unravelling it
dynamically, or temporarily cordoning off regions if direct movement
towards them would lead to resets.
Another idea that my colleague Rhys Yahata and I have explored
has been what we call the “Pipes and Rooms” design. The idea would
be to lay out the environment in way that you have a set of rooms
connected with pipes. Pipes are the linear segments where redirec-
tion is being applied, and when you enter a room, redirection is dis-
abled. In this design, the redirection is planned out in a way that the
room will fully coincide with the available physical space so the user
can freely explore the room without interruption. This lends itself
nicely to a level-based game design where the user goes from one
state to another, potentially even supporting branching rooms and
back-tracking.
10.5 perception
Though the perception of redirection hasn’t been the focus of this
work, I have identified its place within this work and alluded to nec-
essary future research in the background chapter. I reiterate those
points here again for completeness. For a deeper discussion on the
topic refer to Chapter 2.
10.6 ad hoc redirection 150
10.5.1 Calibration Procedure
Since previous research [Grechkin et al.,2016] has shown how greatly
detection thresholds between users and is possibly influenced by hard-
ware, applying average detection thresholds for all users may not be
the best approach. Arguably, the definitive solution to the percep-
tual component of redirection would be in the form of a calibration
process determining thresholds on a per user, per virtual experience
(including environment and user task), and per hardware setup. Such
customized thresholds would move us towards the optimal balance
of user comfort and redirection efficacy for individual users.
10.5.2 Gain Smoothing
As we know gains can still be noticeable if they are varied rapidly
within detection thresholds. This warrants further inspection of what
causes gains to remain unnoticed when they are changed, in order
to develop effective gain-smoothing mechanisms. Again this sensitiv-
ity may depend on the user, hardware and virtual experience so this
might warrant its own calibration sequence of sorts as well. Perhaps
this problem can also be solved along with finding detection thresh-
olds, especially if we have a better understanding of the science of
detection. Ideally a control procedure can determine at each point
how much a gain value can go up or down based on the calibration
and even perhaps the user’s velocity to help the redirection strategy
make choices that don’t cause detection or unintended discomfort to
the user.
10.6 ad hoc redirection
With the growing prevalence of inside-out tracking solutions (such
as the Microsoft Mixed Reality headset that achieve tracking without
reliance of external hardware placement), the idea of what is consid-
ered a “physical space” for virtual reality experiences is changing.
The most important effect this has on redirection is the emergence of
dynamic physical spaces.
10.6.1 Dynamic Physical Space
Inside-out tracking means facing circumstances in which the physical
space available is not known in advance and it is instead dynamically
updated. This means first of all we need to develop ways to use infor-
mation from our surroundings to create a map of the physical space,
partitioning regions into either walkable, obstacle, or unknown. From
there we need to develop strategies that can use this information ef-
fectively. A variety of questions may arise that include: 1) How do
10.7 multi-user redirection 151
you deal with unknown parts of the physical space? Do you treat
them as obstacles and avoid them or do you instead incentivise mov-
ing towards them to minimize the unknown regions? 2) How do you
deal with dynamic obstacles in the environment? It would be inter-
esting to see how much more effective advanced strategies would be
than just simply using general strategies or just the null redirection
strategy. Furthermore, it remains to be seen how effective redirection
can be in small room-scale settings with additional uncertainty and
moving obstacles when we already have a difficult time in the ideal
static planning scenario.
10.7 multi-user redirection
As the focus of VR shifts from single-person experiences to multi-
user, shared, and collaborative interactions, it becomes increasingly
important to accommodate multiple co-located users within a shared
real-world space. The introduction of multiple users moving both vir-
tually and physically creates additional challenges, the most impor-
tant of which is the obvious collision prevention, and another which
I refer to as the convergence problem.
10.7.1 Collision Prevention
As the name suggests, collision prevention involves preventing users
from physically colliding with each other. This can either be done by
using redirection to gradually keep them from getting dangerously
close to each other or when necessary, triggering events to stop users
from colliding. The most current work in this area is my first exam-
ination of this topic [Azmandian et al., 2017] in which I address the
subtleties of the problem and its requirements. The greatest challenge
is managing two potentially contending objectives: 1) avoiding colli-
sion between users 2) avoiding collisions with physical boundaries.
An advanced collision prevention mechanism would also account the
physical space limitations in addition to an oncoming user. Similarly,
reorientation heuristics can account for other users within the space
to make better informed decisions.
10.7.2 Convergence
While the co-location of users experiencing VR can increase through-
put and makes for better use of resources, the main advantage of
multi-user redirection is enabling physical interaction. However, since
redirection changes the mapping between real and virtual words for
each user differently, the users’ references of the world diverge. But
in order to have users perform a virtual and physical handshake, they
need to synchronize and align their mappings between the real and
10.7 multi-user redirection 152
virtual worlds. This requires the redirection to bring the world ref-
erences for the users closer until they converge by the time the two
users come in physical contact.
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Abstract (if available)

Abstract Real walking is the most intuitive locomotion metaphor for virtual reality applications. Despite its many benefits, real walking inherently restricts users to a confined physical space. Redirected walking is a perceptual illusion introduced to overcome this limitation by leveraging the characteristics of the human perception system. While redirection has come a long way since its conception, a majority of the research in the field has been focused on the perceptual aspects of redirection. Though crucial, the human component of redirection is just one piece of the puzzle and it does not provide us with an application method. Harnessing the potential of redirected walking requires acknowledging the multiple facets of the problem, and designing a system that addresses its requirements methodically. This work provides the theoretical foundation to achieve this, bridging the gap between understanding redirection and employing it. ❧ I begin first by providing a formal definition and hierarchical design for the envisioned redirection system. The hierarchy illustrates how redirection techniques—as the building blocks—are used to form heuristics, in turn forming strategies, and ultimately shaping the structure of a complete redirection system. For a holistic conception of a system’s performance, at each level of the hierarchy, a notion of performance is defined that corresponds to the objectives of that level. Measuring this nuanced understanding of performance is made possible by the evaluation methodology and platform. The methodology controls for factors that affect the system’s behavior

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Asset Metadata

Creator Azmandian, Mahdi (author)

Core Title Design and evaluation of adaptive redirected walking systems

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Computer Science

Publication Date 02/15/2018

Defense Date 12/08/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag 3d user interfaces,locomotion,OAI-PMH Harvest,redirected walking,virtual reality

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Suma Rosenberg, Evan (committee chair), Ayanian, Nora (committee member), Fisher, Scott (committee member), Rosenbloom, Paul (committee member), Scherer, Stefan (committee member)

Creator Email azmandia@usc.edu,mahdiazmandian@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-474280

Unique identifier UC11265833

Identifier etd-AzmandianM-6041.pdf (filename),usctheses-c40-474280 (legacy record id)

Legacy Identifier etd-AzmandianM-6041.pdf

Dmrecord 474280

Document Type Dissertation

Rights Azmandian, Mahdi

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA