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University of Southern California Dissertations and Theses
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Novel soft and micro transducers for biologically-inspired robots
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Novel soft and micro transducers for biologically-inspired robots
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Content
Copyright 2020 Ariel Calder on
Novel Soft and Micro Transducers for
Biologically-Inspired Robots
by
Ariel Calder on
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
Mechanical Engineering
August 2020
Dedicated to my parents
Nibaldo Calder on and Pur sima Avenda~ no
ii
Acknowledgements
I would like to thank my advisor, Professor N estor O. P erez-Arancibia, for his guidance, encourage-
ment, patience, and support over the past six years, especially for his always constructive criticisms
that have made me grow not only as a researcher but as a person.
I would like to thank professors Eva Kanso and Yong Chen for being part of my dissertation
committee. Also, Professors Satyandra Gupta, Qiming Wang and Henryk Flashner for their input
during my Qualifying Exam.
I also thank my former advisor Professor Juan Crist obal Zagal. His support was vital for my
transition from undergrad to grad school. Besides his academic support, he was also a mentor and
a friend.
Thanks to the Chilean National Oce of Scientic and Technological Research (ANID) for
granting me the Becas Chile Fellowship (72160414). Additional thanks to the USC Viterbi School
of Engineering, which supported me through the Global Graduate Fellowship.
Special thanks to the National Science Foundation (NSF), and the Defense Advanced Research
Projects Agency (DARPA) for funding our research through awards and contract awarded to my
advisor.
I am a believer that \the whole is greater than the sum of the parts," and that friendship,
synergy and constructive interactions make us better than if we were individually isolated. I want
to thank the entire Autonomous Micro-Robotic System Lab (old and current members) because
the multidisciplinary work done during my Ph.D. would not be possible without them. Thanks to
Xuan-Truc Nguyen, besides her useful help on my English writing and being an excellent research
partner, she is just a lovely person to talk with. Thanks to Emma Singer, who had the patience
and helped me during a time when my communication skills were lacking. Thanks to Ke Coco Xu
for being an example of how working hard pays o. Thanks to Joey Ge, Xiufeng Yang, Longlong
iii
Chang and Ying Chen for their collaboration over the years and for sharing their fascinating culture,
including those yummy dishes and talks with me. Thanks to the new-gen kids Alberto Rigo, Fares
Maimani, and Ryan Bena for reigniting a passion for research in me that I felt I was starting to
lose.
Special thanks to my girlfriend, Hye-Hyun Nam, who always supported me during the hard
times I had during these years. A furry thanks to my kids Zorro, Shadow and Kitten, whose
presence was the best therapy for the toughest days. Also, thank you to the fur that is not with
me anymore, Gata and Terrible, RIP.
Finally, I would like to thank my family. My parents, to which I owe my entire career and the
person I am. My sister for being a symbol to follow and the strongest woman I have ever met, and
my niece Isabella whose smiles reminded me of the simplicity of enjoying life with simple things.
iv
Contents
Dedication ii
Acknowledgments iii
List of Tables viii
List of Figures ix
Abstract xxiii
1 Introduction 1
1.1 Soft-Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Micro-Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Contributions of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Dissertation Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 New Multi-Material Soft Transducers for Developing Earthworm-Inspired Soft
Robots 8
2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Earthworm-Inspired Sensing and Locomotion . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Robotic Design and Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 System Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Characterization of RWT1's Actuators . . . . . . . . . . . . . . . . . . . . . . 17
2.4.2 Characterization of RWT2's Sensors . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.3 The Use of Protruded Sensors for Attachment Detection . . . . . . . . . . . . 27
2.5 Locomotion Planning and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
v
2.6 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 A New Bee-Inspired FWMAV Able to Perform Controlled Hovering 36
3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Robot Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 Air Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.3 Wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.4 Hinge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.5 Bimorph Piezoelectric Bending Actuators . . . . . . . . . . . . . . . . . . . . 39
3.3.6 Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Wing Trajectory and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Robot Performance and Hovering Test . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.6 Design of a Nonlinear-stifness Hinge for Lift Force Improvement . . . . . . . . . . . . 43
3.6.1 Wing Pitch Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.6.2 Nonlinear-Stiness Hinge Design . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6.3 Hinge Comparison Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6.4 60 mg FWMAV Design and Fabrication . . . . . . . . . . . . . . . . . . . . . 49
3.6.5 Controlled Hovering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Novel High-Frequency SMA Flexible Micro Actuator for the Developing of mg-
Scale Flexible Micro Robots 53
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 SMALLBug a 30 mg Multigait Micro Robotic Crawler . . . . . . . . . . . . . . . . . 55
4.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.2 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.3 Actuator Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.4 Locomotion Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 SMARTI a 60 mg Steerable Micro Robot Crawler . . . . . . . . . . . . . . . . . . . . 67
vi
4.3.1 Modular Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.2 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.3 Open Loop Crawling Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3.4 Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.5 Control Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5 Conclusion and Future Work 74
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 Current and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.1 Soft Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.2 Micro Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.3 Flexible Micro Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Bibliography 78
vii
List of Tables
2.1 Dimensions of the relaxed prototypes RWT1 and RWT2. As can be seen
in Fig. 2.1-(b) and Fig. 2.1-(c), both prototypes are roughly cylindrical with a total
lengthL
R
and diameterD
R
(see Step 4 of Fig. 2.2-(c)). The length of each individual
radial actuator is L
RA
. The average wall-thickness of the soft components is W
R
. . 13
2.2 Locomotion pattern. Values of the robot's state, x
i;k
, during each phase k. . . . 30
4.1 Velocities achieved by SMALLBug during locomotion experiments at dierent actu-
ation frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
viii
List of Figures
1.1 Diagram of the projects performed during the PhD. For soft robotics we
developed earthworm inspired robot, in parallel we developed FWMAV inspired in
bees and
ies. The know-how obtained during these two projects allowed us to create
new "in between" technology:
exible micro robots. Where using a
exible bending
actuator we developed two inchworm inspired robotic crawlers. . . . . . . . . . . . . 3
2.1 Natural and articial worms. (a) Illustration showing the peristalsis-based lo-
comotion of an earthworm during burrowing. The inset shows an enlarged segment
composed of radial muscles (in blue) and longitudinal muscles (in dark brown). (b)
Robotic worm type 1 (RWT1). [1] (c) Robotic worm type 2 (RWT2). . . . . . . . . . 9
ix
2.2 Fabrication method. The fabrication uses 3D-printed acrylonitrile butadiene
styrene (ABS) molds, silicone elastomer (Eco
ex
R
00-50 and 00-30, Smooth-On),
butadiene rubber elastomeric o-rings, sheets of berglass and pneumatic compo-
nents. The total process consists of four parts, each consisting of several steps. (a)
Fabrication of a radial actuator: The actuator is fabricated in seven steps. First,
the two halves of the actuator are cast employing 3D-printed molds. Then, the front
and rear faces of the actuator are sealed with berglass net caps. Once the caps are
bonded and the actuator is sealed, the fabrication of the radial actuator is completed.
(b) Fabrication of the axial actuator: The procedure is similar to that of a radial ac-
tuator, except for Step 6 in which butadiene o-rings are tted into patterned grooves
to constrain the radial deformation and pre-program the axial responses of the sys-
tem. (c) Final assembly: Two radial actuators, an axial actuator and three helical
air feeding lines are integrated into a single functional body. The helical shape of the
air tubes is a critical design feature that allows the extension and shortening of the
soft actuator. (d) Articial skin fabrication and integration: Two layers of silicone
are combined into a single piece that contains an internal meandered channel to be
lled with Galinstan. The layers are produced employing engraved 3D-printed molds
(Step 1) and bonded by spin-coating the top layer with uncured silicone (Step 2).
Then, Galinstan is injected with a syringe (Step 3) and once the channel is lled
the sensor is complete (Step 4). An additional silicone layer is fabricated from a
patterned mold (Step 5), then attached to the sensor using spin-coating. The sensor
is wired and its end are sewn together. It is then wrapped around the corresponding
radial actuator (Step 6), completing the entire process. [1] . . . . . . . . . . . . . . 14
2.3 Characterization of the axial actuator. (a) Axial actuator during characteri-
zation experiments. [1] (b) Experimental strain{pressure curves associated with the
axial actuator. The vertical bars indicate the magnitudes of the experimental stan-
dard deviations with number of trials n=6. . . . . . . . . . . . . . . . . . . . . . . . 17
x
2.4 Characterization of the radial actuator. (a) Radial actuator during character-
ization tests. [1] (b) Experimental strain{pressure curves associated with the radial
actuator. The vertical bars indicate the magnitudes of the experimental standard
deviations with number of trials n=6. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Functional states of RWT2's soft sensors during operation. (a) & (b) Be-
fore attachment, a radial actuator expands freely and the corresponding soft sensor
elongates along the
^
l-axis as idealized in Fig. 2.6-(a). In this situation, we say that
the sensor is in the tension state. (c) After attachment, a radial actuator can no
longer expand, constrained by the internal surface of the pipe. In this situation,
we say that the sensor is in the compression state. In this state, the tension force
exerted on the sensor remains constant, and therefore, all further variations on the
electrical resistance of the sensor are due to compression forces, modeled as shown
in Fig. 2.6-(b). The sensor depicted in this gure has a patterned upper surface,
corresponding to the nal design employed in the fabrication of RWT2, shown in
Fig. 2.2-(d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Idealized depiction of the sensor's experimental tension and compression
states. (a) In tension, forces with opposite directions and magnitudesF
l
are applied
along the axis
^
l to produce an elongation l. This conguration is employed in the
tensile experimental tests discussed in this work. (b) In compression, forces with
opposite directions and magnitudes F
h
are applied along the axis
^
h to produce a
contraction h. This conguration is employed in the compression experimental
tests discussed in this work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
xi
2.7 Stress-strain curves for the sensor in tension and compression. (a) For
the sensor in the pure tension state depicted in Fig. 2.5-(a) and Fig. 2.5-(b), the
experimentally-tuned Mooney{Rivlin model matches almost perfectly the experi-
mental data. The FEA-based simulation replicates the qualitative relationship be-
tween engineering stress and strain. (b) For the sensor in the pure compression state
depicted in Fig. 2.5-(c), the experimentally-tuned Mooney{Rivlin model matches al-
most perfectly the experimental data. The FEA-based simulation matches almost
perfectly the experimental data for strains smaller than 0:04 and replicates the qual-
itative relationship between engineering stress and strain for larger strain values.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.8 Resistance variation as a function of total load (upper plots) and strain
(bottom plots) for the sensor in tension and compression. (a) & (b) The
rst-principles models of both the resistance{load and resistance{strain relation-
ships, derived from (2.9), capture the main trends but do not quantitatively match
the experimental data. The heuristically-corrected model is obtained by solving the
optimization problem in (2.13). (c) & (d) The rst-principles models of both the
resistance{load and resistance-strain relationships, derived from (2.10), fail to cap-
ture the main trends displayed by the experimental data. The heuristically-corrected
model is obtained by solving the optimization problem in (2.14). Note that the curve
of the relationship between F
h
and R
h
has an almost-
at section (F
h
< 10 N). . . 23
2.9 Sensors geometries and their experimental resistance{load curves. (a)
Flat sensor. (b), (c) & (d) Patterned sensors with 75 %, 50 % and 25 % of their
surfaces protruded, respectively. (e) The data come from experiments in which the
sensors are compressed along theh-dimension as illustrated in Fig. 2.6-(b). It can be
observed that the sensitivity of a patterned sensor increases if its protruded surface
is decreased according to the specic patterns . . . . . . . . . . . . . . . . . . . . . 25
xii
2.10 FEA-based simulations comparing the strain distribution of a
at sensor
and a 50 %-protruded sensor under a homogeneous load of 1 N. (a) This
plot shows that, for a homogeneous load, the
at sensor deforms approximately ho-
mogeneously. (b) This plot shows that, for a homogeneous load, the patterned sensor
displays areas of strain concentration. This phenomenon qualitatively explains the
experimental data in Fig. 2.9-(e), as areas of strain concentration can signicantly de-
crease the cross-sectional areas of the embedded liquid wires, thus greatly increasing
the total electrical resistance of the sensor. . . . . . . . . . . . . . . . . . . . . . . . 25
2.11 Onboard test of perceptive articial skin. (a) During the fabrication process
of RWT2 (see Fig. 2.2-(d)), a patterned sensor with 50 % of its surface protruded
(see Fig. 2.9-(c)) is wrapped about a radial actuator to create the robot's perceptive
skin. This graph shows a sensor's voltage outputs as functions of time when the
corresponding radial actuator is in
ated, at a constant rate, under four dierent
conditions: unconstrained and inside pipes with diameters of 32, 40 and 48 mm.
In this case, using standard circuitry, the output voltage is made proportional to
the total electrical resistance of the sensor. These experiments clearly show that the
sensor's output is approximately
at and linear in tension (during free expansion) and
exponentially rises up in compression (after attachment). This behavior is consistent
with the data in Fig. 2.9 and can be qualitatively predicted by nding a relationship
between the actuator's rate of in
ation and a time-dependent function
h
(t) that is
plugged into
R
h
. (b) Diagram shows the connection between the stages dened
in Fig. 2.5 and the results from the experiments. The slope of the voltage output
changes before and after the attachment from approximately linear to exponential
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.12 Five phases used by the robot to generate one stride. At k = 1, the back
radial actuator is anchored to the pipe. At k = 2, the axial actuator is extended
reaching a further point. Atk = 3, the front radial actuator is anchored to the pipe.
At k = 4, the back radial and axial actuators are relaxed. At k = 5, the back and
front radial actuators are anchored to the pipe. [1] . . . . . . . . . . . . . . . . . . . 30
xiii
2.13 Locomotion control scheme. The plant is composed of four types of components:
soft actuators, soft sensors, pneumatic pumps and pneumatic valves. The locomo-
tion rules block generates the control reference to produce the locomotion sequence
in Fig. 2.12. Excited by the control error, the MIMO controller block generates
the control signal that excites the pneumatic pumps and valves. RWT1 uses the
actuators' internal air pressures for feedback control, while RWT2 uses the central
actuator's internal air pressure and perceptive articial skins wrapped around its ra-
dial actuators. The locomotion rules and controllers are run on an Arduino
R
Mega
digital signal processor (DSP). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.14 Horizontal locomotion tests. (a) RWT1 moves horizontally from left to right em-
ploying the internal air pressures of the actuators for feedback locomotion control. [1]
(b) RWT1 initially moves horizontally from left to right until it encounters a 45
-up-
turn in the locomotion path. Then, the robot complies to environmental geometrical
variations and passively adapts its body to maneuver through this obstacle. As in
the rst test, RWT1 employs the internal air pressures of the actuators for feedback
locomotion control. [1] (c) RWT2 moves horizontally from left to right employing
the radial actuators' perceptive articial skins and central actuator's internal air
pressure for feedback locomotion control. Attachment is directly detected employing
real-time touch information and the data in Fig. 2.11. While locomoting, RWT2
encounters three dierent diameters:
1
= 32 mm,
2
= 40 mm and
3
= 48 mm.
In this case, the robot passively adapts its body to environmental changes, but ac-
tively senses these changes for control purposes. In all the stills, time is indicated
in minutes : seconds. The complete experiment can be found in the supplementary
movie SoftRobots.mp4 (http://www.uscamsl.com/resources/Calderon thesis 2020/-
SoftRobots.mp4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
xiv
2.15 Vertical locomotion tests. (a) RWT1 moves vertically inside a cylinder with con-
stant diameter, employing the internal air pressures of the actuators for locomotion
control. [1] (b) RWT2 moves vertically employing the radial actuators' perceptive
articial skins and central actuator's internal air pressure for feedback locomotion
control. Attachment is directly detected employing real-time touch information and
the data in Fig. 2.11. While locomoting, RWT2 encounters three dierent diameters:
1
= 32 mm,
2
= 40 mm and
3
= 48 mm. (c) RWT2 climbs between three paral-
lel cylinders, labeled 1
, 2
and 3
. (d) RWT2 climbs between two divergent planes
(4
angle from vertical axis). These tests demonstrate that both robots can adapt
their bodies to time{shape variations of the surroundings and that, when tactile
information is used for control, a priori geometrical information about the locomo-
tion path becomes less relevant or unnecessary. In all the stills, time is indicated
in minutes : seconds. The complete experiment can be found in the supplementary
movie SoftRobots.mp4 (http://www.uscamsl.com/resources/Calderon thesis 2020/-
SoftRobots.mp4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 Robot design. (a) The robotic bee is composed of ve parts, the airframe which
serves as a structural part, the actuators that generate bending motion, the trans-
mission that translates the bending motion of the actuator to
apping motion by a
four bar mechanism, the hinge which passively produces the wing pitching required
for
ying and lastly, the wings (b) shows a zoom of the transmission mechanism, the
actuators de
ect delta which then produces a change of angle of the wing ' (c) A
photograph of one of our robotic bees assembled. . . . . . . . . . . . . . . . . . . . 38
3.2 The fabrication process for elements of the RoboBee: (a) Airframe, (b)
Actuators, (c) Transmission, (d) Wings. Step 1 is the creation of the stack, which
may contain layers that need to be cured. Step 2 is the release cutting of the parts,
and Step 3 shows the parts ready for assembly. The RoboBee transmission is the
only part that must be folded into position before it can be used. . . . . . . . . . . 40
xv
3.3 Input signals for the generation of body torques. (a) Dierence of amplitude
in each wing is translated into a roll torque (b) a bias in the
apping is translated
into a pitch torque (c) changing the velocity for upstroke and downstroke is called
split cycle, it takes fraction of the period to perform upstroke and (1-) for down-
stroke. Generating yaw torque, this has not been fully implemented. The robots
ap at natural frequency so increasing further the
apping velocity would reach the
bandwidth of the system, decreasing the
apping amplitudes. . . . . . . . . . . . . 42
3.4 Robobee control hovering experiment. (a) Photographic sequence of the RoboBee
prototype during the position control experiments, The robot is able to hover around
the desired position for about 20 s. (b) Position control of RoboBee. The dashed
lines represent the reference position signals, and the solid lines represent the ac-
tual position regulation results. The RoboBee
apping-wing robot is commanded to
hover at a desired position, and the experiment lasts for almost 20 s indicating the
mechanical robustness and the performance consistency of the attitude and position
controllers. The complete experiment can be found in the supplementary movie FW-
MAVExperiments.mp4 (http://www.uscamsl.com/resources/Calderon thesis 2020/-
FWMAVExperiments.mp4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5 Lift/Drag dependency to pitching angle. Lift coecient, drag coecient, and
their ratio as a function of the instantaneous pitching angle of the wing. Plot based
on the results from [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6 60 mg
ying prototype using the new hinge design. (a) A photograph of
the 60-mg FWMAV with nonlinear-stiness hinges. A U.S. penny (19:05 mm in
diameter) is included for scale. The inset shows a CAD rendering of the new hinge.
(b) The nonlinear-stiness hinge design. Through a sleeve-stop mechanism, the hinge
prevents the wing's pitching angle
max
from surpassing 70
. . . . . . . . . . . . . . 45
xvi
3.7 Photographs of maximum pitching angle during force measurement ex-
periments for a
apping angle of 99
. The left and right images show upstroke
and downstroke, respectively. The nonlinear-stiness hinge is shown in (a), while the
regular hinge is shown in (b). Since the photographs depict bottom views, the nar-
rower projections of the wing seen in (a) indicate that the wing is, in fact, exhibiting
smaller pitching angles than the one in (b). . . . . . . . . . . . . . . . . . . . . . . . 46
3.8 Results for the hinge comparison experiments. (a) Pitching angle versus
apping angle for both the regular and nonlinear-stiness hinge experiments. Trend
lines are tted using a cubic least-squares method. The wing pitching angle for
the nonlinear-stiness hinge does not surpasses 70
, indicating that the new hinge
design successfully limits the pitching angle. (b) Lift force generation for both hinges,
including error bars. Trend lines are tted using a cubic least-squares method. When
the
apping angle is below 80
, the regular hinge seems to outperform the nonlinear-
stiness hinge. However, above 80
apping, the nonlinear-stiness hinge generates
more lift than the regular hinge. This aligns with our hypothesis that a pitching
angle of approximately 70
is preferable. For a given
apping angle, whichever hinge
produces a pitching angle closer to 70
will generate a higher lift force. . . . . . . . 47
3.9 Instantaneous force during
apping. (a) nonlinear-stiness hinge, and (b) reg-
ular hinge. The negative regions of the plot are smaller for the bounded case, con-
tributing to a higher average lift force compared to the unbounded case despite
having smaller peaks. Since one trough is more negative, we can infer that there is
an asymmetry (between upstroke and downstroke) in the lift force generation. This
is a result of fabrication errors and imperfections in the parts. . . . . . . . . . . . . 48
xvii
3.10 Results from experiments using the 60 mg prototype. (a) Force genera-
tion of the lighter bee prototype. The maximum lift achieved was 147 mg, com-
pared to only 130 mg using the heavier 75-mg prototype with the old hinge design.
(b) A photographic sequence of the bee during controlled hovering. (c) Reference
and measured altitude of the bee during
ight. The lighter bee is capable of fol-
lowing the reference altitude, showing that the robot can perform controlled hov-
ering. (d) Roll and pitch angles of the bee during
ight. Results suggest good
performance of the robot. The complete experiment can be found in the sup-
plementary movie FWMAVExperiment.mp4 (http://www.uscamsl.com/resources/-
Calderon thesis 2020/FWMAVExperiments.mp4) . . . . . . . . . . . . . . . . . . . 50
4.1 Photograph of SMALLBug. An SMA bending micro actuator connects the two
halves of the sigma body frame. Anisotropic friction legs allow forward motion when
the actuator bends cyclically. A U.S. dime is included for scale. . . . . . . . . . . . . 55
4.2 SMALLBug Design. (a) The robot consists of three elements: a high-frequency
SMA bending actuator, the sigma body frame, and anisotropic friction legs. (b)
This diagram depicts the forward motion generation. The geometry of the legs
allows smooth rotation in the heel direction (backward) while preventing rotation
in the forward direction due to the foot acting as a physical stop when rotated in
the foot direction (forward). The interaction of the anisotropic friction legs with the
ground upon activation of the bending actuator produces forward motion. . . . . . 56
xviii
4.3 Fabrication of the elements of a SMALLBug prototype. (a) Fabrication of
the SMA-based bending actuators. The fabrication consists of four steps. First,
a copper-coated CuFR4 (a berglass-epoxy laminate material) layer is cut with an
appropriate shape and holes to hold the SMA wires. During step 2, an SMA wire is
threaded through these holes, then held in place by a simple knot at the end of the
holes. During step 3, a strip of carbon ber is glued onto the back of the jig using
cyanoacrylate glue in order to maintain the SMA wire in tension. Finally in step
4, the jig is laser-cut to release the actuators. Electrical connections are made by
attaching wires to the copper terminals using conductive epoxy. (b) Fabrication of
the sigma body frame and anisotropic friction legs. First, a multi-material stack is
made from two layers of carbon ber and an intermediate layer of polyimide Kapton
lm. A sheet adhesive (Dupont Pyralux) is used to bond the layers. This stack is
cured at high temperature and pressure using an automatic hydraulic press. The
carbon ber pieces contain pre-cut features that allow easy folding. In step 2, the
stack is released using a high-resolution laser-cutter to obtain the sigma body frame
and anisotropic friction legs. Finally, in step 3, the sigma body frame is folded from
a 2-D shape to a 3-D structure, giving it the characteristic sigma shape. The legs,
once released, are ready to be assembled to the body using the interlocking features. 58
4.4 Displacement measurement and input signal for the 90mm bending ac-
tuator. The input signal is a pulse-width modulated (PWM) signal with a pulse
magnitude of 10 V when on. The duty cycle is the fraction of the period during
which the signal is maintained at its high value. As the instantaneous measurements
show, the SMA wire contracts during the \on" portion of the signal as it heats up
its crystal structure changes from martensite to austenite. For the remainder of the
period, the current through the wire is maintained at zero to allow cooling, which
corresponds to expansion of the wire back to its original length. . . . . . . . . . . . . 60
xix
4.5 Duty cycle sweep experiment. In order to nd the duty cycle that results in
maximum displacement, we performed experiments at a series of duty cycles for
each frequency tested. A clear trend emerged at all frequencies, in which a trade-
o between heating and cooling times produces a maximum displacement at some
preferred duty cycle, and duty cycles smaller or larger than that resulted in lower
displacements. This plot shows the experiments performed on an actuator with a
carbon ber thickness of 90 m at 1 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.6 Characterization experiments for three dierent central carbon ber sti-
nesses. (a) Frequency-displacement plot for three dierent thicknesses of carbon
ber. From the experiments mentioned in Fig. 4.4, we found the maximum dis-
placement for each frequency and for each of the three actuator thicknesses exam-
ined. For each experiment, the input signal was a pulse-width modulated signal with
a value of 10 V when it was on. The results show that the actuator with the largest
displacement was obtained using the actuator with a central carbon ber layer that
was 90 m. (b) Photographic sequence of the experiments for the actuator whose
central carbon ber was 90 m. These photographs show the bending achieved by
the SMA wire's contraction upon heating. . . . . . . . . . . . . . . . . . . . . . . . . 62
4.7 Plots of the actuator's displacement during characterization experiments
for the 90- m micro bending actuators. (a) Displacement for a duty cycle of
7:5 % at 5 Hz. Under these parameters, some drift can be seen, indicating that there
is not enough time for the wire to completely cool and return to its original length.
The maximum displacement during the cycle is 2:3 mm. (b) Displacement for a
duty cycle of 10 % at 10 Hz. The actuator reaches steady state after its position
drifts almost 2 mm. The maximum displacement is 0:95 mm after this point. (c)
Displacement for a duty cycle of 10 % at 15 Hz. As the frequency increases, less time
is available for the wire to heat up and cool down. The drift here is almost 2:3 mm,
and the maximum displacement is 0:5 mm. (d) Displacement for a duty cycle of 10 %
at 20 Hz. Here, the drifting is even more apparent, reaching approximately 2:4 mm.
However, the displacement is 0:37 mm, which is more than adequate for microrobotic
actuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
xx
4.8 Photographic sequence of crawling experiments. (a) Locomotion experiment
at 2 Hz. (b) Tracked position of the robot during the experiment. At this frequency,
the robot uses the crawling gait, and the plot shows its characteristic behavior of
taking discrete steps. (c) Locomotion experiment at 10 Hz. (d) Tracked position
of the robot during the experiment. At this frequency, the robot uses the shuing
gait, and the plot shows an approximately constant velocity, characteristic of this
type of motion. (e) Locomotion experiment at 20 Hz. (f) Tracked position of the
robot during the experiment. Here, the SMALLBug uses the galloping gait, with
small jumps. The plot shows sudden changes in slope, indicating that the velocity
of the robot changes in an unpredictable manner during the experiment. At this
frequency, the maximum average speed obtained was 17 mm s
1
(1.4 Bl/s). The
complete experiment can be found in the supplementary movie SMALLBug.mp4
(http://www.uscamsl.com/resources/Calderon thesis 2020/SMALLBug.mp4) . . . . 65
4.9 SMARTI design. (a) The design of SMARTI is composed of two SMALLBugs in
parallel. Each SMALLBug has its own SMA bending actuaotr, sigma bodyframe
and anisotropic friction legs. (b) SMARTI can steer to the right and left direction
by modulating the velocity of the left and right unit. If the velocities are the same,
the SMARTI should move straight forward. . . . . . . . . . . . . . . . . . . . . . . 68
4.10 SMARTI fabrication. (Step 1) A multi layered stack composed of two layers of
carbon ber and and middle layer of Kapton is processed with high temperature and
pressure. (step 2) The actuator are glued to the stack utilizing slots that match the
cross shape at the end of the actuators. (step 3) The stack is re aligned and cut in
the hugh resolution laser cutter. Releasing the body of the robot in 2-D. (step 4) The
body is folded into 3-D structure, using features similar to a pop-up book. (step 5)
The anisotropic friction legs are attached and glued to the robot using interlocking
features. Finally, 49 AWG wires are glued to the actuators using conductive epoxy
for electrical connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
xxi
4.11 SMARTI open loop experiments. (a) Photographic sequency during SMARTI
locomotion, the robot is able to move forward succesfully. However, with a clear
tendency to steer to the left. (b) Tracked position of the robot during the exper-
iment. (c) Lateral error of the robot in open loop, taking in account the robot
the robot should follow a straight path. The complete experiment can be found
in the supplementary movie SMARTI.mp4 (http://www.uscamsl.com/resources/-
Calderon thesis 2020/SMARTI.mp4) . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.12 SMARTI control strategy. (a) block diagram of the control scheme used for the
control experiments of SMARTI. The controller was desgied by lab mate and control
expert Ryan Bena. (b) Vicon camera obtain the yaw angle of the robot and compare
it to the desired trajectory. Modulating the duty cycles of the actuators to mantain
the robot in the desired path. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.13 SMARTI control experiment following a straight trajectory. (a) Photo-
graphic sequence of SMARTI. (b) Tracked path during the experiment, arrows show
the direction of the robot. (c) Lateral error plot. The complete experiment can
be found in the supplementary movie SMARTI.mp4 (http://www.uscamsl.com/-
resources/Calderon thesis 2020/SMARTI.mp4) . . . . . . . . . . . . . . . . . . . . . 72
4.14 SMARTI control experiment, turning right. (a) Photographic sequence of
SMARTI. (b) Tracked path during the experiment, arrows show the direction of the
robot. (c) Lateral error plot. The complete experiment can be found in the supple-
mentary movie SMARTI.mp4 (http://www.uscamsl.com/resources/Calderon thesis-
2020/SMARTI.mp4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.15 SMARTI control experiment, turning left. (a) Photographic sequence of
SMARTI. (b) Tracked path during the experiment, arrows show the direction of the
robot. (c) Lateral error plot. The complete experiment can be found in the supple-
mentary movie SMARTI.mp4 (http://www.uscamsl.com/resources/Calderon thesis-
2020/SMARTI.mp4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
xxii
Abstract
Animals in nature exhibit remarkable abilities that facilitate their survival. Millions of years of
evolution through natural selection have produced a variety of solutions to dierent problems,
which while not necessarily optimal, have already been proven to work. Humans have attempted
to imitate those abilities for hundreds of years. However, the fabrication capabilities required to
extract the bio-inspired ideas and convert them into functional objects have emerged only in the
last few decades. This improvement in fabrication capabilities has brought about the existence of
bioinspiration as a eld of research.
In this work, we developed the methods for the design, fabrication and control of a series of
bioinspired robots. First, we take inspiration from burrowing earthworms, which are animals that
can locomote through complex and intricate environments despite being limbless, and can even
create its own path by burrowing underground. We mimic the basics of their metameric bodies to
develop a pneumatic soft robot that is able to locomote inside pipes and other similarly shaped
environments. The internal coelomic
uid, radial and longitudinal muscles are translated into
articial muscles with internal air chambers and similar directional motion.
The expansion and contraction of the articial muscles which interact with the environment
generate the forces required for forward motion. We also designed and fabricated an articial skin
which allows the robot to detect geometry changes and forces applied by the environment. This
feature allows for the use of feedback control to improve locomotion. It also allows the robot to
discover its environment, which is an essential feature for future implementation in areas such as
search and rescue.
Second, We designed and fabricated
apping-wing micro air vehicles bioinspired by bees and
ies. Their capabilities to maneuver in the air and incredibly fast reaction times are extremely im-
pressive. The design and fabrication of elements such as frames, transmission, actuators and wings
xxiii
at this scale required sophisticated methods that we learned from the state of the art and improved
upon. We experimentally tested our rst 75-mg prototype via a hovering controlled experiment.
Biological studies suggest that a wing pitch rotation around 70
improves the performance of the
wing.
We designed and fabricated a non-linear stiness hinge which prevents the wings from over-
rotating (reaching angles over 70). We studied and compared the performance of the new hinge
with a classical hinge and showed that the wing was able to generate more lift force with smaller
apping angles. This enabled the design of a new prototype with smaller actuator displacement
requirements and could use shorter and lighter actuators. This new prototype, which is only 60
mg, was able to generate 10% more lift than the original prototype. Due to this decrease in weight,
the lift force to weight ratio was improved from 1.7 to 2.5. The robot was also tested in a control
hovering experiment and shown to be able to sustain
ight.
Last, the knowledge obtained by building soft and micro-robots allowed us to create a new robot
that is bio-inspired by inchworms. Inchworms are soft and small, which are the characteristic of
both previous projects mentioned. We designed and fabricated a novel 6 mg
exible SMA bending
actuator, which is able to produce considerable displacements (500 m) at 20 Hz. We used this
actuator in SMALLBug, a 30-mg
exible micro robot able to crawl on
at surfaces with speeds as
fast as 17 mm=s. The modular design of this robot was used to create a second 60-mg prototype
called SMARTI, which consists of two SMALLBugs in parallel. The conguration enables steering
capabilities, which were tested via control experiments where the robot followed prescribed paths
such as a straight line and two orthogonal straight lines that demonstrated its ability to turn left
and right.
xxiv
1 Introduction
Animals and plants have beneted from millions of years of improvements, thanks to evolution.
They increase their probability of survival by adapting and nding solutions through changing the
structures and functions of elements of their bodies. Humans have observed those solutions and
become inspired to create new technologies by mimicking nature's processes and materials: this is
called bioinspiration. The creation of bioinspired robotic systems designed by extracting principles
from animals allows us to recreate features that have already been proven to be successful. Also, this
provides understanding in the reverse direction where we can use the robots to learn about biological
systems by testing those features in a lab environment. One example of bioinspiration is the
generation of robotic systems using locomotion methods seen in animals such as crawling, swimming
and
ying. Another example is the invention of Velcro. George the Mistral rst conceptualized
the idea during a hunting trip, when he realized that burdock burrs (seeds) kept sticking to his
clothes and his dog's fur. After examining the seed under a microscope, he noted hundred of small
hooks on the surface that became attached to any surface with loops, such as clothing, animal fur,
etc. From this observation, he created the idea of Velcro, which uses one surface with hooks and
another with loops to stick to each other with easy reversibility. This example shows how curiosity
about nature can drive the creation of dierent man-made products.
The idea of extracting ideas from nature to create articial systems is not new. We can cite
Davinci's work aiming to create
ying machines inspired by bat wings during the 1500s. However,
bioinspiration as a eld started a couple of decades ago. The reason for this was the rise of new
design and fabrication processes that allowed the creation of such systems. An example of this is
mimicking the continuous and
exible movement of muscles, which was enabled by the development
of the soft robotic eld. This research eld introduced new design and fabrication paradigms to build
such systems using unconventional materials. Another example is the idea of creating systems at
1
the insect scale. The physics at this scale work dierently than at a macroscopic scale. For example,
friction plays a more critical role, making the implementation of elements such as rotational motors
and bearings practically useless. Also, the fabrication of elements at such small scale requires new
methods to make elements reliable and robust.
In this work, we used bio-inspiration from animals to design three types of robots. First, inspired
by the soft bodies of earthworms, we created soft robots able to locomote inside pipes, mimicking the
expansion and contraction of earthworm muscles and obtaining the forces required for locomotion
from the body-environment interaction. Second, inspired by
ying insects. We build
apping-
wing micro-robots able to sustain controlled hovering. Finally, with the knowledge obtained by
developing both technologies, we build a new system in between, a \
exible microrobot." In
order to do this, we developed a novel 6 mg high-frequency
exible SMA bending actuator. Then,
inspired by inchworm locomotion and using this new actuator mechanism, we designed SMALLBug,
a 30-mg
exible crawling robot, and SMARTI, a 60-mg steerable crawling robot composed of two
SMALLBugs in a parallel conguration. Next, we will introduce soft and micro-robotics in the
following subchapters.
1.1 Soft-Robots
The term \robot" comes from the Czech word \robota," which means \forced labor," and it was
rst used in a 1920 play R.U.R. (Rossum's universal robots) [4]. In the play, robots were not
electromechanical systems but humanoids with
esh and blood. They were envisioned to be far
superior to today's classical robot. Classical robots are designed to perform repetitive and dangerous
tasks. An example of this application is when robots work in assembly lines in factories. They can
assemble, paint, screw, etc. at a rate that no human could compete with. However, in order to
do this, they must always perform actions in a structured environment, which is a space that is
clearly and meticulously dened with no variability. When robots face the real world, which is an
environment that is in constant change, their performance is generally poor, which is a problem for
some applications. For example, when robots try to interact with humans, their erratic actions can
be dangerous because of the materials used for building the robots (metals and plastics). Indeed,
2
Figure 1.1: Diagram of the projects performed during the PhD. For soft robotics we developed
earthworm inspired robot, in parallel we developed FWMAV inspired in bees and
ies. The know-how
obtained during these two projects allowed us to create new "in between" technology:
exible micro robots.
Where using a
exible bending actuator we developed two inchworm inspired robotic crawlers.
There are documented accidents in factories such as the Ford accident in 1979 in which a worker
was killed by a robot [5].
On the other hand, in nature, most animal bodies are made of soft materials. For example, a
human's body is constituted by around 15% in mass of hard materials (bones) that are used for
structural purpose. The rest is soft tissue, including the moving parts (muscles). Soft robots is an
emerging eld using the paradigm of using unconventional materials (soft materials such as silicone
rubber) for the fabrication of robots, taking advantage of their compliance, which increases the
adaptability and robustness of the robots.
Soft robots will not replace classical robots. Instead, they are envisioned to be used in tasks
where classical hard robots are not suitable. An example of this would be picking an egg, which
can be a complicated task for hard robots since a feedback loop to control stress applied is required
with the information of force applied and area of contact. The dicult sensing requirements makes
this task complex in terms of hardware and calculations. Meanwhile, a soft robot such in [6] can
grab an egg with a single input and no feedback control, showing the capabilities of the use of
3
compliant materials. Other applications where soft robots exhibit excellent properties are in rescue
and exploration, such the robot in [7] that is able to withstand high and low temperatures, even
surviving a car running over the elastomeric legs of the soft robot. Finally. we can mention the
tentacle soft robot in [8] whose design and compliant properties enables the vision of safe human-
machine interactions in the future.
1.2 Micro-Robots
Micro-robots were rst envisioned in science ction, such as in the movie Fantastic Voyage (1966)
in which introduced the dream of performing surgery by traveling through the circulatory system.
Micro-robots can be the answer to many problems such as rescue, pollination, exploration, etc. To
do this, they must be able to face harsh conditions, including toxicity, radioactivity, rough terrains,
and constrained paths. In order to make these robots real, we require the development of dierent
topics of studies such as new materials, fabrication methods, actuation mechanisms, power sources,
and control. At this small scale regular paradigms used for macroscale robots do not work. For
example, friction play a more signicant role and traditional transmission methods will not work as
expected. Some answers to this have been the development of the smart composite microstructures
(SCM) method, which enables the use of carbon ber composites with high mechanical resistance
and light weight, electroactive materials such as piezoelectric ceramics which allow high precision
and high-frequency actuation, or the use of
exible joints for mechanisms that take advantage of
the restoring properties of materials such as Kapton at this scale.
1.3 Contributions of the dissertation
We specify the contributions achieved in each of the projects conducted:
Soft Robots Contributions
Development of the methods for the creation of multi-material multi-actuator soft systems.
The method uses the concept of pre-programming soft actuator systems via the addition of
internal multi-material structures that create anisotropic properties that allow for directional
motions, mimicking the directionality of natural muscles.
4
The creation of a fully soft pneumatic earthworm-inspired robot able to locomote inside pipes.
The locomotion is possible thanks to the use of articial muscles that mimic the elements of
an earthworm metamere, instead of radial and axial muscles. We use soft actuators for radial
and longitudinal deformations. The peristaltic wave passing through earthworms' bodies
is recreated via locomotion rules that activate the articial muscles to expand or contract.
Similarly to natural earthworms, the environment-body interactions (pipe-robot body) allows
forward motion.
Development of the methods for the creation of fully soft articial skin, which is able to
sense geometrical deformations and compressive forces using a single output signal. The
sensor contains internal channels lled with liquid metal creating an internal deformable
circuit. The electrical resistance of this deformable circuit varies when forces are applied
due to the generation of geometrical deformations in the sensor. We analyzed and model
how forces and deformation in specic directions changes the output response of the sensor.
Also, the method allows for changing the sensitivity range of the sensors via the addition of
grooves, which changes the area of contact with the input force, creating stress and strain
concentrations|all utilizing only one single layer of
exible circuit.
We implemented this new soft sensor into the earthworm-inspired soft robot for feedback
control. The sensor allows for sensing geometrical changes of the robot during the expansion
of the articial muscles. Also, it is able to detect the anchoring to the external environment,
allowing the robot to explore and discover its environment.
Micro Robots Contributions
Development of the fabrication methods (including recipes, processes, and equipment) needed
to build micro robots. We validated these methods by building a 75 mg
apping-wing micro-
robot. The robot was tested to perform hovering tests using control algorithms.
Development of a non-linear stiness hinge for the improvement of lift generation for the
apping-wing microrobot. The design consists of a micro passive hinge design that avoids
overrotation of the wings during
apping. We use micro force sensors to test and compare
the lift force generation to that of the previous hinge design.
5
The results obtained for the new hinge mechanism enabled the creation of a 60 mg
apping-
wing microrobot. The new robot had smaller actuator de
ection requirements to generate
enough lift force. This allowed for the use of shorter and lighter actuators, which considerably
decreased the weight of the robot. The new robot achieved a maximal force of 147 mg and
was able to perform control hovering.
Flexible Micro Robots Contributions
Creation of a novel
exible high-frequency SMA bending actuator. The know-how and meth-
ods developed during both projects mentioned previously were synthesized to create
exible
micro technology. We use thin SMA wires and a carbon-ber structure, which is used as a
spring, to produce directional motions at a micro-scale. The actuator is only 6 mg and can
even produce around 500 m deformations at 20 Hz, which is a signicant result since SMA
based actuators are typically known for being slow (frequencies <1Hz).
The new
exible micro actuation technology allowed us to create SMALLBug, a 30-mg mi-
crorobot able to crawl over
at surfaces. The microrobot is able to crawl using dierent
actuation frequencies showing dierent locomotion gaits across a range of frequencies. The
maximal speed was found at 20 Hz, where the forward speed was 1.4 bl/s.
Development of SMARTI, a 60-mg micro-robot composed of two SMALLBugs in parallel
conguration. The steerability is a result of actuating one of the SMALLBugs units to move
with a higher velocity than the other, generating a dierential eect. The robot was tested
not only to perform steering but also to locomote along predened paths using a control
algorithm. SMARTI was tested to follow straight lines and to turn 90
in both the right and
left directions.
1.4 Dissertation Structure
This dissertation is structured in the following manner: chapter 2 details the research related
to the development of soft robots, where we created a multi actuator-sensor robot bio-inspired by
earthworms able to crawl inside pipes. Chapter 3 details the design and fabrication of a bee-inspired
apping FWMAV able to produce controlled hovering, including the design of a new micro hinge
6
mechanism for the improvement of lift force generation. Chapter 4 explains the work on
exible
microrobots, where a novel bending actuator is created and implemented in two inchworm-inspired
crawling robots. Finally, conclusions and future work are discussed in chapter 5.
7
2 New Multi-Material Soft Transducers for Developing
Earthworm-Inspired Soft Robots
2.1 Motivation
Earthworms are simple-shaped invertebrates, yet they exhibit an ample repertoire of motor behav-
iors and navigation skills. Earthworm's body shape allows them to dig and burrow underground
while also crawling above ground. Exhibiting sophisticated locomotion capabilities as they maneu-
ver inside intricate cavities, pass through narrow passages, and climb inclined and vertical rough
surfaces.
Instead of limbs, these animals employ hydrostatic tubular structures, powered by radial and
longitudinal muscles, to geometrically transform and dynamically adapt, while transmitting forces
to the environment. Dynamic responses are induced by retrograde peristaltic waves, produced
by the relaxation and contraction of longitudinal and segmented circular muscles, thus generating
coordinated axial and radial deformations of the animals' metameres [9{12]. This type of dynamic
response enables worms to move eectively in unstructured environments such as burrows, plowed
lands, trees and convoluted pathways [9,13].
Animal locomotion simultaneously enables and requires the acquisition of information from
the environment, a task performed by the animals' sensory nervous systems. Since earthworms
are blind and deaf, they rely on highly perceptive internal hydrostatic structures and skins to
function. Their body structures have evolved to sense mechanical variables such as pressure and
vibrations [9,10,14{17], and their skins to detect chemicals, light and touch [16{18]. These sensory
systems are essential components of the neural feedback loops that produce the wide gamut of body
responses and adaptive behaviors observed in earthworms. Namely, food foraging, chemical sensing
of soils, mate selection, re
exive avoidance of predators, burrowing and above-ground navigation;
8
Figure 2.1: Natural and articial worms. (a) Illustration showing the peristalsis-based locomotion of
an earthworm during burrowing. The inset shows an enlarged segment composed of radial muscles (in blue)
and longitudinal muscles (in dark brown). (b) Robotic worm type 1 (RWT1). [1] (c) Robotic worm type 2
(RWT2).
relatively simple behaviors that can serve as inspiration for the creation of the control primitives
required for the devolvement of fully autonomous soft robots capable of operating and surviving in
complex environments.
In this work, we introduce a new soft robot that integrates elements inspired by the locomotion
mechanisms and sensory systems of earthworms, developed upon state-of-the-art multi-material soft
technologies [19]. The realization of conceptual designs into physical systems that integrate soft
actuation and soft sensing is achieved through rapid prototyping techniques based on 3D-printed
molding, casting of curable liquid silicone and soft lithography [20, 21], thus, continuing the work
we presented in [1,22].
From the perspective of actuation for locomotion, the research in this work extends recent
advances in pneumatically-driven in
atable structures. Ideas and methods are drawn from: [23],
which presents a multi-gait highly-
exible pneumatically-driven walking soft robot; [8], which de-
scribes a biologically-inspired robotic limb able to replicate the movements of an octopus' tentacle;
and [24{28], which introduce multi-material actuators, pre-programmable to deform in specied
9
directions, constrained by the geometry of internal cavities and material composition of the soft
structure. This notion of soft-material-based structural pre-programmable dynamic behavior is a
key element of the proposed approach to mimic the fundamental features of worm actuation. In
contrast, previous research attempts at replicating worm locomotion have mostly relied on rigid ac-
tuation techniques [29]. For example, the prototypes described in [12,30,31] employ shape-memory
alloys (SMAs), the device in [32] utilizes a hard actuator driven by magnetic
uids, the crawlers
in [13,33,34] employ electric motors, and the semi-soft robots in [35,36] are actuated by semi-rigid
pneumatic actuators.
Several studies of earthworm locomotion have been already performed. Simulations and ex-
periments with prototypes aiming for gait optimization have used dierent methods for control,
such as: adaptive control [37], gait generation and optimization [38], [39], intersegmental coordina-
tion [40], [41], etc. Theoretical ndings show that the addition of contact feedback (skin sensing)
can improve the eciency, speed and consistent forward movement [42]. A robot with these ca-
pabilities is also built in [43], but limited by a semi-rigid body and relying in regular motors with
integrated sensors.
The perceptive articial skin introduced in this work is composed of deformable electric circuits,
fabricated employing the technology in [44{48] that has enabled the development of pressure and
strain sensors made of stretchable micro-channels lled with conductive liquid metal eutectic alloys
(EGaIn
1
and Galinstan
2
). The proposed control and signal processing algorithms are an extension
of the approach in [49], which is one of the rst works to combine soft robotics and feedback control.
To generate sensor designs compatible with the synthesis and implementation of tactile-perception-
based feedback controllers, here we introduce a data-driven approach to sensor modeling.
Extensions of the ideas and results presented in this work can help create a wide variety of
mechatronic systems, including autonomous robots for internal pipe inspection, millirobotic assis-
tive tools for cardiac and gastrointestinal surgeries that would extend the methods in [28,33,34,50],
and even microrobots capable of navigating inside the human body's circulatory and digestive
systems to perform microsurgical or pharmacological tasks, as imagined by some science ction
writers [51].
1
Eutectic Gallium-Indium.
2
Gallium-Indium-Tin.
10
The rest of the section is organized as follows. Section 2.2 discusses earthworm-inspired sensing
and locomotion for soft robotic development, Section 2.3 describes the proposed robot's design
and fabrication methods, Section 2.4 presents the mechanical characterization of the system, and
Section 2.5 the locomotion planning and control algorithms. Lastly , experimental results are
presented and discussed in Section 2.6.
2.2 Earthworm-Inspired Sensing and Locomotion
Earthworms' metameres connect to each other in series as shown in Fig. 2.1-(a). Each metamere
contains similar components of all the animal's major organ systems, embedded in a structural
muscle chamber lled with liquid, known as a coelomic compartment [52]. Each compartment
contains a sealed constant amount of liquid and forms part of a serial structure referred to as
a hydrostatic skeleton. Despite the name, these structures are
exible and deformable due to the
action of circular and longitudinal muscles, depicted in blue and dark brown in Fig. 2.1-(a). Because
a liquid's volume remains constant at constant temperatures and pressures, in hydrostatic skeletons,
contraction of the longitudinal muscles causes a metamere to shorten, whereas contraction of the
circular muscles causes a metamere to lengthen and become thinner (see Fig. 2.1-(a)).
The segmented muscle-action pattern in metameric congurations is what enables worms to
generate the alternating body waves of contractions and elongations observed during crawling and
burrowing. Some biologists have argued that the evolution of hydrostatic skeletons composed of
separate metameres greatly increased the eciency of the worm's dynamics [9], because the force
of local muscle contraction within one segment is not transferred and dampened along the length of
the animal. Also, earthworms' skins have small bristle-like rods, called setae, used during crawling
and burrowing to anchor parts of the body to the ground or surrounding soil. These bristles are
necessary because the epidermises of earthworms' skins evolved to minimize friction to prevent
abrasion during burrowing.
Earthworms employ two distinct modes of locomotion: crawling above ground and burrowing
under ground. Fig. 2.1-(a) depicts the mechanisms specic to burrowing taken as inspiration in the
design process of the proposed robots. Here, we dene a stride as the cyclical kinematic process that
occurs between two consecutive identical geometrical congurations of the worm-burrow system, or
11
equivalently, one cycle of peristalsis. This is an idealization for the purposes of analysis, in which
two congurations are considered identical if in both of them, the same segments are anchored
or detached, regardless of other physical variables. This denition is analogous to that of the
human case, in which a stride equals one complete cycle of a leg, or two steps. In the biological
literature [11], the kinematics of peristalsis-based crawling and burrowing are described as functions
of four variables: stride length, the distance traveled by the rst worm's segment during a cycle;
protrusion time, the amount of time in a cycle during which the rst worm's segment is moving
forward; stance time, the amount of time in a cycle during which the rst worm's segment remains
anchored to the ground or burrow; and stride period, the sum of the protrusion time and stance time.
This is the model adopted for locomotion planning and control synthesis, discussed in Section 2.5.
In the design of soft robots intended to travel inside narrow spaces, tunnels or pipes, burrowing
has several advantages over other locomotion methods. Most notably, the interactions of the
robot's soft structures with the rigid surroundings can be directly used to passively generate some
of the actions that form a stride. Similarly, worm-inspired tubular
exible structures are inherently
compliant, and therefore, they can adapt to sudden variations of the locomotion paths. However,
our proposed approach to robotic design can be extended to the creation of a wide variety of
compliant soft robots and not only to burrowing worm-like systems. This is the rst step in
the development of segmented congurations made of modular identical soft units with an inherent
robustness against accidents and component failure, and an intrinsic capability for recongurability
and versatility.
Here, we introduce two kinds of earthworm-inspired pneumatically-actuated soft robots. The
rst type corresponds to the rst generation of development, designed to emulate the kinematic and
dynamical behaviors of worms, and controlled employing the internal air pressures of the composing
soft actuators. This prototype, denominated RWT1
3
, is shown in Fig. 2.1-(b). The second type
corresponds to the next generation of development in which the locomotion mechanics, sensing
methods and controllers are all biologically inspired. In this second case, the sensors utilized in
the implementation of the control loops are embedded in the outer layers that wrap two sections
3
Robotic worm type 1.
12
Table 2.1: Dimensions of the relaxed prototypes RWT1 and RWT2. As can be seen in Fig. 2.1-(b)
and Fig. 2.1-(c), both prototypes are roughly cylindrical with a total length L
R
and diameter D
R
(see
Step 4 of Fig. 2.2-(c)). The length of each individual radial actuator is L
RA
. The average wall-thickness of
the soft components is W
R
.
Prototype L
R
D
R
L
RA
W
R
RWT1 (controlled using air-pressure feedback) 130 mm 35 mm 25 mm 2 mm
RWT2 (controlled using perceptive articial skin) 93 mm 29 mm 24 mm 2 mm
of the robot, thus forming a mechanically perceptive articial skin. This prototype, denominated
RWT2
4
, is shown in Fig. 2.1-(c).
2.3 Robotic Design and Fabrication
RWT1 is composed of three articial muscles: front and back radial actuators and a central axial
actuator. From the biologically-inspired engineering perspective, RWT1 replicates the functional
capabilities of an earthworm's single metamere, illustrated between blue rings in Fig. 2.1-(a)
5
. The
axial actuator, shown as part of the whole robot in Fig. 2.1-(b) and during a mechanical test in
Fig. 2.3-(a), is driven pneumatically and emulates the features of earthworms' longitudinal muscles.
This structural conguration allows for linear axial extensions and shortenings as functions of the
internal air pressure, while preserving, to a signicant extent, the radial dimension. A radial
actuator, shown as part of the whole robot in Fig. 2.1-(b) and during a mechanical test in Fig. 2.1-
(a), replicates the features of earthworms' circular muscles. This structural conguration allows
for radial expansions and contractions as functions of the internal air pressure, while preserving, to
some extent, the axial dimension.
In the conceptual robotic design of RWT1, the main purpose of the back and front actuators is
to anchor the robot to the surrounding terrain (in this case, the internal surface of a pipe), while
the axial central actuator enables the controlled extensions and shortenings of the robot during
locomotion. The proposed articial muscles mimic the mechanical functions of natural muscles,
but their underlying mechanisms are fundamentally dierent. Natural muscles are incapable of
4
Robotic worm type 2.
5
This is a simplied description of the muscle anatomy of an annelid segment. In reality, circular muscles slide
along longitudinal muscles, constrained within a shared cylindrical volume [15]. Thus, the robotic prototype in
Fig. 2.1-(b) can be also thought of as two articial metameres in series with two independent circular actuators and
a shared central longitudinal actuator.
13
Figure 2.2: Fabrication method. The fabrication uses 3D-printed acrylonitrile butadiene styrene (ABS)
molds, silicone elastomer (Eco
ex
R
00-50 and 00-30, Smooth-On), butadiene rubber elastomeric o-rings,
sheets of berglass and pneumatic components. The total process consists of four parts, each consisting of
several steps. (a) Fabrication of a radial actuator: The actuator is fabricated in seven steps. First, the two
halves of the actuator are cast employing 3D-printed molds. Then, the front and rear faces of the actuator
are sealed with berglass net caps. Once the caps are bonded and the actuator is sealed, the fabrication of
the radial actuator is completed. (b) Fabrication of the axial actuator: The procedure is similar to that of
a radial actuator, except for Step 6 in which butadiene o-rings are tted into patterned grooves to constrain
the radial deformation and pre-program the axial responses of the system. (c) Final assembly: Two radial
actuators, an axial actuator and three helical air feeding lines are integrated into a single functional body.
The helical shape of the air tubes is a critical design feature that allows the extension and shortening of
the soft actuator. (d) Articial skin fabrication and integration: Two layers of silicone are combined into
a single piece that contains an internal meandered channel to be lled with Galinstan. The layers are
produced employing engraved 3D-printed molds (Step 1) and bonded by spin-coating the top layer with
uncured silicone (Step 2). Then, Galinstan is injected with a syringe (Step 3) and once the channel is lled
the sensor is complete (Step 4). An additional silicone layer is fabricated from a patterned mold (Step 5),
then attached to the sensor using spin-coating. The sensor is wired and its end are sewn together. It is
then wrapped around the corresponding radial actuator (Step 6), completing the entire process. [1]
elongating actively, so deformation is always produced by active contraction [53]. Therefore, in the
natural case, the word relaxation is typically used as a synonym for passive elongation. In contrast,
the soft actuators composing the robots presented here expand actively and contract passively,
and therefore, in the cases of prototypes RWT1 and RWT2, the word relaxation is employed as a
synonym for passive contraction.
From the actuation and functionality perspectives, RWT2 is essentially identical to RWT1.
From the sensor and real-time control perspectives, RWT2 is radically dierent from RWT1, since,
as can be seen in Fig. 2.1-(c), RWT2 is built with sensors embedded in the skin of its back and front
14
radial actuators. The fabrication methods and construction sequence of both robotic prototypes
are graphically described in Fig. 2.2. Here, the processes in Figs. 2.2-(a), 2.2-(b) and 2.2-(c) pertain
to both RWT1 and RWT2, and the process in Fig. 2.2-(d) pertains solely to RWT2. Figs. 2.2-(a)
and 2.2-(b) illustrate the casting processes employed to fabricate the radial and axial actuators,
respectively. The fabrication methods for both types of actuators use 3D-printed acrylonitrile
butadiene styrene (ABS) molds, silicone elastomer (Eco
ex
R
00-50, Smooth-On), butadiene rubber
o-rings, sheets of berglass and pneumatic components. The nal prototype RWT1, shown in Step 4
of Fig. 2.2-(c), is 130 mm in length and 35 mm in diameter, with an approximately constant wall-
thickness of all the components of 2 mm. These dimensions were chosen empirically in order to
create a robot easily testable in laboratory conditions using o-the-shelf transparent pipes. Further
details of the fabrication of the actuators and assembly can be found in [1].
The fabrication process of the second prototype, RWT2, has an additional stage shown in
Fig. 2.2-(d), required to add perceptive articial skins to the outer layers of both radial actuators.
The fabrication of the tactile receptors composing the articial skins is based on the process de-
scribed in [46], which consists of the rst ve steps depicted in Fig. 2.2-(d). The process starts by
casting curable liquid silicone into 3D-printed molds to create two complementary patterned layers
of cured silicone elastomer that, after being adhered, congure a meandered continuous micro-
channel with a square cross-sectional area and side length of approximately 500 microns. Then, as
illustrated in Step 3 of Fig. 2.2-(d), the micro-channel is lled with Galinstan to create a stretchable
resistive electrical circuit, as shown in Step 4 of Fig. 2.2-(d), whose response can be calibrated to
measure strain and mechanical pressures (tactile signals). During the development of RWT2, it
was observed that for the purposes of locomotion control inside a pipe, the functionality, resolution
and accuracy of the robot's articial skins were increased by adding thin patterned silicone layers
to their outer surfaces. The fabrication of one of these patterned layers is illustrated in Step 5
of Fig. 2.2-(d), showing a simple grooved design to amplify the pressure sensitivity of the sensor.
Finally, once the sensors are wrapped and adhered around the radial actuators, as shown in Step 6
of Fig. 2.2-(d), actuator deformation and external pressures can be measured simultaneously. In
this conguration, when the diameter of a radial actuator varies, the corresponding sensor expands
or relaxes, sensing strain. During locomotion, actuator deformations exert mechanical pressures on
the surroundings, which can also be measured by the sensing conguration in Fig. 2.2-(d).
15
The functionality of the stretchable sensors employed in the construction of articial skins can
be understood from rst principles. If the sensor is tensioned, it lengthens along the axis of tension.
Similarly, if the sensor is compressed, it contracts along the axis of compression. In both cases,
the material deforms in the other directions according to its Poisson's ratio. The 3D geometry of
the internal liquid metal is varied, varying also the average cross section of the conductive path,
and consequently, the total electrical resistance of the circuit. This change can be estimated from
simple topological and geometrical considerations as
R
l
c
+ l
c
(w
c
+ w
c
)(h
c
+ h
c
)
l
c
w
c
h
c
; (2.1)
where R is the variation of the total electrical resistance due to geometrical variations of the
sensor, is the resistivity of the Galinstan, l
c
is the total length of the meandered conductive
path, and w
c
and h
c
are the average width and height, respectively, of the meandered channel.
Accordingly, l
c
, w
c
and h
c
are the changes in total length of the conductive path, and average
width and height of the channel, respectively [46]. Thus, a variation in any of the dimensional
variables (l
c
, w
c
, h
c
) changes the total resistance of the liquid circuit, a phenomenon that with
proper calibration can be used to measure strain and pressure.
In principle, from the one-dimensional form of R, it follows that, without specic information
about the experimental situation, the sensor can be calibrated to measure only one scalar variable
at a time. However, in this work, employing information about the actuators' geometry and robot-
environment interactions, we use a single sensor per radial actuator to measure strain and detect
pressure variations on RWT2's articial skins. These variables are fedback into the algorithms
that run the robot's locomotion control, as discussed in Section 2.5. The proposed sensing scheme
is capable of measuring variations in strain and detecting touch, while animals' skins can sense
multiple stimuli in a distributed manner. The creation of more complex articial skins is a matter
of current and further research.
2.4 System Characterization
In general, real-time implementation of robust locomotion strategies requires obtaining complete
dynamic models of the robots to be controlled. Typically, system models for controller design
16
Figure 2.3: Characterization of the axial actuator. (a) Axial actuator during characterization exper-
iments. [1] (b) Experimental strain{pressure curves associated with the axial actuator. The vertical bars
indicate the magnitudes of the experimental standard deviations with number of trials n=6.
are derived from rst principles or through a process of system identication. Here, considering
the low actuation frequency of the robotic prototypes during operation, we adopt a dierent ap-
proach. Thus, instead of nding complete dynamical descriptions, we characterize the system's
actuators and sensors separately, employing quasi-static experiments. As examples, we present the
characterizations of RWT1's actuators and RWT2's sensors.
2.4.1 Characterization of RWT1's Actuators
In open loop, the dynamics of the robot's three actuators are essentially uncoupled; therefore,
they are characterized independently. An experimental test for the characterization of the axial
actuator is shown in Fig. 2.3-(a) and the associated strain{pressure curve is shown in Fig. 2.3-(b).
Similarly, an experimental test for the characterization of a radial actuator is shown in Fig. 2.4-(a)
and the associated strain{pressure curve is shown in Fig. 2.4-(b). In these experiments, the strain{
pressure curves are obtained by measuring a set of static points of pressure and deformation in
cycles of increasing{decreasing pressure. To obtain each data point, the internal actuator pressure
is regulated and measured employing a pneumatic assembly composed of a relief solenoid valve (12-
V/4-psi generic) in series with a pressure pump (12-V ROB-10398) and a digital serial silicon sensor
(Honeywell ASDX), whose output is sent to an Arduino
R
Mega board used for data acquisition
and signal processing. The other entry of each data point (static strain of the tested actuator) is
simply measured with a caliper. For each actuator, the measurement cycles are repeated six times.
17
Figure 2.4: Characterization of the radial actuator. (a) Radial actuator during characterization
tests. [1] (b) Experimental strain{pressure curves associated with the radial actuator. The vertical bars
indicate the magnitudes of the experimental standard deviations with number of trials n=6.
In the characterization of the axial actuator (Fig. 2.3), each test cycle is composed of 13
expanding-direction static data points and 13 relaxing-direction static data points. As can be
seen in Fig. 2.3-(b), the static air pressure is increased in increments of approximately 0.1 psi from
1.3 psi to 2.6 psi, and then, decreased in decrements of 0.1 psi from 2.6 psi to 1.3 psi. In Fig. 2.3, the
relaxed length of the actuator is 80 mm, reaching a maximum elongation of 106 mm (an expansion
of 33 %) at 2.6 psi. The radial expansion of the axial actuator is not shown, as it is negligible
compared to the axial deformation. In Fig. 2.3, the actuator exhibits a small but non-negligible
hysteretic behavior and each strain data point exhibits a signicant experimental variance.
In the characterization of the radial actuators (Fig. 2.4), each test cycle is composed of 19
expanding-direction static data points and 19 relaxing-direction static data points. As can be seen
in Fig. 2.4-(b), the static air pressure is increased in increments of approximately 0.1 psi from 1.3 psi
to 3.1 psi, and then, decreased in decrements of approximately 0.1 psi from 3.1 psi to 1.3 psi. In
Fig. 2.4, the relaxed diameter of the actuator is 40 mm, reaching a maximum size of 62 mm (an
expansion of 87 %) at 3.1 psi. While the axial actuator does not deform noticeably in the radial
direction, the radial actuator deforms signicantly in both directions. Also, similar to the axial
actuator case, from Fig. 2.4-(b) it can be inferred that the radial actuator exhibits hysteresis and
each deformation data point shows a non-negligible experimental variance, which indicates the need
for feedback control in the implementation of locomotion strategies.
18
2.4.2 Characterization of RWT2's Sensors
The proposed robot's locomotion mode requires the periodic expansion and contraction of the
central axial actuator, and the synchronized periodic anchoring and unanchoring of the radial
actuators to the internal surface of the pipe. As discussed in Section 2.5, in order for the robot
to move its center of mass consistently in a desired direction (forward or backward), at least one
of the two radial actuators must remain attached to the pipe at all times. In this scheme, the
soft-sensor-based perceptive skins of prototype RWT2 operate in two distinct functional states,
which are depicted in Fig. 2.5.
In the rst state, the corresponding radial actuator is not in contact with the pipe's surface.
Thus, as the actuator's radius expands, the wrapped soft sensor stretches freely along the l-
dimension, as illustrated in Fig. 2.5-(a) and Fig. 2.5-(b). Consequently, we say that the sensor
is in the tension state, modeled as shown in Fig. 2.6-(a). In the second state, the corresponding
radial actuator is anchored to the pipe by friction as the actuator presses against the pipe's inter-
nal surface, as depicted in Fig. 2.5-(c). In this condition, the sensor is homogeneously compressed
along the h-dimension, as illustrated in Fig. 2.6-(b). Accordingly, we say that the sensor is in the
compression state. Note that when the sensor is in the compression state, the tension along the
l-dimension is positive and approximately constant. In both states shown in Fig. 2.5, the sensor's
geometry is dierent from that in the relaxed condition, which implies that the electrical resistance
of the sensor's liquid circuit is also dierent from that in the relaxed state.
Here, we show that the external perimeter of a radial actuator can be accurately measured
when the sensor is in the tension state (Fig. 2.5-(a) and Fig. 2.5-(b)) by experimentally nding
the relationship between length and resistance variation predicted by (2.1). Also, we show that
the sensor can be employed to measure compression in the conguration depicted in Fig. 2.5-(c).
Furthermore, the proposed sensor's patterned layer (Fig. 2.2-(d) and Fig. 2.5) enables the reliable
detection of transitions between the tension and compression states by increasing the sensitivity of
the mapping that relates resistance variation and mechanical load.
In order to nd mathematical relationships between strain and resistance variation in the ten-
sion state (Fig. 2.5-(a) and Fig. 2.5-(b)), and between resistance variation and total load in the
compression state (Fig. 2.5-(c)), we employ heuristic models with experimentally-identied param-
19
Figure 2.5: Functional states of RWT2's soft sensors during operation. (a) & (b) Before at-
tachment, a radial actuator expands freely and the corresponding soft sensor elongates along the
^
l-axis
as idealized in Fig. 2.6-(a). In this situation, we say that the sensor is in the tension state. (c) After
attachment, a radial actuator can no longer expand, constrained by the internal surface of the pipe. In
this situation, we say that the sensor is in the compression state. In this state, the tension force exerted on
the sensor remains constant, and therefore, all further variations on the electrical resistance of the sensor
are due to compression forces, modeled as shown in Fig. 2.6-(b). The sensor depicted in this gure has a
patterned upper surface, corresponding to the nal design employed in the fabrication of RWT2, shown in
Fig. 2.2-(d).
Figure 2.6: Idealized depiction of the sensor's experimental tension and compression states.
(a) In tension, forces with opposite directions and magnitudesF
l
are applied along the axis
^
l to produce an
elongation l. This conguration is employed in the tensile experimental tests discussed in this work. (b)
In compression, forces with opposite directions and magnitudes F
h
are applied along the axis
^
h to produce
a contraction h. This conguration is employed in the compression experimental tests discussed in this
work.
eters. First, we consider the case of simple
at sensors strained by tension along the l-dimension,
as shown in Fig. 2.6-(a), and
at sensors under compression along the h-dimension, as shown in
Fig. 2.6-(b). This modeling process is further informed and enhanced by simulations based on nite
element analysis (FEA) to explain the eect of the grooved pattern on the sensor's response during
compression.
The basic models and analyses of the sensors used in RWT2 are based on the Mooney{Rivlin
formulation [54, 55], which is used to describe hyperelastic isotropic incompressible rubber-like
20
materials [56{58]. This modeling method is derived from the notion of strain energy density function
(with units of J m
3
= N m
2
), dened as
W =C
1
I
1
3
+C
2
I
2
3
; (2.2)
where
I
1
and
I
2
are the rst and second invariants of the unimodular component of the left Cauchy-
Green deformation tensor [55], andC
1
areC
2
are constants to be found empirically. As explained in
[57],
I
1
and
I
2
can be expressed as functions of the principal non-dimensional stretches,f
1
;
2
;
3
g,
namely
I
1
=
2
1
+
2
2
+
2
3
; (2.3)
I
2
= (
1
2
)
2
+ (
2
3
)
2
+ (
1
3
)
2
: (2.4)
We assume that the force distributions acting on the sensors are perfectly decoupled and uni-
directional, as depicted in Fig. 2.6. Thus, the Cauchy stress along the rst principal direction is
given by
1
=
1
@W
@
1
: (2.5)
Also, the incompressibility and isotropy assumptions of the Mooney{Rivlin formulation imply that
1
2
3
= 1, from which we can derive the approximations
2
1
2
1
and
3
1
2
1
that allow us
to write
1
1
@
@
1
C
1
2
1
+
2
1
3
+C
2
2
1
+
1
2
1
3
= 2
C
1
+
C
2
1
2
1
1
1
: (2.6)
Thus, directly from (2.6), the corresponding engineering stress can be estimated as
1
=
1
1
2
C
1
+
C
2
1
1
1
2
1
; (2.7)
21
Figure 2.7: Stress-strain curves for the sensor in tension and compression. (a) For the sensor
in the pure tension state depicted in Fig. 2.5-(a) and Fig. 2.5-(b), the experimentally-tuned Mooney{
Rivlin model matches almost perfectly the experimental data. The FEA-based simulation replicates the
qualitative relationship between engineering stress and strain. (b) For the sensor in the pure compression
state depicted in Fig. 2.5-(c), the experimentally-tuned Mooney{Rivlin model matches almost perfectly the
experimental data. The FEA-based simulation matches almost perfectly the experimental data for strains
smaller than 0:04 and replicates the qualitative relationship between engineering stress and strain for larger
strain values.
which is the relationship for which we experimentally estimate C
1
and C
2
in order to understand
the behavior of the dierent sensing congurations discussed in this work.
To simplify the analysis of the sensors, we assume that the tension state can be represented
by the idealization in Fig. 2.6-(a), i.e., there is a single unidirectional force distribution along the
l-dimension. Similarly, we assume that the compression state can be represented by the idealization
in Fig. 2.6-(b), i.e., a single unidirectional force distribution along the h-dimension. This assump-
tion is reasonable because in compression, the sensor output is dominated by the in
uence of the
force distribution along the h-dimension and the tension along the l-dimension is constant and
signicantly less important. For the analysis and simulation of the tension state, we set
1
=
l
,
2
=
h
and
3
=
w
, where
l
=
l + l
l
;
h
=
h + h
h
;
w
=
w + w
w
: (2.8)
In accordance with the denitions in Fig. 2.6, l, h and w are variations of the dimensions l,
h and w. For the analysis and simulation of the compression state, we set
1
=
h
,
2
=
l
and
3
=
w
, with
h
,
l
and
w
given by (2.8).
In a rst modeling approach, we assume that the liquid electrical circuits embedded in the
rubber material deform according to the same stretch ratios as those of the silicone. Thus, using
22
Figure 2.8: Resistance variation as a function of total load (upper plots) and strain (bottom
plots) for the sensor in tension and compression. (a) & (b) The rst-principles models of both
the resistance{load and resistance{strain relationships, derived from (2.9), capture the main trends but do
not quantitatively match the experimental data. The heuristically-corrected model is obtained by solving
the optimization problem in (2.13). (c) & (d) The rst-principles models of both the resistance{load
and resistance-strain relationships, derived from (2.10), fail to capture the main trends displayed by the
experimental data. The heuristically-corrected model is obtained by solving the optimization problem in
(2.14). Note that the curve of the relationship betweenF
h
and R
h
has an almost-
at section (F
h
< 10 N).
(2.1), we obtain that for the
at sensor in the tension state, the relationship between resistance
variation and rubber deformation can be estimated as
e
R
l
=
l
c
w
c
h
c
2
l
1
: (2.9)
Similarly, we obtain that for the
at sensor in the compression state, the relationship between
resistance variation and rubber deformation can be estimated as
e
R
h
=
l
c
w
c
h
c
1
h
1
: (2.10)
23
To nd the relationship between
1
=
l
and
1
=
l
associated with the tension state, and
between
1
=
h
and
1
=
h
associated with the compression state,C
1
andC
2
are identied using
data from force{deformation tests, by solving the least-squares (LS) problem
min
C
kA
C
C +B
C
k
2
2
; (2.11)
whereC =
C
1
C
2
T
,A
C
2R
N2
with itsith row given byA
C
(i; :) =
1
(i)
2
1
(i)
2 2
1
1
(i)
andB
C
2 R
N1
with its ith entry given byB
C
(i) =
1
(i), i =f1; ;Ng. The parameter N
indicates the number of data points employed to solve (2.11). Data is collected using an Instron uni-
versal testing machine 5942 (IUTM 5942), capable of replicating the forces exerted on the sensor
during locomotion, in both the tension and simplied compression states, as illustrated in Fig. 2.6.
The tension state is reproduced by performing a tensile test on the sensor at a displacement rate of
3 mmmin
1
with a maximum elongation of 30 mm along thel-dimension. Similarly, the simplied
compression state is reproduced by performing a compression test on the sensor at a force rate of
5 N min
1
with a maximum compression force of 20 N along the h-dimension. Here, N = 2361
for the compression test and N = 4503 for the tension test.
The parametersC
1
andC
2
for the model in (2.7), estimated for both the tension and compression
states, are used in the implementation of the FEA-based simulations executed by the NX Nastran
software package. Fig. 2.7-(a) compares the empirical engineering stress{strain (
l
;
l
) curve to those
produced with the Mooney{Rivlin formulation and through FEA simulations, for the
at sensor
of Fig. 2.6 in the tension state. Similarity, Fig. 2.7-(b) compares the empirical engineering stress{
strain (
h
;
h
) curve to those produced with the Mooney{Rivlin formulation and through FEA
simulations, for the
at sensor of Fig. 2.6 in the simplied compression state. In both gures, the
heuristic model matches the experimental data almost perfectly and the FEA simulation matches
both of them reasonably well. This comparison indicates that, in this case, the LS-estimated
Mooney{Rivlin model described by (2.7) captures the essential characteristics of the relationship
between engineering stress and strain.
During both types of displacement{force tests, the electrical resistances of the sensors' liquid
circuits are indirectly measured using a voltage divider circuit and Ohm's laws. The signal pro-
cessing is performed using an Arduino
R
UNO running at a sampling rate of 120 Hz. The plots in
24
Figure 2.9: Sensors geometries and their experimental resistance{load curves. (a) Flat sensor.
(b), (c) & (d) Patterned sensors with 75 %, 50 % and 25 % of their surfaces protruded, respectively. (e) The
data come from experiments in which the sensors are compressed along the h-dimension as illustrated in
Fig. 2.6-(b). It can be observed that the sensitivity of a patterned sensor increases if its protruded surface
is decreased according to the specic patterns
Figure 2.10: FEA-based simulations comparing the strain distribution of a
at sensor and a
50 %-protruded sensor under a homogeneous load of 1 N. (a) This plot shows that, for a ho-
mogeneous load, the
at sensor deforms approximately homogeneously. (b) This plot shows that, for a
homogeneous load, the patterned sensor displays areas of strain concentration. This phenomenon quali-
tatively explains the experimental data in Fig. 2.9-(e), as areas of strain concentration can signicantly
decrease the cross-sectional areas of the embedded liquid wires, thus greatly increasing the total electrical
resistance of the sensor.
Fig. 2.8 compare experimentally-obtained and model-based graphs of the sensor's resistance vari-
ations induced by the sensor's deformations along the l-dimension in tension and h-dimension in
compression. Fig. 2.8-(a) shows the relationship between the resistance variation, R
l
, and mea-
sured total mechanical load, F
l
=
l
wh, for the sensor in tension. In this case, the model-based
curve is found in four steps: F
l
is instantaneously measured with the IUTM 5942; the engineering
stress is estimated as
l
= F
l
(wh)
1
; the stretch
l
is estimated by employing (2.8); using the
estimated
l
, R
l
is computed by employing (2.9). Similarly, Fig. 2.8-(b) shows the relationship
between strain,
l
, and resistance variation, R
l
, for the sensor in tension. In this case, the model-
25
based curve is found in three steps: l is instantaneously measured with the IUTM 5942; the strain
along thel-dimension is computed as
l
=l
1
l; and then, R
l
is computed employing (2.9) with
l
=
l
+ 1. The experimental curves in both Fig. 2.8-(a) and Fig. 2.8-(b) represent the averages of
three non-destructive tensile tests, performed at a constant displacement rate of 3 mm min
1
.
In Fig. 2.8-(a), it can be observed that the model of the mapping from total force, F
l
, to
resistance variation, R
l
, captures the main qualitative characteristics of the experimental behavior
of the corresponding true mapping. However, there exists a signicant quantitative mismatch
between the model-based and experimental curves. Similarly, in Fig. 2.8-(b), it can be observed
that the model of the mapping that relates
l
with F
l
represents the main qualitative but not
quantitative characteristics of the true relationship between these two variables. This phenomenon
is consistent with the experimental results reported in [59]. Considering that, as demonstrated
by Fig. 2.7, the model in (2.7) predicts almost perfectly the experimental relationship between
l
and
l
, we infer that the expression that relates
l
and R
l
in (2.9) does not fully capture the
true dependency between these two variables. This discrepancy suggests that the liquid circuits
embedded in the stretchable silicone may not deform in conjunction with the micro-channels of the
sensor. Also, it is possible that the shape of the internal channels does not vary as predicted by
(2.9), because this is based on geometric approximations. This modeling issue can be corrected
with the introduction of a heuristic exponential term, which yields the expression
R
l
=
l
c
w
c
h
c
2
l
1
e
l(1
2
l
)
: (2.12)
Here, we nd the parameter
l
by solving the least-squares problem
min
l
kA
l
l
+B
l
k
2
2
; (2.13)
whereA
l
2 R
N1
with its ith entry given byA
l
(i) = 1
2
l
(i) andB
l
2 R
N1
with its ith
entry given byB
l
(i) = log [R
l
(i)]+log
l
c
2
l
(i) 1
log [w
c
h
c
]. The heuristically corrected
curves are shown in green in both Fig. 2.8-(a) and Fig. 2.8-(b).
Fig. 2.8-(c) shows the relationship between the resistance variation, R
h
, and measured total
mechanical load, F
h
=
h
wl, for the sensor in compression. As done in the tension case, the
26
model-based curve is found in four steps: F
h
is instantaneously measured with the IUTM 5942; the
engineering stress is estimated as
h
= F
h
(wl)
1
; the contraction
h
is estimated by employing
(2.8); using the estimated
h
, R
h
is computed by employing (2.10). Similarly, Fig. 2.8-(d) shows
the relationship between strain,
h
, and resistance variation, R
h
, for the sensor in compression.
In this case, the model-based curve is found in three steps: h is instantaneously measured with
the IUTM 5942; the strain along the h-dimension is computed as
h
= h
1
h, and then, R
h
is computed employing (2.10) with
h
=
h
+ 1. The experimental curves in both Fig. 2.8-(c)
and Fig. 2.8-(d) represent the averages of three non-destructive compression tests, performed at a
constant force rate of 5 N min
1
.
Both Fig. 2.8-(c) and Fig. 2.8-(d) clearly show that the standard geometry-based model in
(2.10) captures neither the qualitative nor quantitative characteristics of the true behavior of the
sensor in compression. Further experiments indicate that this discrepancy is even more signicant
for patterned sensors such as those illustrated in Fig. 2.2-(d). As in the tension case, the mismatch
observed in Fig. 2.8-(c) and Fig. 2.8-(d) is corrected with the introduction of an exponential term,
which yields the heuristic expression
R
h
=
h
l
c
w
c
h
c
1
h
1
e
h
(1
h
)
2
: (2.14)
The structure of this model contains an exponential function in order to account for the sudden
increase in magnitude of the empirically measured R
h
as F
h
and
h
increase. The heuristically
corrected curves are shown in green in both Fig. 2.8-(c) and Fig. 2.8-(d). For
at sensors,
h
and
h
can be thought of as tting parameters. A slightly dierent interpretation can be given to
h
for sensors with grooved patterns to be discussed in the next subsection.
2.4.3 The Use of Protruded Sensors for Attachment Detection
As can be seen in Fig. 2.8-(c), the observed relationship between F
h
and R
h
for a
at sensor
in compression is represented by a curve with an linear section and an exponential section. The
transition from linear to exponential can be employed to detect the anchoring of a radial actuator
to the internal surface of the pipe through which the robot moves. Also, using experiments and
simulations, we demonstrate that the addition of patterned protrusions decrease the load required
27
Figure 2.11: Onboard test of perceptive articial skin. (a) During the fabrication process of RWT2
(see Fig. 2.2-(d)), a patterned sensor with 50 % of its surface protruded (see Fig. 2.9-(c)) is wrapped
about a radial actuator to create the robot's perceptive skin. This graph shows a sensor's voltage outputs
as functions of time when the corresponding radial actuator is in
ated, at a constant rate, under four
dierent conditions: unconstrained and inside pipes with diameters of 32, 40 and 48 mm. In this case,
using standard circuitry, the output voltage is made proportional to the total electrical resistance of the
sensor. These experiments clearly show that the sensor's output is approximately
at and linear in tension
(during free expansion) and exponentially rises up in compression (after attachment). This behavior is
consistent with the data in Fig. 2.9 and can be qualitatively predicted by nding a relationship between
the actuator's rate of in
ation and a time-dependent function
h
(t) that is plugged into
R
h
. (b) Diagram
shows the connection between the stages dened in Fig. 2.5 and the results from the experiments. The slope
of the voltage output changes before and after the attachment from approximately linear to exponential
respectively.
for transition, increasing the sensitivity of the sensor during compression. Here, we experimentally
study the three simple patterns shown in Fig. 2.9. Fig. 2.9-(e) compares the resistance{load rela-
tionships of four dierent sensors. In this plot, the percentages in the legend (25 %, 50 %, 75 %)
indicate the proportion of external surface covered by protrusions according to the congurations
illustrated in Fig. 2.9-(a-d). For each type of sensor, Fig. 2.9-(e) shows both an experimental
curve and a heuristic relationship produced with the use of (2.14). In each case,
h
and
h
can
be identied from data by solving an optimization problem similar to the one described in the
previous subsection. We identify
h
and set
h
= 1,
h
= 0:75,
h
= 0:5 and
h
= 0:25 for
at,
75 %-protruded, 50 %-protruded and 25 %-protruded sensors, respectively. These values for
h
are
selected to represent dierences in the surfaces of contact between the sensor and the environment.
The experimental data show a pattern in which the sensitivity of the sensor is increased by
decreasing the total protruded area. This nding is consistent with intuition and the FEA-based
simulation in Fig. 2.10, which clearly explains the mechanism by which the sensor's sensitivity is
modied. As can be seen in Fig. 2.10-(a), when a constant and homogeneously-distributed loadF
h
is
28
applied to compress the sensor along theh-dimension, the
at sensor deforms homogeneously. This
type of deformation induces a uniform reduction of the cross-sectional areas of the liquid wires and
a resistance variation estimatable with (2.14) for
h
= 1. On the other hand, as shown in Fig. 2.10-
(b), when a constant and homogeneously-distributed force F
h
is applied to compress the sensor
along the h-dimension, a sensor with a protruded pattern does not deform homogeneously since
strain is concentrated beneath the protrusions. This type of deformation induces an inhomogeneous
reduction of the cross-sectional areas of the liquid wires such that signicant resistance variations
occur in the zones of strain concentration.
Notice that the increase of sensitivity comes at the cost of saturation. Saturation appears
in this kind of soft sensors when excessive local deformations around the micro-channel generate
open circuits. The use of protruded geometries show a trade-o between increasing sensitivity and
reduction of sensing range. As our robot work with small forces we do not see this as an issue.
From Fig. 2.9-(e) and Fig. 2.10 we infer that any of the sensors in Fig. 2.9 can be employed to
measure the total load F
h
and detect the attachment of a radial actuator to the internal surface
of the pipe inside which the robot moves. However, the use of protruded patterns allows for the
development of sensors with higher sensitivity and lower transition thresholds, more suitable for
the creation of perceptive skins for locomotion control and other robotic applications. This feature
is exemplied in Fig. 2.11, which shows the responses of a patterned skin sensor wrapped around
a radial actuator operating in four dierent conditions. In this plot, the curve in blue shows the
output from the sensor (in Volts/ R
h
) as a function of time during free expansion. As predicted
by Fig. 2.8-(a), the curve remains almost linear because during free expansion the sensor is in the
pure tension state. The curve in orange shows the expansion of a radial actuator inside a pipe with
a diameter of 32 mm. In this case, while the actuator expands freely, the sensor's output behaves
linearly as predicted by Fig. 2.8-(a). Once the actuator reaches to the tube's internal surface, the
sensor's output exponentially rises up as predicted by Fig. 2.8-(c). The same behaviors are observed
when the actuator expands inside pipes with diameters of 40 mm and 48 mm. This experiment
clearly indicates that the proposed patterned sensors, with proper calibration and modeling, are
suitable not only for measuring force and pressure but also to detect attachment during locomotion.
29
Figure 2.12: Five phases used by the robot to generate one stride. At k = 1, the back radial
actuator is anchored to the pipe. At k = 2, the axial actuator is extended reaching a further point. At
k = 3, the front radial actuator is anchored to the pipe. At k = 4, the back radial and axial actuators are
relaxed. At k = 5, the back and front radial actuators are anchored to the pipe. [1]
Figure 2.13: Locomotion control scheme. The plant is composed of four types of components: soft
actuators, soft sensors, pneumatic pumps and pneumatic valves. The locomotion rules block generates the
control reference to produce the locomotion sequence in Fig. 2.12. Excited by the control error, the MIMO
controller block generates the control signal that excites the pneumatic pumps and valves. RWT1 uses
the actuators' internal air pressures for feedback control, while RWT2 uses the central actuator's internal
air pressure and perceptive articial skins wrapped around its radial actuators. The locomotion rules and
controllers are run on an Arduino
R
Mega digital signal processor (DSP).
Table 2.2: Locomotion pattern. Values of the robot's state, x
i;k
, during each phase k.
Actuator k = 1 k = 2 k = 3 k = 4 k = 5
Back Radial (i=1) 1 1 1 0 1
Central Axial (i=2) 0 1 1 0 0
Front Radial (i=3) 0 0 1 1 1
2.5 Locomotion Planning and Control
The locomotion mode employed by both robots is implemented with the actuation sequence shown
in Fig. 2.12. In this case, ve phases are dened to generate one stride. Consistent with this
30
scheme, we dene two possible conditions for each actuator, according to the discrete state
x
i;k
=
8
>
<
>
:
1; if on
0; if o
: (2.15)
The index i =f1; 2; 3g denotes each actuator according to the convention back, central and front,
and the index k =f1; ; 5g denotes each actuator's phase, as shown in Fig. 2.12.
During locomotion, RWT1 is controlled employing internal air pressure sensors, according to the
real-time implementation shown in Fig. 2.13. In this case, for the ith actuator of RWT1, x
i;k
= 1
if p
mi
p
ti
and x
i;k
= 0 if p
mi
< p
ti
, where p
mi
is the measured pressure and p
ti
is a threshold,
empirically chosen for controlled expansion and relaxation. In this scheme, a simple digital linear
time-invariant (LTI) diagonal multi-input{multi-output (MIMO) experimentally-tuned controller
is employed to regulate the actuators' internal pressures necessary to generate the state sequence in
Table 2.2. Since the robot is composed of three actuators and three internal pressures are measured,
the MIMO controller in Fig. 2.13,K(q
1
), is 33. Each diagonal entry ofK(q
1
) has the standard
proportional{integral{derivative (PID) structure
K
ii
q
1
=K
Pi
+K
Ii
1
1q
1
+K
Di
1q
1
; (2.16)
where q
1
denotes the discrete-time unit-delay operator. In this scheme, the input to K(q
1
)
is the vector control error e
K
= p
r
p
m
, where p
r
is the vector pressure reference for the three
actuators composing the robot and p
m
=
p
m1
p
m2
p
m3
T
. The output from K(q
1
), u
K
=
K(q
1
)e
K
, are the eective air
ow rates inputted to the robot's three actuators. The instantaneous
value of u
K
is manipulated by turning on and o the actuators' pumps and valves by employing
standard pneumatic feedforward control techniques [60]. The sample-and-hold period employed
for signal processing and control is T
s
= 29 ms. Note that despite the use of feedback control,
the method to control RWT1 is indirect because the attachment of a radial actuator to the pipe
is not directly detected but inferred from the internal pressure of the actuator, employing the
characterized mechanics in Fig. 2.4 and a priori geometrical information about the locomotion
path.
31
During locomotion, RWT2 is controlled employing articial skins built with the patterned sen-
sors described in Section 2.4. This method is direct because employing the force{resistance rela-
tionship in Fig. 2.9-(e) and behavioral patterns in Fig. 2.11, the robot is enabled to perceive contact
and detect attachment. As can be observed in Fig. 2.11, during a radial actuator's free expansion
at a constant in
ation rate, the skin sensor's voltage output, v
j
(t) for j =f1 (back); 3 (front)g, is
approximately linear. In contrast, as predicted by Fig. 2.8-(c) and can be observed in Fig. 2.11,
in compression at a constant in
ation rate, the skin sensor's voltage output, v
j
(t), displays a
nonlinear monotonically-increasing behavior. Thus, in the absence of noise, if the time-derivative
_ v
j
(t) remains approximately constant, it is inferred that the sensor is in the tension state and the
corresponding radial actuator is not exerting pressure on the pipe's surface. Conversely, if the
time-derivative _ v
j
(t) varies drastically over time, it is inferred that the sensor is in the compression
state and the corresponding radial actuator is exerting pressure on the pipe's surface.
One major diculty with the proposed attachment detection method is that the presence of
noise can make the estimation of _ v
j
(t) inaccurate. In this case, we eliminate the eect of noise by
low-pass ltering the measured signal v
j
(t), and then, under-sampling it before _ v
j
(t) is estimated.
Thus, at discrete-time t
d
, the signal _ v
j
(t) is estimated as
b
_ v
j
(t
d
) =
[Fv
j
] (t
d
) [Fv
j
] (t
d
n
o
T
s
)
n
o
T
s
; (2.17)
where F is a low-pass averaging digital nite impulse response (FIR) lter, i.e., with the form
F (q
1
) =
1
n
o
no1
X
n=0
q
n
: (2.18)
In this estimation method, the positive integer n
o
determines both the under-sampling rate in
(2.17) and the order of F in (2.18). Here, n
o
= 100; t
d
=T
s
k, withk2Z; andv
j
(t
d
) = 0 ift
d
< 0.
From a high-level abstract perspective, RWT2 is controlled according to the scheme in Fig. 2.13
and the controller associated with the central actuator is essentially identical to that used in the
RWT1 case. However, in the RWT2 case, the entries of the MIMO controller associated with both
radial actuators are based on sets of simple logical rules, which is an adequate method because
attachment to the pipe is directly detected by the robot's perceptive skin. Specically, we dene
32
Figure 2.14: Horizontal locomotion tests. (a) RWT1 moves horizontally from left to right employing
the internal air pressures of the actuators for feedback locomotion control. [1] (b) RWT1 initially moves
horizontally from left to right until it encounters a 45
-up-turn in the locomotion path. Then, the robot
complies to environmental geometrical variations and passively adapts its body to maneuver through this
obstacle. As in the rst test, RWT1 employs the internal air pressures of the actuators for feedback locomo-
tion control. [1] (c) RWT2 moves horizontally from left to right employing the radial actuators' perceptive
articial skins and central actuator's internal air pressure for feedback locomotion control. Attachment
is directly detected employing real-time touch information and the data in Fig. 2.11. While locomoting,
RWT2 encounters three dierent diameters:
1
= 32 mm,
2
= 40 mm and
3
= 48 mm. In this case,
the robot passively adapts its body to environmental changes, but actively senses these changes for control
purposes. In all the stills, time is indicated in minutes : seconds. The complete experiment can be found
in the supplementary movie SoftRobots.mp4 (http://www.uscamsl.com/resources/Calderon thesis 2020/-
SoftRobots.mp4.
a threshold value _ v
t
that, from the data in Fig. 2.11, indicates that during constant-rate in
ation
or de
ation, a radial actuator has changed its state to attached or detached, respectively. Thus, in
order to implement the locomotion sequence in Fig. 2.12, when during constant-rate in
ation the
signal
b
_ v
j
(t
d
) reaches a value signicantly larger than _ v
t
, the air
ow inputted to the corresponding
radial actuator is stopped by closing the valves. This condition is maintained until the locomotion
rules block in Fig. 2.13 generates a new control reference intended to change the actuator's state
from 1 to 0.
33
Figure 2.15: Vertical locomotion tests. (a) RWT1 moves vertically inside a cylinder with constant
diameter, employing the internal air pressures of the actuators for locomotion control. [1] (b) RWT2 moves
vertically employing the radial actuators' perceptive articial skins and central actuator's internal air pres-
sure for feedback locomotion control. Attachment is directly detected employing real-time touch information
and the data in Fig. 2.11. While locomoting, RWT2 encounters three dierent diameters:
1
= 32 mm,
2
= 40 mm and
3
= 48 mm. (c) RWT2 climbs between three parallel cylinders, labeled 1
, 2
and 3
. (d)
RWT2 climbs between two divergent planes (4
angle from vertical axis). These tests demonstrate that both
robots can adapt their bodies to time{shape variations of the surroundings and that, when tactile informa-
tion is used for control, a priori geometrical information about the locomotion path becomes less relevant or
unnecessary. In all the stills, time is indicated in minutes : seconds. The complete experiment can be found
in the supplementary movie SoftRobots.mp4 (http://www.uscamsl.com/resources/Calderon thesis 2020/-
SoftRobots.mp4).
2.6 Experimental Results and Discussion
Both robotic prototypes, including their respective sensing and control systems, were tested through
horizontal and vertical locomotion tests. As explained in the previous section, RWT1 is entirely
controlled employing the actuators' internal air pressures and RWT2 is partially controlled employ-
ing the articial skins in Fig. 2.1-(c). RWT1 operates with a sample-and-hold rate of 120 Hz and
RWT2 of approximately 34:48 Hz (T
s
= 29 ms). Fig. 2.14-(a) shows RWT1 moving from left to
34
right inside a perfectly horizontal transparent pipe, Fig. 2.14-(b) shows RWT1 transitioning from
horizontal to oblique locomotion inside a slope-varying pipe and Fig. 2.14-(c) shows RWT2 moving
from left to right inside a diameter-varying pipe.
The experiment in Fig. 2.14-(a) demonstrates the basic gait of RWT1, locomoting at a speed
of approximately 24 cm min
1
. In contrast to the operation of hard robots, RWT1 locomotes
by complying to the shape of the external environment while passively deforming as the internal
air pressures of its actuators vary. This case exemplies the potential capabilities of soft robots of
this type, which have dynamics with innite-dimensional states. The capability of RWT1 to adapt
passively is further demonstrated by the experiment in Fig. 2.14-(b). In this case, employing the
simple control structure in Fig. 2.13, RWT1 seamlessly performs a maneuver that would be very
dicult to achieve by a hard robot. The experiment in Fig. 2.14-(c) demonstrates the ability of
RWT2 to geometrically adapt to changes in the locomotion path, and also to perceive these changes
and use them for feedback control, while locomoting at a speed of 10 cm min
1
.
The capability of the prototypes to climb against gravity is shown in Fig. 2.15. In Fig. 2.15-
(a), RWT1 moves upward at a speed of approximately 10 cm min
1
, employing the feedback
control scheme in Fig. 2.13 and implemented with air pressure sensors embedded in the actuators.
Similarly, Fig. 2.15-(b) shows RWT2 moving upward at a speed of approximately 6 cm min
1
,
employing the feedback control scheme in Fig. 2.13 and implemented with the perceptive articial
skin sensors shown in Fig. 2.1-(c). As explained in Section 2.5, when tactile information is used for
control, geometrical information about the locomotion path becomes less relevant or unnecessary.
This fact is exemplied by the experiments in Fig. 2.15-(c) and Fig. 2.15-(d), which show RWT2
climbing between three parallel cylinders and climbing between two divergent planes, respectively.
In both cases, RWT2's controller uses no a priori information of the environment in which the
robot moves.
35
3 A New Bee-Inspired FWMAV Able to Perform Con-
trolled Hovering
3.1 Motivation
Insect-sized Flapping-wing micro air vehicles are centimeter-scale
ying robots with potential ap-
plications in search and rescue, hazardous environment exploration, assisted agriculture and re-
connaissance. In the past several years, new designs bioinspired by animals such as bees and
ies
have emerged. Flying insects have already demonstrated the ability to
y and hover with high
maneuverability and eciency at the millimeter-centimeter scale.
The motivation behind the development of FWMAVs is not limited to the applications men-
tioned above, but also include the study of the dynamics of
apping wing animals, since this
phenomena does not have a complete generalized model yet. Additionally, there are challenges to
be solved in terms of design and fabrication for the construction of vehicle elements (transmissions,
hinges, actuators, etc.) at such a small scale. Paradigms used for larger robots do not work at
micro-scale. For example, friction plays a much more signicant role in the transmission of motion,
and traditional transmission methods will not work as expected. The most successful solution was
the development of the smart composite microstructures (SCM) method [61], which uses lightweight
carbon ber composites with high tensile strength. Actuation is possible using electroactive mate-
rials such as piezoelectric that allow high precision and high-frequency actuation; and the use of
exible joints in the manufacture of transmission mechanisms that utilize the restorative properties
of materials such as polyimide lm (Kapton) at this scale.
There have been several projects that focus on the design and fabrication of FWMAVs. The de-
velopment of more precise and reliable fabrication procedures (implementation of the SCM method)
led to the Harvard RoboBee [62]. The rst generation prototype in [63] was driven by a single bi-
morph piezoelectric actuator driving two wings, producing the rst lifto for a robot at this scale
36
but constraining its motion to a single, vertical degree of freedom via guide wires. The limitation
of using a single actuator impeded the robot's ability to be controlled to produce hovering
ight.
Further improvements in the fabrication procedure enabled the split actuator bee [64], which uses
two bimorph piezoelectric actuators, each driving a single wing. This design enabled controlled
hovering
ight for the rst time.
Using the those past works as a framework, we rst developed our own fabrication system
and methods to fabricate our own 75 75 mg split bee. The fabrication of the micro
apper was
a training to continue the development of our own family of microrobots. In this work, We will
detail the fabrication methods used for the fabrication of our own "split bee", and then, detail how
we optimized the lift generation by improving the pitching mechanism and how this improvement
ended in a prototype which is 20% lighter (total 60 mg) and able to generate 10% more lift force.
This prototype was also able to perform controlled hovering.
3.2 Robot Design
The micro-robot is based on the design shown in [64]. It is composed of ve parts, as depicted in
Fig. 3.1-(a): air-frame,
exure transmission,
exure hinge, wings and bimorph bending piezoelectric
actuators.The actuators motion drive the
exure transmission to a periodic
apping motion. The
transmission, which is shown in Fig. 3.1-(b) is based on a four-bar mechanism, to translate linear
( actuator de
ection) into angular motion ('
apping angle). The wings and hinge are glued to a
single component, which then is attached to the angular output of the
exure transmission. During
apping, the hinge provides wing pitch rotation which is required for the lift force generation. Notice
that during this passive rotation, the pitching angle is dependent of the entire system dynamics
(hinge stiness, wings inertia, etc), which means that variable
apping motion would also generate
variable pitching angles. A prototype fully assembled can be seen in Fig. 3.1-(c).
3.3 Fabrication
The fabrication relies on the SCM method presented in [61]. Each component must be made indi-
vidually, then assembled manually under a microscope. The fabrication of each element depicted
in Fig. 3.2 follows the same general procedure. First, the layers that comprise the part are micro-
37
Figure 3.1: Robot design. (a) The robotic bee is composed of ve parts, the airframe which serves as a
structural part, the actuators that generate bending motion, the transmission that translates the bending
motion of the actuator to
apping motion by a four bar mechanism, the hinge which passively produces the
wing pitching required for
ying and lastly, the wings (b) shows a zoom of the transmission mechanism,
the actuators de
ect delta which then produces a change of angle of the wing ' (c) A photograph of one
of our robotic bees assembled.
machined using a precision diode-pumped solid-state laser (Photonics Industries DCH-355-3) with
a beam diameter of 10 m, then assembled into a pin-aligned stack between two aluminum plates.
This stack may contain uncured carbon ber pre-preg or sheet adhesive, in which case it will then
be placed into the appropriate equipment and receive the required temperature and pressure treat-
ment to laminate. The stack then undergoes a nal cut to release the parts in their desired shapes
before being assembled. The specics for fabrication of each component are explained next:
3.3.1 Air Frame
The airframe is the main body of the robot and consists of three pieces of cured carbon ber and
ve pieces of a berglass composite (FR4). The carbon ber stack used for the fabrication of the
frame consists of four layers of unidirectional carbon ber pre-preg (Teijin Carbon Tenax
R
Prepreg)
carbon ber, each with a thickness of approximately 25 m in a 0-90-90-0 angle orientation. The
cured carbon ber and FR4 are laser cut and prepared for assembly. The parts have features to
help the assembly under the microscope using tweezers and glue.
3.3.2 Transmission
The transmission is composed of a sandwich of carbon ber, Kapton and adhesive. The carbon
ber stack consists of three layers of intermediate modulus carbon ber in an angle orientation of
0-90-0, an intermediate 7 m Kapton layer, which is used to create
exible joints, and an adhesive
layer of Pyralux. The fabrication process consists of pre-cutting the carbon ber layers adding the
gaps required for the
exure joints. After this, the layers are placed in a metal plate tool with
38
pin-alignment holes. Then, the plate is processed using an automatic hydraulic press that applies
117 psi at 180
C for one hour. Finally, the stack is then re-aligned in the laser system to release
cut the features. A diagram of the process is shown in Fig. 3.2-(b)
3.3.3 Wings
The wings are composed of three layers. First, the structural layer, made of three layers of inter-
mediate modulus carbon ber in an angle orientation 0-45-0, this orientation is used to increase the
strength of the layers in these two specic directions (parallel to the spars of the wings). This is a
crucial feature since the frame of the wings is only around 150 width, the use of other orientation
would make the wings too weak to bending moments, producing undesired deformations during
apping. The second layer is a
exible sheet made of a polyester lm (Mylar), which acts as a
membrane similar to real insect wings. Finally, an intermediate layer made of Pyralux is placed in
between the two before mentioned layers. The fabrication consists of the precut of the carbon ber
with the internal shapes of the wings. Then, the layers are placed in a metal plate with pinholes
for alignment. A prole of pressure and temperature melts the Pyralux adhesive and eliminates air
gaps, gluing the carbon ber with the mylar. Finally, the stack is re-aligned and released cut in our
high-resolution laser cutter, notice that due to small sizes in the spars of the wings, the tolerance
during laser alignment is minimal. A diagram of the process is shown in Fig. 3.2-(c)
3.3.4 Hinge
As mentioned before, the hinge allows the passive rotation of the wings during
apping, the layup
of the stack and fabrication procedure is identical to the transmission. Where the central Kapton
layer is used to create the hinge that allows for hinge rotation.
3.3.5 Bimorph Piezoelectric Bending Actuators
The bimorph actuator stacks are composed of two layers containing alumina and a piezoelectric
ceramic (lead zirconate titanate, or PZT) positioned within an FR4 frame, and a layer of unidi-
rectional carbon ber pre-preg (Torayca
R
M46J) between them. The carbon ber serves as the
central electrode for a parallel connection to the actuator faces. The alumina is an inert material
with features that mate with the airframe and transmission, and the PZT serves as the active layer
39
(a)
(b)
(c)
(d)
Step 1 Step 2 Step 3
Figure 3.2: The fabrication process for elements of the RoboBee: (a) Airframe, (b) Actuators,
(c) Transmission, (d) Wings. Step 1 is the creation of the stack, which may contain layers that need to
be cured. Step 2 is the release cutting of the parts, and Step 3 shows the parts ready for assembly. The
RoboBee transmission is the only part that must be folded into position before it can be used.
whose piezoelectricity allows the actuator to bend. The stack, along with weights that apply 15
psi, is put into an oven at 180
C for two hours to cure the carbon ber pre-preg. A nal release cut
to the stack allows the fabrication of multiple bimorph actuators from each stack, each weighing
approximately 25 mg. Because the bimorph actuators are much thicker than the other parts, they
require two release cuts|one from the top surface, then another from the opposite side. Due to
the diculty of aligning the two cuts and the necessity of having clean and
at sides that ensure
separation of the active layers, the actuators in the stack will sometimes not all be usable.
3.3.6 Assembly
Three subassemblies are assembled separately. The rst is the airframe, which utilizes tab-and-
slot features to position and orient the pieces relative to each other, and cyanoacrylate (CA) glue
to adhere the parts rmly. The second one is the wing-hinge subassembly. Wings are attached
to hinges with the toothed mating features using CA glue. The third is the actuator-transmission
40
subassembly which consists of joining tabs on the extension tips of two bimorph actuators to mating
slots in the transmission. Next, the actuator-transmission subassemblies are rmly glued into the
base of the airframe. We use orthogonal contact surfaces between the actuators and the base as
constraints to guarantee precision during assembly. Also, ground linkages of the transmissions
are axed to the airframe using glue. The last step is attaching the wing-hinge subassemblies to
the transmissions. Their assembly relationships are less constrained, allowing nal adjustments to
compensate for any errors in previous steps. Protective spars and legs micromachined from cured
carbon ber are added to stabilize the robot on a
at surface and prevent damage to the main
body if a crash occurs.
3.4 Wing Trajectory and Control
The wings trajectory is driven by actuators motion, which is prescribed by an input voltage. This
signal contains the path and also the energy required for motion. In order to get a cyclical
apping, a
sinusoidal signal is used. The signal is composed of an amplitude (V
amp
), a biasV
bias
, and a variable
that denes a split-cycle asymmetry or dierences of velocities during upstroke and downstroke
motion. We vary the amplitudes symmetrically, by dening a V
avg
and a variation V
dif
so, one
actuator is driven by V
amp
=V
avg
+V
dif
and the other with a V
amp
=V
avg
V
dif
, this generates
the torques required for generation of roll, pitch and yaw motions. The description of the signal
variations is shown in Fig. 3.3
In order to perform hovering, a control algorithm is required since the
ying procedure is highly
unstable. Lab member and control expert Ying Chen developed a control algorithm based on his
research with quadrotors. The attitude and position of the robot are tracked and used to close the
feedback loop during the control experiments. The tracking is done using a motion capture camera
system (VICON); with this information, the controller is able to generate the
apping patterns
required for the controlled hovering. The details of this are not given here since it was not part of
my research, but they are published in [65].
41
Figure 3.3: Input signals for the generation of body torques. (a) Dierence of amplitude in each
wing is translated into a roll torque (b) a bias in the
apping is translated into a pitch torque (c) changing
the velocity for upstroke and downstroke is called split cycle, it takes fraction of the period to perform
upstroke and (1-) for downstroke. Generating yaw torque, this has not been fully implemented. The
robots
ap at natural frequency so increasing further the
apping velocity would reach the bandwidth of
the system, decreasing the
apping amplitudes.
3.5 Robot Performance and Hovering Test
The robot performance was similar to the Harvard prototype. It showed a natural frequency of
100 Hz, a maximum
apping angle of 150
at a peak to peak voltage of 220 V. Next, We used our
capacitive force sensor published in [66] to measure the lift forces during
apping. The maximal
average lift force measured was 135 mg which is also very similar to the one reported by [64].
Finally, we performed a hovering test to test the controllability properties of the robot, where the
robot was able to stand hovering on the air using attitude and position control. The results of the
performance, including a photographic sequence can be seen in Fig. 3.4.
42
Figure 3.4: Robobee control hovering experiment. (a) Photographic sequence of the RoboBee
prototype during the position control experiments, The robot is able to hover around the desired po-
sition for about 20 s. (b) Position control of RoboBee. The dashed lines represent the reference posi-
tion signals, and the solid lines represent the actual position regulation results. The RoboBee
apping-
wing robot is commanded to hover at a desired position, and the experiment lasts for almost 20 s in-
dicating the mechanical robustness and the performance consistency of the attitude and position con-
trollers. The complete experiment can be found in the supplementary movie FWMAVExperiments.mp4
(http://www.uscamsl.com/resources/Calderon thesis 2020/FWMAVExperiments.mp4)
3.6 Design of a Nonlinear-stifness Hinge for Lift Force Improve-
ment
3.6.1 Wing Pitch Aerodynamics
For an FWMAV, the cycle-averaged lift forcef
L
generated by one wing can be estimated using [67]
f
L
=C
L
( )
2
2
0
S (3.1)
where is the
apping frequency,
0
is the
apping amplitude, S is the area of the wing, and
C
L
is the lift coecient, which is a function of the aerodynamic mean angle of attack , i.e., the
complementary angle of the mean wing pitch angle. Most of the existing research has focused on
improving the FWMAV's lift generation by increasing the
apping amplitude
0
or the operating
frequency. However, there has been little research eort dedicated to nding a method to regulate
. Fig. 3.5 shows the results of [68] where the relations between and the coecients of lift and
drag are displayed. Upon rst glance, we can observe that the largest coecient of lift is obtained
at an of 45
. However, the
apping angle is dependent on so we should take into account the
coecient of drag. The larger the , the smaller the coecient of drag force is. This results in a
lessened opposition of the wing to
ap, resulting in higher
apping angles from the same energy
43
Figure 3.5: Lift/Drag dependency to pitching angle. Lift coecient, drag coecient, and their ratio
as a function of the instantaneous pitching angle of the wing. Plot based on the results from [3].
input. Thus, we obtain an increase in lift force. Both coecients resulting in a trade-o, and the
ideal case appearing when the lift to drag ratio is maximized. In other words, the best-case scenario
should be for pitching angles around 70
. This result is consistent with observations of bees and
ies, which tend to pitch around that pitching angle.
For all FWMAVs using a passive hinge element for wing pitching, the value of is dependent
on the
apping angle, frequency, wing geometry and hinge stiness. We would be able to set a
target pitching angle for if we maintain the other variables constants. However, during control
experiments, the pitching angle is continually changing due to the controller varying the
apping
motion to maintain the robot on the air in vertical position. Because of this, it would be hard with
a constant stiness to maintain this desirable pitching angle for all the dierent
apping ranges.
To solve this, we designed and fabricated a new hinge mechanism that is able to provide higher
stinesses at non-desired pitching angles in order to avoid over-rotation.
3.6.2 Nonlinear-Stiness Hinge Design
The standard hinge, which design is presented in [69], is an element that interfaces with the wing
and the transmission, allowing the wing to pitch, i.e., rotate about its leading edge. It contains a
exible component made of Kapton, a polyimide lm, that bends passively during
apping due to
the wing's interaction with the surrounding air. The pitching angle depends on the wing's
apping
angle and frequency, as well as the stiness of the
exible element.
To prevent the wing pitching angle from surpassing 70
, we added Kapton tabs to both sides of
the hinge that slide into conning sleeves as the hinge bends. These new hinges, shown in Fig. 3.6,
are based on the sleeve-stop hinges introduced in [70]. They have a physical limit that increases
44
Figure 3.6: 60 mg
ying prototype using the new hinge design. (a) A photograph of the 60-mg
FWMAV with nonlinear-stiness hinges. A U.S. penny (19:05 mm in diameter) is included for scale. The
inset shows a CAD rendering of the new hinge. (b) The nonlinear-stiness hinge design. Through a
sleeve-stop mechanism, the hinge prevents the wing's pitching angle
max
from surpassing 70
.
the stiness and eectively enforces a limit on the bending after either of the Kapton tabs reach
the end of its sleeve.
The fabrication of the nonlinear-stiness hinges is similar to that of the regular hinges described
in [69]. They are fabricated using a pin-aligned stack of layers of dierent materials. In addition to
the layers used in the regular hinges, we added two additional layers of Kapton on top and bottom
of the original hinge stack. The rst Kapton layer consists of tabs that can slide to the rotation
of the hinge. The second layer is a sleeve that maintains the rst inside a pocket where the tab
slides limiting only to a one-directional motion. The hinge is composed of: carbon ber, chosen for
its high stiness, high tensile stress, and lightweight; Kapton, whose
exibility allows bending; and
Pyralux, which is used for gluing the layers together.
3.6.3 Hinge Comparison Test
Our hypothesis is that for a given frequency and
apping angle, the lift generated when the pitching
angle is approximately 70
will be higher than when the pitching angle is greater than 70
. To
test this, we performed two sets of experiments|one using a regular hinge that can pitch freely
and the other using the aforementioned nonlinear-stiness hinge. We held the
apping frequency
constant at 100 Hz and actively controlled the
apping angle to sweep the range 60
to 100
using
the controller described in [71]. The only variable was the hinge mechanism, and by extension, the
pitching angle; therefore, any dierence in lift generation can be attributed to that feature.
To perform experiments that can directly compare the performance of both hinges. We must
be able to control the
apping angle between the two sets of experiments. Despite being designed
to have the same performance, there are dierences in behavior among dierent actuators due to
material variations and fabrication errors. Furthermore, the actuators do not maintain a consistent
45
Figure 3.7: Photographs of maximum pitching angle during force measurement experiments
for a
apping angle of 99
. The left and right images show upstroke and downstroke, respectively. The
nonlinear-stiness hinge is shown in (a), while the regular hinge is shown in (b). Since the photographs
depict bottom views, the narrower projections of the wing seen in (a) indicate that the wing is, in fact,
exhibiting smaller pitching angles than the one in (b).
bending response to the input voltage across the faces over time, but rather degrades throughout
the actuator's lifespan. In addition, the transmissions and hinges also degrade in performance,
the more they are used due to fatigue. We therefore cannot assume that a given control signal
will produce consistent and reliable bending. To ensure that our
apping angles can be generated
reliably regardless of the individual actuator used or its age, we use a controller written in MAT-
LAB's Simulink Real-Time, running at 10 000 Hz. Using feedback from a laser displacement sensor
(Keyence LK-031), we are able to produce the desired bending in the actuator. For a xed fre-
quency, we can nd a relatively consistent mapping between the displacement of the actuator body
and the
apping angle, measured using a high-speed camera and imaging software. The behavior of
the
apping setup can be characterized using system identication, and we can, therefore, prescribe
the
apping angles by choosing the actuator displacement that corresponds to the desired angle.
The control algorithm for the
apping is based on the adaptive feedforward scheme presented
in [71]. The plant, i.e., the actuator-transmission-wing assembly, can be approximated as a linear
time-invariant system. System identication is performed in MATLAB's Simulink Real-Time to
nd a transfer function that captures its behavior, allowing estimation of the plant output. The
input is the voltage signal sent to the piezoelectric drivers for the actuator, and the output is the
reading from the laser displacement sensor, which corresponds to the actuator bending.
Flapping angles from 60
to 100
are used for both sets of hinge experiments. The
apping
amplitude is prescribed using the controller to maintain approximately the same
apping angle
throughout the entire experiment. The force is measured using a micro-force sensor, whose design
and fabrication procedures are detailed in [66]. This sensor uses a capacitive displacement sensor
46
Figure 3.8: Results for the hinge comparison experiments. (a) Pitching angle versus
apping angle
for both the regular and nonlinear-stiness hinge experiments. Trend lines are tted using a cubic least-
squares method. The wing pitching angle for the nonlinear-stiness hinge does not surpasses 70
, indicating
that the new hinge design successfully limits the pitching angle. (b) Lift force generation for both hinges,
including error bars. Trend lines are tted using a cubic least-squares method. When the
apping angle
is below 80
, the regular hinge seems to outperform the nonlinear-stiness hinge. However, above 80
apping, the nonlinear-stiness hinge generates more lift than the regular hinge. This aligns with our
hypothesis that a pitching angle of approximately 70
is preferable. For a given
apping angle, whichever
hinge produces a pitching angle closer to 70
will generate a higher lift force.
and a cantilever beam made of Invar, which has a very low coecient of thermal expansion, to map
deformations in the cantilever into forces generated by the robot. The experiments were recorded
using a Phantom high-speed camera at 5000 frames per second.
We recorded the lift force generation experiments before described using a high-speed camera
phantom Miro Lab310 in order to capture the pitching angle resulted from the
apping. We used
Matlab image processing toolbox and a digital pixel measurement tool (MB-Ruler) to obtain the
maximum pitching angle during a series of 20
aps. Then, the maximum pitching is averaged to
obtained an average maximum pitching angle for a dened
apping angle. Static images from the
experiments are shown in Fig. 3.7.
The results of the experiment can be seen in Fig. 3.8. Fig. 3.8-(a) shows the average maximum
pitching angle for the referenced
apping angles during the experiments. Meanwhile, Fig. 3.8-(b)
shows the lift forces generated for the same experiments. The plots can be described in three
dierent sections. First, for low
apping angles (60-75
), the lift force generated is similar for
both cases. However, the pitching angle observed is higher for the regular hinge. At this smaller
apping angles, this dierence in pitching angle is not able to generate signicant dierence in force
generated. The second area is for middle
apping angles (75-85
). Here, the pitching angle and the
47
Figure 3.9: Instantaneous force during
apping. (a) nonlinear-stiness hinge, and (b) regular hinge.
The negative regions of the plot are smaller for the bounded case, contributing to a higher average lift force
compared to the unbounded case despite having smaller peaks. Since one trough is more negative, we can
infer that there is an asymmetry (between upstroke and downstroke) in the lift force generation. This is a
result of fabrication errors and imperfections in the parts.
force generated are similar. Here, we can say that the regular and nonlinear-stiness hinge work
in a similar manner. Finally, for higher
apping angles (85-100
), the pitching angle of the regular
hinge keeps increasing while the non-linearities of the bounded hinge close to 70
start to be noticed
and the pitching angles generated are smaller (getting closer to 70
). This smaller pitching angles
(in the range around 70
) generated a higher lift force which agrees with our hypothesis and also
with real bees method during
ying. The results also show that the hinge improves the lift force
due to a stiening of the hinge at higher pitching angles more than the boundedness of it. Results
show that for
apping angles above 85
, the nonlinear-stiness hinge produces a larger average lift
force than the regular hinge.
Fig. 3.9 shows the instantaneous force corresponding to a
apping angle of 99
for both bounded
and non-bounded cases. Even though the average lift force is higher for the nonlinear-stiness case,
the instantaneous force for the regular hinge case exhibits larger extremes. This means that we can
achieve a similar average lift force using the nonlinear-stiness hinge while loading the system with
smaller instantaneous forces. Increasing the life expectancy of the robot since the stresses applied
to its components are smaller.
The nonlinear-stiness hinge behaves dierently from the regular hinge in two ways. First, the
new hinge design prevents wing pitching angles over 70
due to an increase of stiness close to the
70
mark. Second, since the resulting maximum pitching angles are smaller, it avoids over-rotation
48
during the
apping rotational phase, which can be seen by a decrease in the negative region of the
instantaneous force plot.
Another advantage of the nonlinear-stiness hinge comes from the observation that during
controlled hovering experiments performed in [65], the FWMAV's
apping angle is likely to change
abruptly in order to compensate for the body's pitching and rolling. These changes make it more
likely that the wings will over-pitch, reducing the lift that the robot can generate. The range of
forces for the nonlinear-stiness hinge is higher which should be translated in better stability during
control experiments.
The experimental results show that the new nonlinear-stiness hinge design allows the genera-
tion of larger forces utilizing a similar
apping angle compared with the regular hinge. The 75 mg
robot showed in the sections above used
apping angles over 120 in order to generate the forces
required for the control experiments. These new results suggest that we can use smaller
apping
angles to generate higher forces. Smaller
apping requirements can be translated into a decrease of
actuator displacement. These new requirements allow for the use of smaller and lighter actuators,
which can also decrease the weight of the total micro-robot considerably. We tested this by the
design and fabrication of a new prototype taking advantage of the non-linear stiness hinge.
3.6.4 60 mg FWMAV Design and Fabrication
The new prototype was built using actuators 14 % shorter, decreasing the actuator mass by 5 mg,
i.e., a reduction of 20 % of mass weight. The total mass of the new full prototype is approximately
60 mg which is also approximately 20 % lighter than the original 75-mg prototype. Shortening the
actuators increased their stiness, which alters the dynamics of the entire system|increasing the
natural frequency of the system from 100 Hz to 110 Hz.
The ability of the FWMAV to generate lift was tested using the micro-force sensor
apping the
wing with a periodic signal with dierent voltage amplitudes. The results are shown in Fig. 3.10,
and indicate that the robot can achieve a mean maximal lift force of 147 mg with a
apping angle
of approximately 100
while being driven by 220 V peak to peak. This force is around 10 % larger
than the maximum force achieved using the previous prototype.
49
0
0
0
Figure 3.10: Results from experiments using the 60 mg prototype. (a) Force generation of the
lighter bee prototype. The maximum lift achieved was 147 mg, compared to only 130 mg using the heavier
75-mg prototype with the old hinge design. (b) A photographic sequence of the bee during controlled
hovering. (c) Reference and measured altitude of the bee during
ight. The lighter bee is capable of
following the reference altitude, showing that the robot can perform controlled hovering. (d) Roll and pitch
angles of the bee during
ight. Results suggest good performance of the robot. The complete experiment
can be found in the supplementary movie FWMAVExperiment.mp4 (http://www.uscamsl.com/resources-
/Calderon thesis 2020/FWMAVExperiments.mp4)
3.6.5 Controlled Hovering
We veried the controllability properties of the lighter FWMAV by performing hovering tests using
the controller presented in [65]. We used a Vicon motion capture camera system and retrore
ective
markers installed on the FWMAV for attitude and altitude feedback. This experiment successfully
demonstrated that we could achieve hovering with our new prototype. A photographic sequence
showing the robot during hovering is shown in Fig. 3.10-(b). Fig. 3.10-(c)-(d) show the measured
altitude and attitude of the robot, respectively.
50
Tuning experiments were performed to nd the parameters required for the proportional-
{integral-{derivative controller to achieve stable hovering. Since the prototype discussed in this
paper has a higher lift to weight ratio that the prototype is shown in [65], the number of trials
required to nd the parameters for stable hovering was considerably decreased, suggesting a higher
gain margin.
3.7 Discussion
We have demonstrated that the wing pitching angle in FWMAVs, which to this point has not been
studied extensively, is crucial to the amount of lift generated. While
apping angle and frequency
are essential to the force an FWMAV can produce, being able to tune the pitching angle can
strongly in
uence lift, as well.
Based on biological literature and aerodynamic analyses, we hypothesized that during
apping,
a wing pitching angle of around 70
would result in higher lift forces.
That is, for any given
apping angle, the closer the pitching angle was to 70
, the more lift that
prototype would generate
To test this, we developed a new hinge design with a mechanism to avoid pitching angles higher
than the desired, and conducted two sets of experiments, measuring the lift force generated at
dierent
apping angles.
Results showed that at
apping angles of 85
, where the non-linear stiness hinge mechanism
starts to act to avoid higher pitching angles, a corresponding increase in lift force generated is
observed. Demonstrating the advantages of constraining the pitching angle for lift force generation.
These results enabled the design of a lighter bee made using shorter, lighter actuators, that could
generate 147 mg of lift at a frequency of 110 Hz. By decreasing the FWMAV weight and increasing
lift, we increased the thrust-to-weight ratio from 1.7 to 2.5, an improvement of about 40 %.
As insects such as bees and
ies have muscles to control their
apping and pitching angles during
ight, allowing for remarkable maneuverability, FWMAVs are still limited to passive wing pitch
rotation. A clear path for future work is the addition of an active-controlled pitching angle. This
would make the system less underactuated and would open to the possibility for the performance
of high-speed maneuvers. Another critical feature to be improved is autonomy, since there are still
51
no batteries with energy density high enough to power robots at this scale. Searching for high
energy density sources and moving out from piezoelectric technologies can be a crucial element for
the future of microscale
ying robots.
52
4 Novel High-Frequency SMA Flexible Micro Actuator
for the Developing of mg-Scale Flexible Micro Robots
4.1 Motivation
Inchworms are animals that have the interesting characteristic of being small and soft. They are
incredibly robust in terms of being able to locomote through dierent surfaces, even in vertical
directions. They move using a looping movement where anterior and posterior legs alternately
anchor and deanchor to surfaces. The contraction of the longitudinal muscle leads to bending
deformation of the central part of the body, which results in a shortening of it overall length. The
combination of these two actions results in forward motion.
The simplicity of inchworm locomotion has awaken the inspiration of many research to create
robots that mimic this locomotion method. Also, mimicking the characteristics of being small and
exible are useful for a robotic system. In terms of size, a small robot would take advantage of
getting to places that are inaccessible for other larger systems. In terms of
exibility, it would take
advantage of the continuous and robust motion that soft systems are characterized.
At microscale, the way objects interact with their environment is vastly dierent from the
way they behave at the macroscale. For example, we live in a world in which inertial and other
bulk forces dominate our motion. However, at the microscale, friction, drag, and adhesion all
play critical roles in driving motion [72], so the development of entirely new actuation mechanisms
and methods are required to build robots at this scale. This constraint limits the possibilities for
actuation methods used in micro-robotics.
The most successful actuation technologies for micro-robotics are piezoelectric, electromagnetic
and SMA. Each of them has advantages and disadvantages. Piezoelectric is able to generate high-
frequency actuation but with high voltage requirements, which is translated in need of voltage
53
ampliers and other bulky electronics. Electromagnetic allows for microrobots to be tetherless, with
displacement and bandwidth. However, the actuators require a magnetic eld which is generated
by a bulky magnetic eld generators|constraining the robots to lab environments. SMA has the
simplicity of low voltage requirements, binary inputs which are translated in simple hardware.
However, they are constrained in terms of small strain (4 % of their length) and slow frequencies
(usually limited to their cooling times).
Some examples of SMA based micro-robotic crawlers are: RoACH [73], which uses SMA wires as
linear actuators to power legs that propel forward motion. This robot is fully autonomous and has
a speed of almost 1 body length per second (Bl/s). In [74], another SMA-based crawling prototype
is presented. This design uses SMA springs in order to obtain higher actuator displacements,
achieving a velocity of 0:1 Bl/s. In [75], the SMA wire also utilized a spring shape to increase the
displacement output. However, due to limitations of cooling time, the robot was only able to work
at 1 Hz, and the maximum velocity was still below 10 mm s
1
(0:06 Bl/s).
The limitation mentioned above in actuation speed has inspired research that aims to achieve
SMA actuation at higher frequencies. In [76] and [77], a new method using thin SMA wires in a
central 3-D printed piece allows faster actuation. However, fabrication limitations meant that this
design was limited to a scale over 20 mm. We apply this idea on a new level by using new design
and fabrication methods to utilize those features in microscale bending actuators that weigh only
6 mg and can actuate at frequencies up to 20 Hz with output displacements over 300 m. This was
made possible by the extremely small diameter of the SMA wire used in the design (0:0015 in). We
take advantage of the fact that the rate of heat transfer is proportional to the surface area of an
object, and the thermal energy a body contains is proportional to its volume. Using very thin wires,
we are able to heat the wire to its transition temperature quickly due to their small thermal mass,
while their relatively large surface area facilitates quick cooling through convection. We performed
characterization experiments on these actuators by varying parameters such as actuator stiness,
frequency, and heating time.
Using this new SMA actuation method. We designed, fabricated, and experimentally tested a
30-mg crawling robot called SMALLBug: Shape Memory Alloy Little Locomoting Bug, illustrated
in 4.1. At 20 Hz, we were able to achieve an average speed of 17 mm s
1
, or 1:4 Bl/s. Then,
using the modularity properties of SMALLBug we built SMARTI (Shape Memory Alloy Robotic
54
Figure 4.1: Photograph of SMALLBug. An SMA bending micro actuator connects the two halves of
the sigma body frame. Anisotropic friction legs allow forward motion when the actuator bends cyclically.
A U.S. dime is included for scale.
Traveling Insect), which is composed of two SMALLBugs in parallel, enabling not only forward
locomotion but also steerability. The design, fabrication and experiments performed for the robots
are explained in the following subchapters
4.2 SMALLBug a 30 mg Multigait Micro Robotic Crawler
4.2.1 Design
SMALLBug is composed of three main components, depicted in Fig. 4.2-(a): the SMA-based
bending actuator, a sigma body frame composed of two halves (that each look like the uppercase
Greek letter ) and the anisotropic friction legs. The SMA wire's temperature-induced contraction
is utilized by installing it onto two ends of an actuator that is
at when the SMA is in its longer,
martensitic phase, and bent when the SMA is in its shorter, austenitic phase. The actuator's
bending motion produced by the heating and cooling of the SMA wires is transmitted to the sigma
body frame, which changes the angles of contact between the legs and the ground. This interaction
produces forward motion after a full bending and straightening cycle, as explained in Fig. 4.2-(b).
SMALLBug locomotion is dependent on the frequency of motion, displacement of the actuator,
and the contact area between the legs and the ground. Through the intentional design of the shape
of the legs, we can pre-program the robot to travel in the desired forward direction. The following
subsections will explain the details of each robotic component.
High Frequency Flexible Micro Bending SMA Actuator
The actuator consists of copper-coated ends for easy electrical connection, a loop of SMA wire
that is threaded through holes in these copper-coated ends, and a central carbon ber beam that
55
Figure 4.2: SMALLBug Design. (a) The robot consists of three elements: a high-frequency SMA
bending actuator, the sigma body frame, and anisotropic friction legs. (b) This diagram depicts the forward
motion generation. The geometry of the legs allows smooth rotation in the heel direction (backward) while
preventing rotation in the forward direction due to the foot acting as a physical stop when rotated in the
foot direction (forward). The interaction of the anisotropic friction legs with the ground upon activation
of the bending actuator produces forward motion.
connects the ends and provides the restoring force to straighten the actuator after it bends. The
SMA wires are tied and glued into place to maintain the wires in tension. The wire is connected
such that it functions as two parallel wires connecting each end, as shown in Fig. 4.2-(a). When
a voltage is applied across the copper surfaces at the ends of the actuator, an electric current
passes through the SMA wires, heating them past their transition temperature and causing them
to contract. Since the ends of the central carbon ber beam are xed to the copper extremes,
the SMA contraction pulls the copper sections closer together, inducing bending in the actuator.
This eectively pre-programs a desired response for the actuator by utilizing elements that enable
unidirectional motion [78]. In this case, xing the SMA wire to the ends of the actuator results in
a coupling of the length of the wire to the distance between the copper ends. The
exibility of the
carbon ber allows it to act as a spring, storing elastic energy and bending rather than breaking
under stress. This allows the bending to be reversed when the voltage is terminated, and the cycle
can repeat.
In order to achieve high-frequency actuation utilizing SMA wires, we implement two design
innovations. First, in order to address the slow cooling of the wires, which is a major problem
associated with SMAs, we used wires with a very small diameter of 0:0015 in. At this size, the
small thermal mass of the wire means that it can both heat up to the transition temperature and
cool down to room temperature relatively quickly. The main drawback of using thin wires is the
limit on the force that the wires can apply. In order to compensate, we use a longer SMA wire
56
loop that eectively acts as two parallel wires. In this conguration, the wire still cools quickly,
but the force generated is twice that of a single wire, and large enough to bend the central carbon
ber beam. Using this design, we can easily achieve the forces we need to bend the actuators and
drive the 30-mg robot. The second design innovation is the addition of the central carbon ber
that maintains the length of the actuator and keeps the wire in tension. We characterize the eect
of the stiness of the central carbon ber on the performance of the bending actuators in section
V. With these improvements in design, we believe that the use of thin SMA wires at this scale is
ideal for our operating conditions. We were able to fabricate extremely robust 12-mm actuators
that weigh only 6 mg each.
Sigma Body Frame
The sigma body frame consists of two halves, each made from a multi-material stack composed of
two layers of carbon ber and an intermediate layer of a polyimide lm called Kapton. The purpose
of the intermediate layer is to allow the integration of folding features that enables the transition
from a 2-D shape to a 3-D sigma shape that characterizes the body frame, which can be seen in
Fig. 4.2-(b). This geometry allows the transmission of the actuator's bending into a change in the
angle of contact of the legs with respect to the ground.
Anisotropic Friction Legs
SMALLBug has two front and two back anisotropic friction legs that are attached to the sigma
body frame. These legs are a simple mechanism to achieve forward motion through a cyclic motion
inspired by inchworm locomotion. The legs rely on geometric constraints to generate anisotropic
friction. Their geometry is designed so that motion is favored in one direction. The legs contain
a long foot pointing toward the front and a round heel in the back. At rest, the feet are in a
horizontal position, allowing two possible motions. In the heel direction, the leg will rotate easily
because of its rounded shape, which facilitates rolling. However, in the foot direction, rotation is
constrained due to the
atness of the foot. As the actuator bends and straightens, the legs interact
with the crawling surface to produce forward motion with each full bending cycle.
57
Figure 4.3: Fabrication of the elements of a SMALLBug prototype. (a) Fabrication of the SMA-
based bending actuators. The fabrication consists of four steps. First, a copper-coated CuFR4 (a berglass-
epoxy laminate material) layer is cut with an appropriate shape and holes to hold the SMA wires. During
step 2, an SMA wire is threaded through these holes, then held in place by a simple knot at the end of the
holes. During step 3, a strip of carbon ber is glued onto the back of the jig using cyanoacrylate glue in
order to maintain the SMA wire in tension. Finally in step 4, the jig is laser-cut to release the actuators.
Electrical connections are made by attaching wires to the copper terminals using conductive epoxy. (b)
Fabrication of the sigma body frame and anisotropic friction legs. First, a multi-material stack is made
from two layers of carbon ber and an intermediate layer of polyimide Kapton lm. A sheet adhesive
(Dupont Pyralux) is used to bond the layers. This stack is cured at high temperature and pressure using
an automatic hydraulic press. The carbon ber pieces contain pre-cut features that allow easy folding.
In step 2, the stack is released using a high-resolution laser-cutter to obtain the sigma body frame and
anisotropic friction legs. Finally, in step 3, the sigma body frame is folded from a 2-D shape to a 3-D
structure, giving it the characteristic sigma shape. The legs, once released, are ready to be assembled to
the body using the interlocking features.
4.2.2 Fabrication
The robot fabrication is based on the smart composite microstructures (SCM) method [63], in
which a stack composed of dierent materials is built in order to create features such as hinges
or slots for easy assembly. The fabrication processes for each element of the robot are described
below:
58
Actuator Fabrication
The SMA bending actuator is made of a copper-coated berglass-epoxy laminate material (CuFR4),
SMA wire, and carbon ber. First, a CuFR4 jig is laser-cut using a precision laser-cutting system.
This jig contains holes through which the SMA wire can be threaded. Because one side of the
material is coated with copper, it provides a convenient surface to which electrical connections
can be made in order to heat the SMA wire to induce SME. After the jig is cut, SMA wire is
looped through the holes and tied in a simple knot to maintain tension and secure its position. For
security, a small amount of cyanoacrylate (CA) glue is applied at the knot to prevent unraveling
and to hold the wire in place on the CuFR4 jig. A thin strip of carbon ber is then glued onto the
copper-coated actuator ends on the jig to serve as a spring to maintain the length and structure of
the actuator. The stiness of the actuator is primarily determined by the thickness of the carbon
ber; we fabricated actuators with thicknesses of 90 m, 180 m and 230 m in order to test dierent
stinesses. After the carbon ber is attached to the CuFR4, a nal release cut is performed to
separate the actuators from the jig and prepare them for installation onto SMALLBug. Fig. 4.3-(a)
presents a fabrication diagram illustrating the individual steps of the process.
Sigma Body Frame Fabrication
The two body frame halves of SMALLBug are made of carbon ber and an intermediate layer of
Kapton. The layers of precut carbon ber, Kapton, and adhesive are prepared and aligned, then
cured into a single stack. The sigma body frame contains integrated features that facilitate folding.
Once released, the piece is folded and secured with CA glue to transform the 2-D template to a
3-D structure and give the piece its characteristic sigma shape. Fig. 4.3-(b) depicts the steps of
this process in a detailed fabrication diagram.
Anisotropic Friction Legs Fabrication
The anisotropic legs are fabricated from the same multi-material stack from which the sigma body
frames are cut. The legs are directly laser-cut and ready to be assembled without any folding or
other post-processing. Fig. 4.3-(b) depicts the steps of fabrication in detail.
59
Figure 4.4: Displacement measurement and input signal for the 90mm bending actuator. The
input signal is a pulse-width modulated (PWM) signal with a pulse magnitude of 10 V when on. The
duty cycle is the fraction of the period during which the signal is maintained at its high value. As the
instantaneous measurements show, the SMA wire contracts during the \on" portion of the signal as it heats
up its crystal structure changes from martensite to austenite. For the remainder of the period, the current
through the wire is maintained at zero to allow cooling, which corresponds to expansion of the wire back
to its original length.
Assembly
The assembly of SMALLBug relies on slots and easily-connecting joints that are secured with CA
glue. The actuator is installed onto the sigma body frame by engaging with cross-shaped cavities
that aid alignment. The legs are attached to the body frame through interlocking slots, which are
also glued to x their positions. Two 49 AWG copper wires are installed, one on each copper-coated
end of the actuator, to apply the desired power and signal to SMALLBug. These copper wires are
attached to the copper surfaces on the actuator using conductive epoxy (MG Chemicals Extreme
Conductivity Silver Epoxy Adhesive).
4.2.3 Actuator Characterization
The actuators are controlled by a pulse-width modulated (PWM) signal with a specied duty cycle.
Simulink Real-time is used to generate the PWM signal, which is then sent to a MOSFET powered
by an external power supply at the desired voltage. This signal provides energy to the actuator
and induces bending. The displacement of the bending actuators is measured with a Keyence laser
displacement sensor (Keyence LK-031). The data were collected at sample time of 0:001 s.
Fig. 4.4 shows two cycles for a bending actuator. During the \on" portion of the signal, a
voltage is applied across the copper-coated ends of the actuator, causing a current to pass through
60
Figure 4.5: Duty cycle sweep experiment. In order to nd the duty cycle that results in maximum
displacement, we performed experiments at a series of duty cycles for each frequency tested. A clear trend
emerged at all frequencies, in which a trade-o between heating and cooling times produces a maximum
displacement at some preferred duty cycle, and duty cycles smaller or larger than that resulted in lower
displacements. This plot shows the experiments performed on an actuator with a carbon ber thickness of
90 m at 1 Hz.
and heat the SMA wire. The duration of this period is dened by the duty cycle, i.e., the percentage
of time of the cycle during which the signal is high. For the remainder of the cycle, the signal is
zero, eliminating the current and letting the wire to cool down. It is important to note that high
duty cycles cannot be used due to the likelihood that the very thin copper wires used for electrical
connection will overheat. We have observed that the copper wires breaking due to high currents
well before the SMA was damaged. This means that the connecting copper wires are the limiting
factor when choosing the duty cycle, and act as a saturation limit to prevent the SMA wires from
overheating.
We performed a series of experiments to characterize the actuators. First, we built three bending
actuators with dierent central carbon ber stinesses, dictated by the thickness of the carbon ber
beam. Comparing the results of these experiments helped us understand the eect actuator stiness
would have on the output displacement. The selected thicknesses were 90 m, 180 m, and 230 m
to span a range of reasonable thicknesses of carbon ber that are both easy to fabricate and strong
enough to withstand cyclical loading.
For each actuator, we performed experiments at the following frequencies: 1, 2:5, 5, 7:5, 10,
12:5, 15, 17:5, and 20 Hz). For each frequency, we measured the displacement response to dierent
duty cycles at a given amplitude of 10 V. This allowed us to obtain an estimate of the duty cycle
that would result in the maximum displacement of the actuator. An example plot is shown in Fig.
61
Figure 4.6: Characterization experiments for three dierent central carbon ber stinesses.
(a) Frequency-displacement plot for three dierent thicknesses of carbon ber. From the experiments
mentioned in Fig. 4.4, we found the maximum displacement for each frequency and for each of the three
actuator thicknesses examined. For each experiment, the input signal was a pulse-width modulated signal
with a value of 10 V when it was on. The results show that the actuator with the largest displacement was
obtained using the actuator with a central carbon ber layer that was 90 m. (b) Photographic sequence
of the experiments for the actuator whose central carbon ber was 90 m. These photographs show the
bending achieved by the SMA wire's contraction upon heating.
4.5, showing the displacement output for a variety of duty cycles at 1 Hz for the 90 m central
carbon ber. We observed a similar trend for all the frequencies we tested. The pattern is that
for each frequency, there is a preferred duty cycle that corresponds to the maximum achievable
actuator de
ection, and at higher or lower duty cycles, the performance worsened. We suggest that
this is due to a trade-o between the heating and cooling time. For duty cycles larger than the
preferred one, the heating time is longer, so the SMA wire has more time to heat up. However,
since the cooling time is reduced, the SMA does not have as much time to cool down. As a result,
the actuator does not have enough time to return to the original resting position. The opposite
happens when the duty cycle is lower than the preferred one. The SMA wire does not have enough
time to heat up to reach the full austenitic state, producing incomplete bending. In this case, the
cooling time is longer, meaning the bending actuator is able to return to its original resting position
before the next cycle begins.
The results for the frequency sweep can be seen in Fig. 4.6-(a). This plot shows the maximum
displacement obtained at all of the frequencies we tested. The results show that the displacement
decreases as the frequency increases. We suggest two explanations for this behavior. First, at
larger frequencies, the heating and cooling times are reduced because of the period of the cycle is
decreased, so there is less time for the actuator to bend and straighten during each cycle. Second,
dynamic phenomena could start to dominate at higher frequencies, and the force required to move
the actuator might be increased due to the added mass eect that is observed when an accelerating
62
Figure 4.7: Plots of the actuator's displacement during characterization experiments for the
90- m micro bending actuators. (a) Displacement for a duty cycle of 7:5 % at 5 Hz. Under these
parameters, some drift can be seen, indicating that there is not enough time for the wire to completely cool
and return to its original length. The maximum displacement during the cycle is 2:3 mm. (b) Displacement
for a duty cycle of 10 % at 10 Hz. The actuator reaches steady state after its position drifts almost 2 mm.
The maximum displacement is 0:95 mm after this point. (c) Displacement for a duty cycle of 10 % at
15 Hz. As the frequency increases, less time is available for the wire to heat up and cool down. The drift
here is almost 2:3 mm, and the maximum displacement is 0:5 mm. (d) Displacement for a duty cycle of
10 % at 20 Hz. Here, the drifting is even more apparent, reaching approximately 2:4 mm. However, the
displacement is 0:37 mm, which is more than adequate for microrobotic actuation.
or decelerating object must displace the volume of the surrounding
uid as it moves. This means
that the actuator could be experiencing attenuation because it is operating outside of its bandwidth.
For the stiness comparison, the maximum displacement was obtained at 1 Hz for the 90 m
bending actuator. This is consistent with our expectations that the least sti beam, which cor-
responds to the thinnest carbon ber tested, requires smaller forces to bend. As the thickness
(and therefore stiness) is increased, the resulting displacement is decreased. Fig. 4.6-(b) depicts
photographic sequences during the experiment for the 90- m bending actuator at 1, 5 and 10 Hz.
Operating the actuator at higher frequencies results in smaller displacements that are dicult to
see in a static image.
63
Fig. 4.7 depicts the instantaneous measured displacement for the actuator with the 90- m
carbon ber. These results demonstrate the trade-o between heating and cooling time. As the
frequency increases, the shorter cooling time means that the SMA wire cannot cool down to a
temperature corresponding to the fully martensitic state, so the actuator remains partially bent
due to a partial contraction of the wire. This changes the initial conditions for the next cycle and
produces drifting in the actuator response. The average temperature of the actuator will increase
over time, and the actuator itself will approach a steady state when it reaches the temperature at
which the SMA wire is fully austenitic. Experiments at higher frequencies exhibit a larger drift of
the actuator's position, as depicted in the plots.
The experiments suggest the use of the 90- m carbon ber as the central piece for the bending
actuator used in the construction of SMALLBug. Since thinner carbon ber results in larger
displacements, the 90- m carbon ber SMA actuator exhibits the largest bending, allowing the
crawler to locomote farther and faster.
Power Estimation
The power consumption of the actuators can be estimated using the average power concept. Eq. 4.1
show the average power over a period T .
P
avg
=
1
T
Z
T
0
V (t)
2
R
dt (4.1)
Where V (t) is the input voltage signal and R is the electrical resistance pf tje actuator. Utilizing
the idea of the actuator being powered by PWM signal which is "on" during some period and "o"
during the rest. We can split V (t) into V
on
and V
off
. So , we can write:
P
avg
=
1
T
(
Z
DCT
0
V
on
(t)
2
R
dt +
Z
T
DCT
V
off
(t)
2
R
dt) (4.2)
Where DC is the duty cycle of the signal sent. Then we know that the Voltage during the o
time is zero. So we can write
Pavg =
1
T
Z
DCT
0
V
on
(t)
2
R
dt (4.3)
64
Finally, since V
on
(t) is constant, we can directly integrate, obtaining
P
avg
=DC
V
2
on
R
(4.4)
Using an constant V
on
of 10 V, an electrical resistance of 100
and a duty cycle of 10%. We can
obtain an estimated average power of 100 mW
Figure 4.8: Photographic sequence of crawling experiments. (a) Locomotion experiment at 2 Hz.
(b) Tracked position of the robot during the experiment. At this frequency, the robot uses the crawling gait,
and the plot shows its characteristic behavior of taking discrete steps. (c) Locomotion experiment at 10 Hz.
(d) Tracked position of the robot during the experiment. At this frequency, the robot uses the shuing gait,
and the plot shows an approximately constant velocity, characteristic of this type of motion. (e) Locomotion
experiment at 20 Hz. (f) Tracked position of the robot during the experiment. Here, the SMALLBug uses
the galloping gait, with small jumps. The plot shows sudden changes in slope, indicating that the velocity
of the robot changes in an unpredictable manner during the experiment. At this frequency, the maximum
average speed obtained was 17 mm s
1
(1.4 Bl/s). The complete experiment can be found in the supplemen-
tary movie SMALLBug.mp4 (http://www.uscamsl.com/resources/Calderon thesis 2020/SMALLBug.mp4)
65
4.2.4 Locomotion Experiments
The locomotive capabilities of the robot were tested on a poster board with grid lines. Three
frequencies (2, 10, and 20 Hz) were tested to compare the velocity of the robot over a distance of
11 cm. The robot was recorded with a video camera from a top view in order to measure the number
of squares traveled in a given amount of time. Additionally, using MATLAB's image processing
toolbox, we tracked the position of the robot during the experiments by analyzing each frame of the
video, which was taken at 30 frames per second. With this information, we were able to calculate
the average velocities for each set of parameters and plot the movement patterns for the dierent
frequencies. Photographic sequences of the experiments, along with their respective position-time
plots, are shown in Fig. 4.8.
The robot was able to locomote successfully at all the frequencies used. Table 4.1 shows the
average velocities obtained for each actuator frequency, showing an approximately proportional
relationship between frequency and speed. The experiments showed that the robot could achieve
three dierent gaits depending on the frequency of actuator bending. At low frequencies, around
2 Hz, SMALLBug moves with a discrete stepping motion. This behavior is similar to that of
inchworms, whose locomotion cycle includes a period in which their center of mass does not move.
We call this rst type of gait crawling. In this mode, SMALLBug reached a maximum average
velocity of 2:5 mm s
1
. Fig 4.8-(b) shows a plot of the distance traveled. The steady cyclical
motion of the crawler characterized by easily distinguishable steps is similar to that of inchworms,
which can also be seen in the worm-like robots presented in [78]. At moderate frequencies, around
10 Hz, the actuation is fast enough that the crawler's motion appears to be continuous rather than
discrete. This makes SMALLBug seem to slide across the ground. We call this the shuing mode
due to the similarities between this type of locomotion and the style of dance often performed to
electronic music. Fig. 4.9 shows a side view photographic sequence of SMALLBug moving using
the shuing gait. The actuator deformation is small and fast, which produces smooth motion,
the individual stages of which are dicult to perceive with the naked eye. Fig. 4.8-(c) and (d)
show the photographic sequence from the top view and the distance traveled plot. As expected,
SMALLBug moves with an approximately constant velocity and does not experience any sudden
changes in speed. The average velocity obtained for this scenario is 7 mm s
1
.
66
Table 4.1: Velocities achieved by SMALLBug during locomotion experiments at dierent actuation fre-
quencies
Frequency (Hz) Velocity (mm s
1
) Gait
2 2.5 Crawling
10 7 Shuing
20 17 Galloping
Finally, at high frequencies such as 20 Hz, SMALLBug can be observed to perform small and
fast jumps during the locomotion sequence. We suggest that this is due to the actuator moving so
quickly that it creates impulses that, in combination with the extremely light weight of the robot,
produce jumping, propelling the robot forward due to inertia. This motion is similar to a fast
gallop that can be seen in horses, so we call this the galloping gait. It is the fastest gait we have
observed, reaching an average velocity of 17 mm s
1
. Fig. 4.8-(e) and (f) show the photographic
sequence from the top view and the distance traveled plot. Sudden changes in velocity can be seen,
as well as a decrease in velocity during the last 2 s. This deceleration occurs because after traveling
such a large distance, SMALLBug's power wires begin to reach their limit, and the tension in those
wires prevents the robot from moving freely.
4.3 SMARTI a 60 mg Steerable Micro Robot Crawler
4.3.1 Modular Design
SMARTI is composed of two SMALLBugs organized in parallel, as depicted in Fig. 4.9-(a). This
conguration allows for the independent actuation of each side of the robot. Applying an input
signal that moves one side faster than the other produces a dierential eect, where the robot is
able to steer in the left or right direction. A diagram showing the steerability of SMARTI is shown
in Fig 4.9-(b)
4.3.2 Fabrication
Since SMARTI is composed of two SMALLBugs, the fabrication is similar. However, instead of
fabricating two SMALLBugs independently and then adding them by an interface. We prefer to
design a fabrication method that creates both units in the same monolithic stack. The reason
for this is to decrease the dierences between the left and right sides of the robot. This stack is
67
Figure 4.9: SMARTI design. (a) The design of SMARTI is composed of two SMALLBugs in parallel.
Each SMALLBug has its own SMA bending actuaotr, sigma bodyframe and anisotropic friction legs. (b)
SMARTI can steer to the right and left direction by modulating the velocity of the left and right unit. If
the velocities are the same, the SMARTI should move straight forward.
composed of carbon ber layers at both ends and a central Kapton layer which is used for the
folding features. The back of the robot connects the left and right body frames. This method
makes sure that both sides are parallel to each other and also that both of them share the same
horizontal plane. Once the stack is nished, the actuators are placed and glued in position with
Ciano acrylate, using slots in the frame that match the cross shape of the actuators. Then the
stack with the actuators is released cut using the high-resolution laser cutter, obtaining a
at 2-D
body. Then, the frame is manually folded using the pre-programmed joints, similar to what is seen
in pop-up books where a 2-D conguration is transformed into 3-D. Finally, 49 AWG wires are
glued with conductive epoxy to the ends of the actuators for electrical connection. With this, the
fabrication of SMARTI is complete. A diagram showing the procedure can be seen in Fig. 4.10
4.3.3 Open Loop Crawling Test
The locomotion capabilities of SMARTI are tested in an open-loop experiment. SMARTI locomotes
using the same parameters for the left and right units. However, to minimize interferences between
the motions of each side, the signals are sent with a phase of 90degree. The parameters used are a
frequency of actuation of 5 Hz, a duty cycle of 5%, and an input voltage of 15 V. A photographic
sequence of the robot moving and plots depicting the path taken and error (compared to follow a
straight line) are shown in Fig 4.11. The path taken by SMARTI was followed using markers and
VICON cameras. The results show that despite each side having the same input, the robot tends
to steer naturally to the left direction. The reason for this tendency can be due to the actuators
68
Figure 4.10: SMARTI fabrication. (Step 1) A multi layered stack composed of two layers of carbon ber
and and middle layer of Kapton is processed with high temperature and pressure. (step 2) The actuator
are glued to the stack utilizing slots that match the cross shape at the end of the actuators. (step 3) The
stack is re aligned and cut in the hugh resolution laser cutter. Releasing the body of the robot in 2-D. (step
4) The body is folded into 3-D structure, using features similar to a pop-up book. (step 5) The anisotropic
friction legs are attached and glued to the robot using interlocking features. Finally, 49 AWG wires are
glued to the actuators using conductive epoxy for electrical connection.
having dierences in displacement output due to fabrication errors. Also, the electrical wires can
produce a considerable disturbance taking into account that SMARTI uses four wires (two per
actuator) and the small inertial properties of the robot. All this shows how important and useful
is to use a control method to steer SMARTI.
4.3.4 Control Strategy
Labmate and control expert Rian Bena designed the control strategy. As described before, the
SMA actuators in each side of the robot receive a PWM signal of varying amplitude, frequency
and duty cycle. Fixing amplitude and frequency, the actuators forward motion is only dependant
to the duty cycle of the signal. Therefore, modulating the duty cycle of each side of the robot
could generate the forces required for steering. Similarly to the open-loop test the signals to both
actuator are phased by half a period to minimize the interaction between each side of the robot.
The steering control scheme for SMARTI, depicted in Fig. 4.12(a), uses a two-step feedback
technique to drive the speed and heading of the robot. In the rst step, the robot's position error
is used to determine the desired heading. Then, in the second step, the position and heading errors
are both used as feedback to drive the crawler in the correct direction at the desired speed, v
r
.
To calculate the desired heading,
r
, the controller computes the error between the current
lateral position, y, and the reference lateral position at a future longitudinal position, y
r
(x +d
r
),
by y
e
=y
r
(x +d
r
)y where d
r
is the controller's look-ahead reference distance in the x direction
69
Figure 4.11: SMARTI open loop experiments. (a) Photographic sequency during SMARTI locomotion,
the robot is able to move forward succesfully. However, with a clear tendency to steer to the left. (b) Tracked
position of the robot during the experiment. (c) Lateral error of the robot in open loop, taking in account the
robot the robot should follow a straight path. The complete experiment can be found in the supplementary
movie SMARTI.mp4 (http://www.uscamsl.com/resources/Calderon thesis 2020/SMARTI.mp4)
andy
e
is the position error. As shown geometrically in Fig. 4.12(b), the desired heading is dened
as
r
=atan
y
e
d
r
; (4.5)
where a smalld
r
will produce a faster, over-responsive robot while a larged
r
will result in a slower,
smoother trajectory.
Once
r
is determined, the SMARTI uses a traditional Proportional-Integral (PI) feedback law
to compute the necessary actuator commands.
4.3.5 Control Experiments
In order to show the controllability properties of SMARTI, we performed three dierent experi-
ments. First, to demonstrate the ability of the robot to regulate lateral deviations SMARTI follows
a straight-line trajectory. Then, the second and third experiments aimed to demonstrate turning
70
+
-
+
-
+
-
Figure 4.12: SMARTI control strategy. (a) block diagram of the control scheme used for the control
experiments of SMARTI. The controller was desgied by lab mate and control expert Ryan Bena. (b) Vicon
camera obtain the yaw angle of the robot and compare it to the desired trajectory. Modulating the duty
cycles of the actuators to mantain the robot in the desired path.
capabilities. The robot follows a path composed of two orthogonal straight lines. Here, the robot
must be able to turn to left and to the right respectively.
The results for the rst experiment can be seen in Fig. 4.13. SMARTI successfully follow the
reference path during 45 s. The distance traveled by the robot was 321 mm with an average
lateral bias of 2mm and root mean square (RMS) error of 2mm. SMARTI average speed during
the experiment was 7 mm/s (0.63 BL/s). The experiments show SMARTI capability of regulating
lateral deviations from a simple straight path.
Fig 4.14 and 4.15 depicts both left and right experiments, with lateral errors of 4 mm and 3
mm respectively. SMARTI show turning rates of 64
=s to the left and 84
=s to the right direction.
As seen in the open-loop experiment, we noticed that the power wires cause the majority of the
position and heading errors as they exerted a considerable force and torque to disturb the robot
motions considering the low inertial properties of SMARTI.
4.4 Discussion
In this chapter, we introduced a novel
exible bending SMA actuator with a weight of only 6 mg.
Results show that the actuator is able to produce large displacement for its size even at frequencies
as high as 20 Hz. We implemented the actuator in SMALLBug, a 30 mg
exible modular micro
robot inspired in inchworms. The robot showed dierent locomotion gaits for dierent frequencies.
With a maximal velocity of 2 BL/S, which is an impressive velocity considering the robot size and
weight. We also created a second prototype SMARTI, using two SMALLBugs in a parallel structure.
This robot is able to steer in both left and right directions. Its capabilities were tested in control
71
Figure 4.13: SMARTI control experiment following a straight trajectory. (a) Photographic se-
quence of SMARTI. (b) Tracked path during the experiment, arrows show the direction of the robot. (c)
Lateral error plot. The complete experiment can be found in the supplementary movie SMARTI.mp4
(http://www.uscamsl.com/resources/Calderon thesis 2020/SMARTI.mp4)
experiments, where the robot successfully was able to locomote following a straight trajectory and
also turning 90
in both directions. Experiments show that being tethered is the primary source
of disturbances for the motion of both prototypes. However, The characteristics of the actuators
used, such as using a binary signal, low voltage, and low power requirements make this actuators
well suited for experimenting in the future with electrical batteries, which is promising to improve
the performance of both micro-robots.
72
Figure 4.14: SMARTI control experiment, turning right. (a) Photographic sequence of
SMARTI. (b) Tracked path during the experiment, arrows show the direction of the robot. (c) Lat-
eral error plot. The complete experiment can be found in the supplementary movie SMARTI.mp4
(http://www.uscamsl.com/resources/Calderon thesis 2020/SMARTI.mp4)
Figure 4.15: SMARTI control experiment, turning left. (a) Photographic sequence of SMARTI.
(b) Tracked path during the experiment, arrows show the direction of the robot. (c) Lateral
error plot. The complete experiment can be found in the supplementary movie SMARTI.mp4
(http://www.uscamsl.com/resources/Calderon thesis 2020/SMARTI.mp4)
73
5 Conclusion and Future Work
5.1 Conclusions
In this dissertation, we developed a series of a bio-inspired soft and micro robots. First, we presented
a new type of earthworm inspired soft robot able to locomote inside pipes and other similarly
constrained paths. In this case, the basic motions of an earthworm's metamere are replicated
using two radial extremal actuators and a central axial oscillatory pneumatically-driven mechanism.
The locomotion strategy and control algorithms driving the robotic prototypes are based on ve
discrete conguration states that dene a stride. In each of these states, one or both of the radial
actuators are attached by pressure and friction to the internal surface of the locomotion path. A
rst prototype, RWT1, indirectly infers attachment by measuring the internal air pressures of the
radial actuators and processing these measurements through the a priori identied dynamics of the
robot's subsystems. A second prototype, RWT2, detects attachment directly by employing tactile
sensors embedded in layers of silicone that, in conjunction, form perceptive articial skins. The
capabilities of the robots and the suitability of the proposed control method were demonstrated
through horizontal and vertical locomotion experiments. These experimental tests indicate that the
proposed methods for actuation, sensing and control will enable the development of large, complex
structures composed of modules designed and fabricated with the techniques introduced in this
work. Specically, it is important to note that the soft robots presented here have the capability
to deform, physically adapt and react employing pre-programmable mechanisms to spatial{time
variations of the environments in which they operate.
Second, we developed the know-how necessary to build FWMAV, which includes the equipment,
design methods, recipes, and manual skills required for the fabrication of the dierent components.
A 75 mg micro-robot with a design inspired in the microrobot presented in [64] was fabricated and
tested. This to conrm we had the capabilities to build our own FWMAV able to sustain
ight.
74
Our robot was successfully able to produce hovering using feedback control. The robot showed an
average maximal average lift force of 135 mg measured by our capacitive force sensor presented
in [66].
Biology research suggests that the best wing pitch angle for maximal average lift generation is
70
. This could be why
ies and bees tend to
ap their wings within that range of pitching angles.
We designed a non-linear stiness hinge mechanism that avoids pitching angles to be over 70
by
the use of soft limits that increase the eective stiness of the hinge at high pitching angles. We
studied and compared the regular and non-linear hinges lift generation via the micro force sensor.
The results showed that the new hinge allows the generation of higher forces using smaller
apping
angles. This by taking advantage of the lift and drag coecient at this range of pitching angles.
This improvement allowed us to generate a new 60 mg prototype by using 20% shorter and lighter
actuators. This because of the smaller displacement requirements. The use of this hinge is also
useful for control experiments. Specically, during control experiments, the
apping patterns are
always changing to compensate body torques, meaning that the wing pitch is always changing.
The new hinge limits the wing pitch of the robot during
apping to 70
, which can improve force
generation during control. The second prototype was able to generate a maximum of 147 mg of
average lift force and produce hovering
ight using feedback control.
Finally, we developed SMALLBug, a 30-mg crawling microrobot that utilizes a 6-mg high-
frequency SMA bending actuator. The bending actuators are characterized in experiments where
dierent input signals with varying duty cycles are used to observe their response.
SMALLBug exhibited three distinct gaits depending on the driving frequencies: crawling, shuf-
ing and galloping. The maximum speed was obtained by galloping, where the velocity was
17 mm s
1
(or 1:4 Bl/s), which is very high compared to existing SMA-based microrobots. Our
design demonstrates that the use of thin (low thermal mass) SMA wires is very promising for the
fabrication of microrobots. The modularity features of SMALLBug allow the design of SMARTI.
A 60 mg crawling robot, which is composed of two SMALLBugs in parallel conguration. Since
both units can be driven independently, SMARTI can steer in the left and right directions. Control
experiments were performed to show the robot's capabilities to follow straight-line paths and turn
to the left and right directions.
75
5.2 Current and Future Work
The current and future work will also be presented by topic
5.2.1 Soft Robots
The results obtained for the earthworm inspired robot show that it is possible to use the current
robot as a module or metamere. This unit can be repeated to create a more complex multi-unit soft
robot. This robot can be used to test how dierent frequencies and wavelengths of the peristaltic
wave passing through the body could produce dierent gaits. The articial skin designed in this
work showed promising results to be used in other systems. The model ended with a variable ;
more experiments can be conducted to nd its physical meaning. The results suggest that the
strain rate can be related to .
5.2.2 Micro Robots
As a result of this work, we obtained the know-how to build microrobots. The design and fabrication
processed learned are the base for the future creation of more microrobots. The generation of our
own 60 60 mg FWMAV shows that there is still space for improvement of the robotic
iers. The
goal would be in the future to be able to build robots with the capabilities to perform high-speed
maneuvers.
5.2.3 Flexible Micro Robots
We want to implement a series of ideas into SMALLBugs and SMARTI robots. For example,
we could implement bidirectional locomotion drawing inspiration from the directional claws in
[79]. Furthermore, the robot's modular design could allow future research to integrate multiple
SMALLBugs in parallel or in series to study steering capabilities and new locomotion gaits. This
could also enable the study and use of distributed control to optimize the congurations for speed
and steering modulation purposes. SMA technology could be applied to create actuators capable
of dierent modes of motion other than bending, for example, twisting as a result of dierent
internal structures in the central carbon ber such as those discussed in [76] and [77]. Our actuator
design also leaves open the possibility for a bimorph bending actuator, which would increase the
76
displacement. Finally, we aim in the future for fully autonomous robots. Our crawler's low voltage
requirements (under 20 V) and digital signal input make the robot an ideal candidate for the use
of batteries [80] or other onboard power sources to be investigated.
77
Bibliography
[1] A. A. Calder on, J. C. Ugalde, J. C. Zagal, and N. O. P erez-Arancibia, \Design, Fabrication
and Control of a Multi-Material{Multi-Actuator Soft Robot Inspired by Burrowing Worms,"
in Proc. 2016 IEEE Int. Conf. Robot. Biomim. (ROBIO 2016), Qindao, China, Dec. 2016, pp.
31{38.
[2] A. A. Calder on, J. C. Ugalde, L. Chang, J. C. Zagal, and N. O. P erez-Arancibia. Supporting
Movie S1.mp4 (Feb. 2018). http://www.uscamsl.com/resources/SR/S1.mp4.
[3] M. H. Dickinson and M. S. Tu, \The Function of Dipteran Flight Muscle," Comp. Biochem.
Phys. A, vol. 116, no. 3, pp. 223{238, Mar. 1997.
[4] K.
Capek, RUR (Rossum's universal robots): a fantastic melodrama. Theatre Guild, 1923.
[5] P. Bizony,, \Focus:# 1 The First Law: A robot may not injure a human being, or, through
inaction, allow a human being to come to harm," Engineering & Technology, vol. 10, no. 6,
pp. 52{53, 2015.
[6] F. Ilievski, A. D. Mazzeo, R. F. Shepherd, X. Chen, and G. M. Whitesides, \Soft robotics for
chemists," Angew. Chem. Int., vol. 50, no. 8, pp. 1890{1895, 2011.
[7] M. T. Tolley, R. F. Shepherd, B. Mosadegh, K. C. Galloway, M. Wehner, M. Karpelson, R. J.
Wood, and G. M. Whitesides, \A resilient, untethered soft robot," Soft Robot., vol. 1, no. 3,
pp. 213{223, 2014.
[8] C. Laschi, M. Cianchetti, B. Mazzolai, L. Margheri, M. Follador, and P. Dario, \Soft Robot
Arm Inspired by the Octopus," Adv. Robot., vol. 26, no. 7, pp. 709{727, 2012.
[9] C. P. Hickman, L. S. Roberts, S. L. Keen, A. Larson, H. I'Anson, and D. J. Eisenhour,
Integrated Principles of Zoology, 14th Edition. New York, NY: McGraw-Hill Higher Education,
2008.
[10] D. Sadava, D. M. Hillis, H. C. Heller, and M. R. Berenbaum, Life: The Science of Biology,
9th Edition. Sunderland, MA: Sinauer Associates Inc., 2011.
[11] K. J. Quillin, \Kinematic Scaling of Locomotion by Hydrostatic Animals: Ontogeny of Peri-
staltic Crawling by the Earthworm Lumbricus Terrestris," J. Exp. Biol., vol. 202, no. 6, pp.
661{674, Mar. 1999.
[12] S. Seok, C. D. Onal, K.-J. Cho, R. J. Wood, D. Rus, and S. Kim, \Meshworm: A Peristaltic Soft
Robot With Antagonistic Nickel Titanium Coil Actuators," IEEE/ASME Trans. Mechatron.,
vol. 18, no. 5, pp. 1485{1497, Oct. 2013.
78
[13] T. Nakamura, T. Kato, T. Iwanaga, and Y. Muranaka, \Development of a Peristaltic Crawling
Robot Based on Earthworm Locomotion," J. Robot. Mechatron., vol. 18, no. 3, pp. 299{304,
Jun. 2006.
[14] J. B. Reece, L. A. Urry, M. L. Cain, S. A. Wasserman, P. V. Minorski, and R. B. Jackson,
Campbell Biology, 10th Edition. Glenview, IL: Pearson, 2014.
[15] A. Kaestner, Invertebrate Zoology, Volume I. New York, NY: Interscience Publishers, 1967.
[16] M. S. Laverack, \Tactile and Chemical Perception in Earthworms I. Responses to Touch,
Sodium Chloride, Quinine and Sugars," Comp. Biochem. Physiol., vol. 1, no. 2, pp. 155{163,
May 1960.
[17] ||, \Tactile and Chemical Perception in Earthworms II. Responses to Acid pH Solutions,"
Comp. Biochem. Physiol., vol. 2, no. 1, pp. 22{34, Jan. 1961.
[18] W. N. Hess, \Photoreceptors of Lumbricus Terrestris With Special Reference to Their Distri-
bution, Structure, and Function," J. Morphol. Physiol., vol. 41, no. 1, pp. 63{93, Dec. 1925.
[19] C. Majidi, \Soft Robotics: A Perspective|Current Trends and Prospects for the Future," Soft
Robot., vol. 1, no. 1, pp. 5{11, Jul. 2013.
[20] Y. Xia and G. M. Whitesides, \Soft Lithography," Annu. Rev. Mater. Sci., vol. 28, no. 1, pp.
153{184, Aug. 1998.
[21] D. Qin, Y. Xia, and G. M. Whitesides, \Soft Lithography for Micro- and Nanoscale Pattern-
ing," Nat. Protoc., vol. 5, no. 3, pp. 491{502, Feb. 2010.
[22] J. Z. Ge, A. A. Calder on, and N. O. P erez-Arancibia, \An Earthworm-Inspired Soft Crawling
Robot Controlled by Friction," in Proc. 2017 IEEE Int. Conf. Robot. Biomim. (ROBIO 2017),
Macau SAR, China, Dec. 2017, pp. 834{841.
[23] R. F. Shepherd, F. Ilievski, W. Choi, S. A. Morin, A. A. Stokes, A. D. Mazzeo, X. Chen, M.
Wang, and G. M. Whitesides, \Multigait Soft Robot," Proc. Nat. Acad. Sci., vol. 108, no. 51,
pp. 20 400{20 403, Dec. 2011.
[24] J.-Y. Nagase, S. Wakimoto, T. Satoh, N. Saga, and K. Suzumori, \Design of a Variable-Stiness
Robotic Hand Using Pneumatic Soft Rubber Actuators," Smart Mater. Struct., vol. 20, no. 10,
p. 105015 (9pp), Oct. 2011.
[25] T. Ranzani, M. Cianchetti, G. Gerboni, I. De Falco, G. Petroni, and A. Menciassi, \A Mod-
ular Soft Manipulator with Variable Stiness," in Proc. 3rd Joint Workshop New Technol.
Comput./Robot Assisted Surgery, Verona, Italy, Sep. 2013.
[26] K. C. Galloway, P. Polygerinos, C. J. Walsh, and R. J. Wood, \Mechanically Programmable
Bend Radius for Fiber-Reinforced Soft Actuators," in Proc. 2013 16th Int. Conf. Adv. Robot.
(ICAR 2013), Montevideo, Uruguay, Nov. 2013.
[27] R. V. Martinez, J. L. Branch, C. R. Fish, L. Jin, R. F. Shepherd, R. M. D. Nunes, Z. Suo,
and G. M. Whitesides, \Robotic Tentacles with Three-Dimensional Mobility Based on Flexible
Elastomers," Adv. Mater., vol. 25, no. 2, pp. 205{212, Jan. 2013.
79
[28] S. C. Obiajulu, E. T. Roche, F. A. Pigula, and C. J. Walsh, \Soft Pneumatic Articial Muscles
with Low Threshold Pressures for a Cardiac Compression Device," in Proc. ASME 2013 Int.
Design Eng. Tech. Conf. & Comput. Inform. Eng. Conf. (IDETC/CIE 2013), Portland, OR,
Aug. 2013.
[29] M. Schulke, L. Hartmann, and C. Behn, \Worm-Like Locomotion Systems: Development of
Drives and Selective Anisotropic Friction Structures," in Proc. 56th Int. Scientic Colloq.,
Ilmenau, Germany, Sep. 2011.
[30] T. Saito, T. Kagiwada, and H. Harada, \Development of an Earthworm Robot with a Shape
Memory Alloy and Braided Tube," Adv. Robot., vol. 23, no. 12{13, pp. 1743{1760, 2009.
[31] B. Kim, M. G. Lee, Y. P. Lee, Y. Kim, and GH Lee, \An Earthworm-Like Micro Robot Using
Shape Memory Alloy Actuator," Sensors Actuat. A: Phys., vol. 125, no. 2, pp. 429{437, Jan.
2006.
[32] N. Saga and T. Nakamura, \Development of a Peristaltic Crawling Robot Using Magnetic
Fluid on the Basis of the Locomotion Mechanism of the Earthworm," Smart Mater. Struct.,
vol. 13, no. 3, pp. 566{569, May 2004.
[33] J. Zuo, G. Yan, and Z. Gao, \A Micro Creeping Robot for Colonoscopy Based on the Earth-
worm," J. Med. Eng. & Technol., vol. 29, no. 1, pp. 1{7, Jan. 2005.
[34] K. Wang, G. Yan, G. Ma, and D. Ye, \An Earthworm-Like Robotic Endoscope System for
Human Intestine: Design, Analysis, and Experiment," Ann. Biomed. Eng., vol. 37, no. 1, pp.
210{221, Jun. 2009.
[35] M. Kubota and T. Noritsugu, \Development of In-Pipe Mobile Robot Using Pneumatic Soft-
Actuator," in Proc. JFPS Int. Symp. Fluid Power, 1999, pp. 195{200.
[36] T. Noritsugu and M. Kubota, \Development of In-Pipe Mobile Robot using Pneumatic Soft-
Actuator," J. Robot. Soc. Japan, vol. 18, no. 6, pp. 831{838, Aug. 2000.
[37] S. Schwebke and C. Behn, \Worm-like robotic systems: Generation, analysis and shift of gaits
using adaptive control," J. Artif. Intell. Res., vol. 2, no. 1, p. 12, 2012.
[38] H. Fang , S. Li, K.W. Wang, and J. Xu, \A comprehensive study on the locomotion charac-
teristics of a metameric earthworm-like robot, Part A," Multibody Syst. Dyn., vol. 34, no. 4,
pp. 391{413, Aug 2015.
[39] H. Fang,, Ch. Wang , S. Li , K.W. Wang, and J. Xu, \A comprehensive study on the locomotion
characteristics of a metameric earthworm-like robot, Part B," Multibody Syst. Dyn., vol. 35,
no. 2, pp. 153{177, Oct 2015.
[40] D. Agostinelli, F. Alouges, and A. De Simone, \Peristaltic waves as optimal gaits in metameric
bio-inspired robots," Frontiers in Robotics and AI, vol. 5, p. 99, 2018.
[41] H. Fang, S. Li, K.W. Wang, and J. Xu, \Phase coordination and phase{velocity relationship
in metameric robot locomotion," Bioinspir. Biomim,, vol. 10, no. 6, p. 066006, 2015.
[42] K. A. Daltorio, A. S. Boxerbaum., A. D. Horchler, K. M. Shaw, H. J. Chiel, and R. D. Quinn,
\Ecient worm-like locomotion: slip and control of soft-bodied peristaltic robots," Bioinspir.
Biomim., vol. 8, no. 3, p. 035003, 2013.
80
[43] A. D Horchler, A. Kandhari, K. A. Daltorio, K. C. Moses, J. C. Ryan, K. A. Stultz, E. N. Kanu,
K. B. Andersen, J. A. Kershaw, R. J. Bachmann, H. J. Chiel, and R. D. Quinn, \Peristaltic
locomotion of a modular mesh-based worm robot: precision, compliance, and friction," Soft
Robot., vol. 2, no. 4, pp. 135{145, 2015.
[44] M. D. Dickey, R. C. Chiechi, R. L. Larsen, E. A. Weiss, D. A. Weitz, and G. M. White-
sides, \Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable
Structures in Microchannels at Room Temperature," Adv. Funct. Mater., vol. 18, no. 7, pp.
1097{1104, Apr. 2008.
[45] R. K. Kramer, C. Majidi, R. Sahai, and R. J. Wood, \Soft Curvature Sensors for Joint Angle
Proprioception," in Proc. 2011 IEEE/RSJ Int. Conf. on Intell. Robots Syst. (IROS 2011), San
Francisco, CA, Sep. 2011, pp. 1919{1926.
[46] Y.-L. Park, B.-r. Chen, and R. J. Wood, \Design and Fabrication of Soft Articial Skin Using
Embedded Microchannels and Liquid Conductors," IEEE Sensors J., vol. 12, no. 8, pp. 2711{
2718, Aug. 2012.
[47] D. M. Vogt, Y.-L. Park, and R. J. Wood, \Design and Characterization of a Soft Multi-Axis
Force Sensor Using Embedded Micro
uidic Channels," IEEE Sensors J., vol. 13, no. 10, pp.
4056{4064, Oct. 2013.
[48] J. K. Paik, R. K. Kramer, and R. J. Wood, \Stretchable Circuits and Sensors for Robotic
Origami," in Proc. 2011 IEEE/RSJ Int. Conf. Intell. Robots and Syst. (IROS 2011), San
Francisco, CA, Sep. 2011, pp. 414{420.
[49] Y.-L. Park, B.-r. Chen, N. O. P erez-Arancibia, D. Young, L. Stirling, R. J. Wood, E. C.
Goldeld, and R. Nagpal, \Design and Control of a Bio-Inspired Soft Wearable Robotic Device
for Ankle{Foot Rehabilitation," Bioinspir. Biomim., vol. 9, no. 1, p. 016007 (17pp), Mar. 2014.
[50] J. Kwon, S. Park, J. Park, and B. Kim, \Evaluation of the Critical Stroke of an Earthworm-
Like Robot for Capsule Endoscopes," Proc. I. of Mech. Eng, Part H: J. Eng. Med., vol. 221,
no. 4, pp. 397{405, May 2007.
[51] I. Asimov, Fantastic Voyage. New York, NY: Bantam Books, 1966.
[52] K. J. Quillin, \Ontogenetic Scaling of Hydrostatic Skeletons: Geometric, Static Stress and
Dynamic Stress Scaling of the Earthworm Lumbricus Terrestris," J. Exp. Biol., vol. 201,
no. 12, pp. 1871{1883, Jun. 1998.
[53] R. M. Alexander, Principles of Animal Locomotion. Princeton, NJ: Princeton University
Press, 2003.
[54] M. Mooney, \A Theory of Large Elastic Deformation," J. Appl. Phys., vol. 11, no. 9, pp.
582{592, Sep. 1940.
[55] R. S. Rivlin, \Large Elastic Deformations of Isotropic Materials IV. Further Developments of
the General Theory," Philos. Trans. R. Soc. A, vol. 241, no. 835, pp. 379{397, Oct. 1948.
[56] B. Song and W. Chen, \Dynamic Compressive Behavior of EPDM Rubber Under Nearly
Uniaxial Strain Conditions," J. Eng. Mater. Technol., vol. 126, no. 2, pp. 213{217, Apr. 2004.
81
[57] P. A. L. S. Martins, R. M. Natal Jorge, and A. J. M. Ferreira, \A Comparative Study of Several
Material Models for Prediction of Hyperelastic Properties: Application to Silicone-Rubber and
Soft Tissues," Strain, vol. 42, no. 3, pp. 135{147, Aug. 2006.
[58] M. Sasso, G. Palmieri, G. Chiappini, and D. Amodio, \Characterization of Hyperelastic
Rubber-Like Materials by Biaxial and Uniaxial Stretching Tests Based on Optical Methods,"
Polymer Testing, vol. 27, no. 8, pp. 995{1004, Dec. 2008.
[59] J.-B. Chossat, Y.-L. Park, R. J. Wood, and V. Duchaine, \A Soft Strain Sensor Based on Ionic
and Metal Liquids," IEEE Sensors J., vol. 13, no. 9, pp. 3405{3414, Sep. 2013.
[60] P. Beater, Pneumatic Drives: System Design, Modelling and Control. Berlin, Germany:
Springer-Verlag, 2007.
[61] R. J. Wood, S. Avadhanula, M. Menon, and R. S. Fearing, \Microrobotics using composite
materials: The micromechanical
ying insect thorax," in Proc. 2003 IEEE Int. Conf. on Robot.
and Automat. (ICRA 2003), vol. 2. IEEE, 2003, pp. 1842{1849.
[62] R. J. Wood, \Design, fabrication, and analysis of a 3DOF, 3cm
apping-wing MAV," in Proc.
2007 IEEE/RSJ Int. Conf. on Intell. Robots and Syst. (IROS 2007). IEEE, 2007, pp. 1576{
1581.
[63] R. J. Wood, S. Avadhanula, R. Sahai, E. Steltz, and R. S. Fearing, \Microrobot design using
ber reinforced composites," J. Mech. Des., vol. 130, no. 5, p. 052304, 2008.
[64] K. Ma, \Design, fabrication, and modeling of the split actuator microrobotic bee."
[65] A. Calder on, Y. Chen, X. Yang, L. Chang, X.-T. Nguyen, E. Singer, and N. P erez-Arancibia,
\Control of
ying robotic insects: A perspective and unifying approach," arXiv preprint
arXiv:1910.11911, 2019.
[66] E. K. Singer, L. Chang, A. A. Calderon, and N. O. Perez-Arancibia, \Clip-brazing for the de-
sign and fabrication of micro-newton-resolution, millimeter-scale force sensors," Smart Mater.
Struct., 2018.
[67] X. Yang, Y. Chen, L. Chang, A. A. Calder on, and N. O. P erez-Arancibia, \Bee
+
: A 95-
mg Four-Winged Insect-Scale Flying Robot Driven by Twinned Unimorph Actuators," IEEE
Robot. Autom. Lett., vol. 4, no. 4, pp. 4270{4277, Oct. 2019.
[68] M. H. Dickinson, F-O. Lehmann, and S. P. Sane, \Wing rotation and the aerodynamic basis
of insect
ight," Science, vol. 284, no. 5422, pp. 1954{1960, 1999.
[69] J. P. Whitney and R. J. Wood, \Aeromechanics of passive rotation in
apping
ight," J. Fluid
Mech., vol. 660, pp. 197{220, 2010.
[70] N. Gravish and R. J. Wood, \Anomalous yaw torque generation from passively pitching wings,"
in Proc.2016 IEEE Int. Conf. on Robot. and Autom. (ICRA 2016), 2016, pp. 3282{3287.
[71] N. O. P erez-Arancibia, J. P. Whitney, and R. J. Wood, \Lift force control of
apping-wing
microrobots using adaptive feedforward schemes," IEEE/ASME T. Mech., vol. 18, no. 1, pp.
155{168, 2011.
[72] E. Diller and M. Sitti, \Micro-scale mobile robotics," Found. Trends R
Robot., vol. 2, no. 3,
pp. 143{259, 2013.
82
[73] A. M. Hoover, E. Steltz, and R. S. Fearing, \RoACH: An autonomous 2.4 g crawling hexapod
robot," in Proc. 2008 IEEE/RSJ Int. Conf. on Intell. Robots and Syst. (IROS 2008). IEEE,
2008, pp. 26{33.
[74] K Saito, M. Takato, Y. Sekine, and F. Uchikoba, \Biomimetics micro robot with active hard-
ware neural networks locomotion control and insect-like switching behaviour," Int. J. Adv.
Robot. Syst., vol. 9, no. 5, p. 226, 2012.
[75] J.-S. Koh and K.-J. Cho, \Omegabot: Crawling robot inspired by ascotis selenaria," in Proc.
2010 IEEE Int. Conf. on Robot. and Autom. (ICRA 2010), 2010, pp. 109{114.
[76] S.-H. Song, H. Lee, J.-G. Lee, J.-Y. Lee, M. Cho, and S.-H. Ahn, \Design and analysis of a
smart soft composite structure for various modes of actuation," Compos. Part B: Eng., vol. 95,
pp. 155{165, 2016.
[77] S.-H. Song, J.-Y. Lee, H. Rodrigue, I.-S. Choi, Y. J. Kang, and S.-H. Ahn, \35 hz shape
memory alloy actuator with bending-twisting mode," Sci. Rep., vol. 6, p. 21118, 2016.
[78] A. A. Calder on, J. C. Ugalde, L. Chang, J. C. Zagal, and N. O. P erez-Arancibia, \An
earthworm-inspired soft robot with perceptive articial skin," Bioinspir. Biomim., vol. 14,
no. 5, p. 056012, 2019.
[79] D. Lee, S. Kim, Y-L. Park, and R. J. Wood, \Design of centimeter-scale inchworm robots
with bidirectional claws," in Proc. 2011 IEEE Int. Conf. on Robot. and Autom. (ICRA 2011).
IEEE, 2011, pp. 3197{3204.
[80] J.-M. Breguet, S. Johansson, W. Driesen, and U. Simu, \A review on actuation principles
for few cubic millimeter sized mobile micro-robots," in Proc. of the 10th Int. Conf. on New
Actuators, 2006, pp. 374{381.
83
Abstract (if available)
Abstract
Animals in nature exhibit remarkable abilities that facilitate their survival. Millions of years of evolution through natural selection have produced a variety of solutions to different problems, which while not necessarily optimal, have already been proven to work. Humans have attempted to imitate those abilities for hundreds of years. However, the fabrication capabilities required to extract the bio-inspired ideas and convert them into functional objects have emerged only in the last few decades. This improvement in fabrication capabilities has brought about the existence of bioinspiration as a field of research. ❧ In this work, we developed the methods for the design, fabrication and control of a series of bioinspired robots. First, we take inspiration from burrowing earthworms, which are animals that can locomote through complex and intricate environments despite being limbless, and can even create its own path by burrowing underground. We mimic the basics of their metameric bodies to develop a pneumatic soft robot that is able to locomote inside pipes and other similarly shaped environments. The internal coelomic fluid, radial and longitudinal muscles are translated into artificial muscles with internal air chambers and similar directional motion. ❧ The expansion and contraction of the artificial muscles which interact with the environment generate the forces required for forward motion. We also designed and fabricated an artificial skin which allows the robot to detect geometry changes and forces applied by the environment. This feature allows for the use of feedback control to improve locomotion. It also allows the robot to discover its environment, which is an essential feature for future implementation in areas such as search and rescue. ❧ Second, We designed and fabricated flapping-wing micro air vehicles bioinspired by bees and flies. Their capabilities to maneuver in the air and incredibly fast reaction times are extremely impressive. The design and fabrication of elements such as frames, transmission, actuators and wings at this scale required sophisticated methods that we learned from the state of the art and improved upon. We experimentally tested our first 75-mg prototype via a hovering controlled experiment. Biological studies suggest that a wing pitch rotation around 70 degrees improves the performance of the wing. ❧ We designed and fabricated a non-linear stiffness hinge which prevents the wings from overrotating (reaching angles over 70 degrees). We studied and compared the performance of the new hinge with a classical hinge and showed that the wing was able to generate more lift force with smaller flapping angles. This enabled the design of a new prototype with smaller actuator displacement requirements and could use shorter and lighter actuators. This new prototype, which is only 60 mg, was able to generate 10% more lift than the original prototype. Due to this decrease in weight, the lift force to weight ratio was improved from 1.7 to 2.5. The robot was also tested in a control hovering experiment and shown to be able to sustain flight. ❧ Last, the knowledge obtained by building soft and micro-robots allowed us to create a new robot that is bio-inspired by inchworms. Inchworms are soft and small, which are the characteristic of both previous projects mentioned. We designed and fabricated a novel 6mg flexible SMA bending actuator, which is able to produce considerable displacements (500 µm) at 20 Hz. We used this actuator in SMALLBug, a 30-mg flexible micro robot able to crawl on at surfaces with speeds as fast as 17mm/s. The modular design of this robot was used to create a second 60-mg prototype called SMARTI, which consists of two SMALLBugs in parallel. The configuration enables steering capabilities, which were tested via control experiments where the robot followed prescribed paths such as a straight line and two orthogonal straight lines that demonstrated its ability to turn left and right.
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Asset Metadata
Creator
Calderón, Ariel A.
(author)
Core Title
Novel soft and micro transducers for biologically-inspired robots
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
08/11/2020
Defense Date
08/10/2020
Publisher
University of Southern California
(original),
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Tag
bio-inspired robotics,flying robotics,micro-robotics,OAI-PMH Harvest,soft robotics
Language
English
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Advisor
Perez-Arancibia, Nestor O. (
committee chair
), Chen, Yong (
committee member
), Kanso, Eva A. (
committee member
)
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aacalder@usc.edu,arcalderaven@gmail.com
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https://doi.org/10.25549/usctheses-c89-363514
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Calderón, Ariel A.; Calderon, Ariel A.
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Tags
bio-inspired robotics
flying robotics
micro-robotics
soft robotics