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Development of biologically-inspired sub-gram insect-scale autonomous robots
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Development of biologically-inspired sub-gram insect-scale autonomous robots
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Content
Development of Biologically-Inspired
Sub-Gram Insect-Scale Autonomous Robots
by
Xiufeng Yang
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)
May 2020
Copyright 2020 Xiufeng Yang
Tomydearparents,eldersister,andgirlfriend
ii
Acknowledgments
First and foremost, I would like to thank my advisor, Dr. Néstor O. Pérez-Arancibia, for
his insightful research guidance and generous help during the past five years. He led
me into a research field I am passionate about and supported me to pursue any ideas
I came out with. I gained some life-long benefits from the research experience with
him, including the notion and exercise of critical thinking, and a rigorous attitude
towards science and technology.
I would also like to thank Dr. Paul Ronney. His suggestions and guidance had
inspired me in many research topics we discussed. Moreover, I would not have been
able to complete the combustion experiments in this dissertation without help from
him and members of his lab, including Yang Shi, Zhenghong Zhou, Dr. Si Shen, and
Dr. Jakrapop Wongwiwat.
I would like to thank all the committee members of my dissertation defense and
qualifying exam, including Dr. Yong Chen, Dr. Mitul Luhar, Dr. Satyandra Gupta, and
Dr. Qiming Wang, for their thoughtful opinions and constructive suggestions for my
research.
I would also like to express my appreciation to all my colleagues at the au-
tonomous microrobotic systems laboratory (AMSL). Namely, Dr. Longlong Chang,
who is not only the best partner in research, but also one of my best friends since
I came to USC; Dr. Zaoyuan Ge for his help in research, conducting experiments,
iii
academic writing, and daily life; Dr. Ying Chen for insightful discussions and valuable
help with the control experiments of Bee
+
. Also, I would like to thank Ariel Calderón,
Xuan-Truc Nguyen, and Emma Singer for helping me to learn the fabrication pro-
cess of microrobots. Additionally, I thank Ke Xu and other members at AMSL for all
their encouragement and support during my Ph.D. experience; and all the friends I
met at USC, including Xingtian Tao, Wenhao Zhang, Dr. Xize Wang, for the precious
friendship in overseas life.
I want to convey my special thanks to my girlfriend, Nicole Lin. Every moment
we have experienced in the past four years is the source of happiness in my heart.
Most importantly, I would like to express my infinite gratitude to my parents and
elder sister. Their unconditional love, care, understanding, and support gave me the
courage and serenity to face anything life throws at me.
At last, I thank the financial support of my research by the USC Viterbi School
of Engineering, the National Science Foundation (NSF), and the Defense Advanced
Research Projects Agency (DARPA) through awards and contracts granted to my
advisor.
Xiufeng Yang
Los Angeles, California
December, 2019
iv
Table of Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Bee
+
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Design and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 Robotic design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Aerodynamic design and analysis . . . . . . . . . . . . . . . . . . . . . 12
2.2 Fabrication of the robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Fabrication of twinned unimorph actuators . . . . . . . . . . . . . . 16
2.2.2 Robotic assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Flight controller design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 System dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Attitude control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.3 Position control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.4 Actuator command generation . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
v
2.4.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2 Simultaneous control of altitude and attitude . . . . . . . . . . . . . 25
2.4.3 Position control experiment . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Catalytic artificial muscle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1 Mechanism of catalytic artificial muscles . . . . . . . . . . . . . . . . . . . . . . 31
3.1.1 Heterogeneous catalytic reactions . . . . . . . . . . . . . . . . . . . . . 34
3.1.2 Mechanism of shape-memory alloys . . . . . . . . . . . . . . . . . . . 37
3.2 Fabrication of catalytic artificial muscles . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 Fast controlled flow actuator . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.2 Temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.3 Real-time controller synthesis . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.4 Wing-flapping mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4.1 System characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4.2 Fuzzy-logic-controlled fast actuation . . . . . . . . . . . . . . . . . . . 57
3.4.3 Wing-flapping motion driven by the artificial muscle . . . . . . . 60
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 RoBeetle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Catalytic NiTi-Pt artificial muscle for microrobot . . . . . . . . . . . . . . . . 65
4.2.1 Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.2 Fabrication method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.3 Characterization experiment . . . . . . . . . . . . . . . . . . . . . . . . . 71
vi
4.3 Design and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.1 Robotic design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.2 Fabrication of the robotic prototypes . . . . . . . . . . . . . . . . . . . 79
4.3.3 Evaporation of methanol experiment . . . . . . . . . . . . . . . . . . . 80
4.3.4 Diffusion of methanol vapor model . . . . . . . . . . . . . . . . . . . . 81
4.3.5 Determination of the leaf-spring stiffness coefficient . . . . . . . 83
4.4 Tethered stationary experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.2 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.4.3 Thermodynamic model of the artificial muscles . . . . . . . . . . . 88
4.5 Autonomous locomotion experiments . . . . . . . . . . . . . . . . . . . . . . . 89
4.5.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.5.2 Experimental estimation of the friction coefficients . . . . . . . . 94
4.5.3 Dynamic model of the locomotion gait . . . . . . . . . . . . . . . . . . 97
4.5.4 Functional capabilities and locomotion performance . . . . . . . 104
4.5.5 Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.6 An application example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.6.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.6.2 On-board RFID chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
vii
Supplementary tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Supplementary movies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
viii
List of Tables
2.1 Comparison of the parameters of Bee
+
, the RoboBee and Four-wings. . . . 8
S1 Energy densities and specific energies of various sources of power. . . . . . 142
S2 Work densities and power densities of different actuation methods. . . . . . 143
S3 Physical parameters of the RoBeetle prototype. . . . . . . . . . . . . . . . . . . . . 143
S4 Locomotion velocities of various robot and insects. (Values estimated
from references are marked with ‘†’) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
S5 Experimentally-estimated friction coefficient of the robot’s forelegs and
hindlegs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
S6 Geometric and inertial parameters of RoBeetle employed in dynamic
simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
S7 Characterized parameters of the input signal employed in dynamic simu-
lation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
ix
List of Figures
2.1 Bee
+
(right), a new four-winged flying microrobot . . . . . . . . . . . . . . . . . . 8
2.2 Schematic diagrams of the four-winged robotic design . . . . . . . . . . . . . . 9
2.3 Fabrication process of a batch of twinned piezoelectric unimorph actuators 16
2.4 Simultaneous real-time control of altitude and attitude . . . . . . . . . . . . . . 27
2.5 Controlled flight experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6 The position control experiment result . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 NiTi-Pt-based composite artificial muscles driven by catalytic combustion 34
3.2 Induction period and thermal runaway of catalytic reaction on the CAM . 36
3.3 Characteristics of SMAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 CAM fabrication method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.6 System identification and LTI controller design for CFA . . . . . . . . . . . . . . 45
3.7 Measurement and processing of the temperature on the surface of the
NiTi-Pt composite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.8 Filters and signal correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.9 Temperature control scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.10 Fuzzy-logic-based controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.11 Micro four-bar transmission mechanism . . . . . . . . . . . . . . . . . . . . . . . . 54
3.12 Experimentally identified hysteresis major loop of the SMA wire . . . . . . . 56
3.13 Experimental controlled operation and thermomechanical characteristics
of the catalytic artificial muscle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
x
3.14 Flapping sequences and thermal images of CAM during one cycle (1 s) of
actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.1 Energy sources and actuation methods for micro-actuation . . . . . . . . . . 66
4.2 Catalytic artificial muscle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Fabrication method of the NiTi-Pt composite artificial muscles . . . . . . . . 70
4.4 Characterization of the NiTi-Pt composite artificial muscles . . . . . . . . . . 73
4.5 Robotic design of the proposed 88-mg insect-scale autonomous robot
powered by fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.6 Evaporation rate of methanol inside the fuel tank . . . . . . . . . . . . . . . . . . 81
4.7 Experimental estimation of the leaf-spring stiffness coefficient . . . . . . . . 83
4.8 Tethered stationary experiments employed to characterize the RoBeetle
prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.9 Autonomous locomotion under two atmosphere conditions . . . . . . . . . . 90
4.10 Static friction coefficients for the legs of the RoBeetle prototype . . . . . . . 95
4.11 Dynamic model of RoBeetle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.12 Numerical simulation results of autonomous crawling inside a gently-
moving atmosphere (8 s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.13 Locomotion under different conditions . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.14 Experiment with on-board RFID chip . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.15 Antenna for the RFID chip and installation . . . . . . . . . . . . . . . . . . . . . . . 110
xi
Abstract
Researches working on the development of mobile robots at the sub-gram millime-
ter scale are mostly inspired by insects surrounding us and motivated by a signifi-
cant number of potential applications. Despite impressive progress in the past two
decades, state-of-the-art microrobots are yet to achieve the same levels of autonomy,
agility, and intelligence exhibited by their natural counterparts while completing
tasks. The most fundamental difficulties lie on stringent constraints on the number
of actuators, and the power and control dependences on external sources.
To overcome these non-trivial challenges, in this work, we explored the funda-
mental and practical aspects of two micro-actuation methods, namely piezoelectric
ceramics and shape-memory-alloys (SMAs). We developed two different microrobots
based on them. The first insect-sized robot is a 95-mg four-winged flying robot, Bee
+
,
driven by two pairs of twinned unimorph piezoelectric actuators. The second one,
named RoBeetle, is an 88-mg autonomous crawling robot actuated by catalyst-coated
SMA composite artificial muscles.
The work in this dissertation makes the following contributions. Firstly, Bee
+
, as a
significant upgrade of current flying robotic insects, is the lightest and smallest four-
winged robot created to date. Its two pairs of twinned unimorph actuators enable
us to increase the independent actuation units without substantially increasing the
weight and the size of the robot. Compared to state-of-the-art bimorph actuators,
xii
the twinned unimorph configuration also reduces the complexity of fabrication and
statistical frequency of microscopic assembly error.
Secondly, we developed a radical new actuator for microrobotic applications,
which is the catalytic composite artificial muscle made of nickel-titanium-alloy (Niti-
nol) and platinum (Pt) black. This actuator inherently possesses the high-work-
density of Nitinol and can convert the chemical energy from high-energy-density
(HED) fuels into applicable mechanical outputs through flameless catalytic com-
bustion. We achieved fast controlled actuation (1 Hz) on this artificial muscle by
implementing a logic-based control algorithm on a custom-made in-house thermo-
mechanical experimental platform.
Last and foremost, we developed RoBeetle, an 88-mg robot actuated by a catalytic
artificial muscle, which is the first sub-gram autonomous robot created to date. An
essential innovation that makes the autonomous-operation of RoBeetles possible
is a feedback control scheme of the catalytic combustion process at the millimeter-
scale. This on-board mechanical control mechanism indirectly utilizes as feedback
the reaction temperature on the surface of the artificial muscle. Specifically, the
mechanism employs the periodical actuation output according to an identified
hysteric mapping, to modulate the flow of the fuel through synchronously adjusting
the openings of micro-valves. The design of this bio-inspired microrobot powered
by HED fuel could serve as a paradigm for the creation of a new diverse generation
of autonomous robotic insects in terrestrial, aquatic, and aerial environments.
xiii
Chapter 1
Introduction
Biologically-inspired microrobotics is a nascent and active research field, aiming at
creating micro-to-millimeter-scale, autonomous, agile, and intelligent mobile robots.
Microrobots are mostly inspired by insects we see around us, such as honeybees, but-
terflies, beetles, and inchworms, and motivated by numerous potential applications,
such as disaster response, inspection of infrastructure and facility, reconnaissance
and surveillance, artificial pollination, and planetary exploration. From a scientific
perspective, due to the multidisciplinary nature of robotics, researches on micro-
robots can also inspire innovations and breakthroughs in many related fundamental
research areas, including microfabrication, micro/nano-materials, new portable
energy sources, control of micro-dynamic systems, and many other fields.
1.1 Background and motivation
In the past two decades, impressive progress in microrobots has been achieved
due to advances in microfabrication and mechatronics. For example, researchers
from Harvard have developed insect-sized flapping-wing flying robots driven by
1
trapezoidal-shaped piezoelectric bimorph actuators (1) or dielectric elastomer actu-
ators (DEAs) (2). These microrobots are fabricated by using a method termed smart
composite microstructures (SCM) (3), which involves composite laminating, precise-
laser-machining, and microscopic assembling. Also, Saito et al. employed micro-
electro-mechanical systems (MEMS) techniques to create quadruped microrobot
(79 mg in weight) actuated by multiple SMA wires. Recently, three-dimensional
microfabrication methods, including additive manufacturing (5), dip-in laser lithog-
raphy (6), etc., were adopted to create microrobots with more complex and precise
structures, significantly reducing the difficulties associated with the assembling pro-
cesses. Moreover, innovative micro-actuation schemes, e.g., piezoelectric polyvinyli-
dene difluoride (PVDF) unimorph (7), nanoporous energetic silicon (8), hygroscopic
films (9), electrostatic inchworm motors (10), have been utilized to drive micro-
robots. Implementations of all these technologies of fabrication and mechatronics
have evolved into many new approaches for creating robotic insects with improved
capabilities in locomotion.
1.2 Contributions
The state-of-the-art microrobots, however, yet to achieve the same levels of auton-
omy, agility, and intelligence for completing tasks as their biological counterparts.
Most of the existing microrobots are highly underactuated and tethered to external
power sources by cables or by wireless fields, e.g., magnetic, light, thermal, etc.
The underlying causes are four long-existing obstacles towards the path of creat-
ing fully autonomous robotic insects, including the integration of multiple actuation
units, development of high-work-density (HWD) actuation methods, exploiting feasi-
ble high-energy-density (HED) power sources and desired on-board control schemes.
2
In this work, we demonstrated our approaches for addressing these nontrivial chal-
lenges through presenting studies and researches on two different microrobotic
prototypes.
The first one, named as Bee
+
, is a 95-mg four-winged flying robot. To our best
knowledge, this robot is the lightest and smallest four-winged robot produced to
date. Its four wings are independently driven by two pairs of twinned unimorph
piezoelectric actuators. The advantage of this new actuation scheme is tow-fold.
Compared to state-of-the-art flying robots driven by bimorph actuators, this method
allows us to integrate more independent actuation units without significantly in-
creasing the weight and size of the robot. Meanwhile, the twinned configuration
of the actuator can also eliminate the probability of misalignment that is usually
inevitable in the microscopic assembling process. In addition, the aerodynamic
design, functionality, and flying performances of Bee
+
are validated through two
sets of real-time controlled flight experiments. We believe that this four-winged
flying robot is a significant upgrade for current sub-gram flying robots in aspects of
achieving higher degrees of control authority and longer life expectancy.
Despite the advantages, Bee
+
has yet to achieve power and control autonomy. So
the second microrobot was developed to obviate the power and control dependence
on external sources. The robot was named as RoBeetle, which is the first sub-gram
insect-sized autonomous robot reported in the literature, to our best knowledge.
Two key innovations that make the autonomous-operation possible are the catalytic
artificial muscle and the control scheme for the catalytic combustion process at
millimeter-scale.
In this work, we comprehensively discussed the fundamental and experimental
studies on this catalyst-coated shape-memory-alloy composite artificial muscle in a
single chapter. The proposed artificial muscle is a radical new actuation method that
3
directly converts the chemical energy from HED fuels (e.g., hydrogen, hydrocarbons,
alcohols) into mechanical outputs for actuation through flameless catalytic combus-
tion. We developed a powder-coating fabrication method that can reliably attach
a micro-scale layer of highly-active platinum (Pt) black on a thin nickel-titanium-
alloy (Nitinol) wire. The thermomechanical characterization and the fast controlled
actuation (1 Hz) of this artificial muscle were achieved on a self-developed catalytic-
combustion-control (CCC) platform. Furthermore, to demonstrate its potential in
microrobotic application, the artificial muscle was controlled to drive an artificial
butterfly wing through a millimeter-scale transmission mechanism. Note that, al-
though experiments of catalytic artificial muscles were conducted on the meter-scale
CCC platform with sophisticated fuel-supply and thermomechanical-measurement
hardware-and-software, the method and knowledge acquired established the foun-
dation of developing microrobotic systems powered by HED fuels.
To achieve the CCC on the 88-mg RoBeetle actuated by the artificial muscle,
we introduced a compact robotic design that integrates all required components
for autonomous operation, including an on-board fuel tank, a mechanical control
mechanism (MCM) and an actuation mechanism.
The MCM is an innovative feedback control scheme for the catalytic combustion
process at the millimeter-scale. Specifically, based on a known hysteric mapping
between strain and temperature obtained from the characterization experiment
conducted on the CCC platform, the MCM can indirectly feedback the temperature
of the artificial muscle to modulate the fuel supply through adjusting the openings
of the micro-valves on the fuel tank. In this way, with the proper design of the MCM,
forelegs of the RoBeetle can generate periodical swinging movement without any
external intervention. Then, inspired by the locomotion scheme of inchworms,
the anisotropic frictions induced by the claws on forelegs and hindlegs enable the
4
RoBeetle to achieve unidirectional locomotion.
The locomotion performance of RoBeetles was thoroughly assessed with sev-
eral sets of experiments, including autonomous crawling under two atmospheric
conditions, climbing ramps, crawling on surfaces with different levels of roughness,
carrying payloads. We also demonstrated the Robeetle locomoting outdoors, which
is the first case that a sub-gram robot operating in a non-laboratory environment
reported in the literature. Furthermore, as an application example, a wireless radio
frequency identification (RFID) sensor was installed on the robot to exhibits its po-
tential capability of interacting with external environments. Besides, the two-anchor
gait of the RoBeetle was also theoretically studied with a dynamic model.
Overall, the results of experiments and analyses on two sub-gram insect-sized
robots, i.e., Bee
+
and RoBeetle, provide cogent evidence that the radical new actuation
schemes, robotic designs, microfabrication methods and control approaches we
developed can propel the researches on creation of autonomous, agile and intelligent
robotic insects.
5
Chapter 2
Bee
+
Insect-sized aerial robots have the potential to be employed in a great number of
tasks such as infrastructure inspection, search and rescue after disasters, artificial
pollination, reconnaissance, surveillance, etc., which has motivated the interest of
many research groups. Consistently, as an emerging field, research on cm-scale
flapping-wing robots driven by piezoelectric actuators has produced numerous
design innovations over the course of more than two decades (11, 12, 13, 14). However,
state-of-the-art flying microrobots, such as those reported in (15) and (16), do not
adequately replicate the astounding capabilities exhibited by flying insects. An
obstacle that has limited progress is the fact that unlike insects which simultaneously
use multiple distributed muscles for flapping and control (17), flapping-wing flying
robots are driven by a small number of discrete actuators due to stringent constraints
in size and weight as well as fabrication challenges.
To achieve underactuated controllability, Harvard researchers developed the
RoboBee, which is driven by two independent bimorph actuators (13). Dynamic
analyses indicate that two-winged robots of this type should be able to perform basic
flight maneuvers such as perching, landing, path following and obstacle avoidance
6
by controlling the six spatial degrees of freedom (DOF) (18). However, during real-
time control experiments, it has been observed that the yaw torque produced via
split-cycle flapping (18) is insufficient to overcome the restoring and damping forces
opposing the yaw rotational motion of the robot (16, 19, 20). A different approach to
achieve controllability at the insect scale is the three-actuator flapping-wing design
in (21), which is composed of one central bimorph actuator employed for power and
control, and two smaller lateral bimorph actuators used exclusively for control. Even
though this robot can roll and pitch, the inability to steer itself has prevented it from
performing agile flying maneuvers.
Recently, following an approach that deviates from the bioinspiration paradigm,
a 143-mg four-winged design was introduced in (16). This robot (dubbed Four-
wings) is composed of four bimorph actuators configured horizontally to form a
90-degree cross, thus resembling the shape of a quadrotor. Due to its configuration,
Four-wings exhibits a significantly-improved payload capacity compared to those of
previous designs and can effectively steer itself, which suggests that it might be able
to perform nontrivial controlled flying maneuvers. Note that these new capabilities
directly follow from the fact that by increasing the number of actuators, the control
authority is also increased (as the degree of underactuation decreases). This notion is
clearly supported by research on larger-scale four-winged flying robots; for example,
the DelFly Nimble (22) (with a weight of 29 g and a wingspan of 330 mm), which is
equipped with two actuators for flapping, one actuator for dihedral-angle control
and one actuator for wing-root control, is able to perform a large number of insect-
inspired aerobatic maneuvers such as 360
-flips and fast banked turns.
Here, motivated by the potential agility and controllability of flying robots with
augmented actuation capabilities, we introduce Bee
+
, a 95-mg insect-scale robotic
design with four independently-driven wings powered by two pairs of twinned uni-
7
Figure 2.1: Bee
+
(right), a new four-winged flying microrobot. This robot has a mass
of 95 mg and measures 33 mm in wingspan. Four retroreflective markers (5 mg) for
motion tracking are attached to the legs and protective spars of the prototype. We
also fabricated a two-winged prototype (left) for comparison. The design of this
robot was adapted from that of the RoboBee (1) originally created at the Harvard
Microrobotics Laboratory. A U.S. one-cent coin indicates the scale.
Table 2.1: Comparison of the parameters of Bee
+
, the RoboBee and Four-wings.
Robot Total
mass
(mg)
Mass of
the ac-
tuators
(mg)
Wingspan
(mm)
Flapping
frequency
(Hz)
Lift
force
(mN)
Wing
area
(mm
2
)
Bee
+
95 56 33 100 1.4 200
RoboBee 75 50 35 120 1.3 104
Four-wings 143 100 56 160 4 218
morph actuators (Fig. 2.1). In this approach, rather than using four bimorph ac-
tuators as in (16), we employ two pairs of twinned unimorph actuators, as shown
in Fig. 2.2, which are fabricated monolithically as shown in Fig 2.3. In the final as-
sembly of the robot, each pair of twinned actuators is installed on each side of the
airframe to independently drive the four wings of the system through four individual
micro-transmissions as depicted in Fig. 2.2A.
The main characteristics and parameters of Bee
+
, compared to those of the
RoboBee and Four-wings are summarized in Table 2.1. These data allows us to
8
Roll axis
Yaw axis
Pitch axis
1
2
3
4
Wire collector Twinned unimorph actuator
Hinge
Transmission
Center of mass
1
Roll
Pitch
Yaw
A A B
2
4
3
n3
n1
n2
b
3
b
1
b
2
M1
b
3
Figure 2.2: Schematic diagrams of the four-winged robotic design. A. This figure
shows the inertial framen
1
-n
2
-n
3
, the body frameb
1
-b
2
-b
3
(shifted for clarity), the
three body rotation axes as well as the numeric labels,f1, 2, 3, 4g, that are utilized
to indicate each wing and the respective unimorph actuator. A detailed view of
the wings, hinges, transmissions is shown in the middle. B. Strategies employed to
generate the control torques about the three orthogonal axes of rotation. The roll
torque is generated by varying the flapping-amplitude difference between the left
wingsf3, 4g and the right wingsf1, 2g. Similarly, by varying the flapping-amplitude
difference between the front wingsf2, 4g and the back wingsf1, 3g the pitch torque is
generated. As discussed in Section 2.1.2, the steering motion about the yaw axisb
3
can be produced employing three different methods (23, 22). In this case, we only
demonstrate the ISP method, which consists in pre-setting the stroke plane to have
an inclination with respect to the steering planeb
1
-b
2
and, then, by adjusting
the flapping amplitudes of the diagonal pairs of wings, i.e., wingsf1, 4g and wings
f2, 3g, the aerodynamic-force components projected on theb
1
-b
2
plane produce the
yaw torque while the cycle-averaged roll and pitch torques remain approximately
zero. The flapping amplitudes are not shown to scale; the red arrows indicate the
directions and magnitudes of the aerodynamic forces.
state the main characteristics of Bee
+
in comparison to the best state-of-the-art
insect-scale robots thus far presented in the technical literature:
(i) The pair of twinned unimorph actuators weighs only 28 mg, i.e., only 3 mg more
than a single bimorph actuator (25 mg) used in the fabrication of the RoboBee and
Four-wings. Consequently, the total weight of Bee
+
is not significantly higher than
that of the two-winged RoboBee and is lighter than that of the Four-wings.
(ii) Due to its compact configuration and the short wingspan (33 mm), the volume
9
of the fictitious parallelepipedal envelop enclosing Bee
+
is almost identical to that
of the RoboBee and significantly smaller than that of Four-wings, which has its four
actuators oriented horizontally.
(iii) The total wing area of Bee
+
is twice as large as that of the RoboBee while its
weight is only 27 % higher, which significantly reduces the total wing-loading on the
robot. Lower wing-loading not only reduces the forces and moments acting on the
robot’ s actuators, which increases the life-expectancy of the mechanical components,
but it is also advantageous from the aerodynamic design viewpoint (see Section 2.1.2).
(iv) The novel design of the proposed twinned unimorph actuators, fabricated using
the methods described in (24), significantly reduces the complexity of the fabrication
process and the statistical frequency of assembling errors compared to that of the
two-winged robots. Also, compared to Four-wings, the circuitry of the four actuators
driving Bee
+
is simpler as it requires only five connection wires instead of six.
In the rest of the chapter, we first describe the design of the proposed four-winged
robot and present a basic aerodynamic analysis of the system. Then, we discuss the
fabrication process of the unimorph actuators employed to drive the robot. Next, we
present the process of controller synthesis and a set of controlled flight experiments.
Finally, we draw some conclusions extracted from the research results.
2.1 Design and analysis
2.1.1 Robotic design
Although four-winged microrobotic flyers provide more options for the design and
implementation of high-performance flight controllers, when compared to proto-
types with two wings, their development brings numerous challenges. From the
10
fabrication perspective, the integration of multiple actuators into a cm-scale airframe
is difficult because the functionality and performance of microrobots greatly depend
on the uniformity of the moving parts, symmetry of the structural components and
precision of the final assembly. In addition, actuators are major contributors to the
total weight of insect-sized robots (for example, approximately 66 % of the weight of
the robot in (11)); therefore, the addition of actuators to a robotic design requires the
generation of significant more lift. We overcame these challenges by introducing an
optimized method for the integration of four actuators into the robot.
As seen in Fig. 2.1, the most distinctive characteristic of Bee
+
is its four-winged de-
sign compactly packaged inside a volume similar to that of the two-winged RoboBee.
The robot has a symmetric configuration with respect to theb
1
–b
3
plane that sepa-
rates the right and left sides of the body frame of reference (as defined in Fig. 2.2); in
this case, by convention, wings 1 and 2 are located in the right half-space and wings 3
and 4 are located in the left half-plane. Each wing flaps only within its corresponding
quadrant defined by the bodyb
1
-b
2
plane, so less amplitude of deflection is required
from each actuator compared to those in the two-winged robot case. The key ele-
ment that makes this design feasible is the pair of twinned unimorph actuators with
a common base that are shown in Fig. 2.2A. Note that each pair of twinned unimorph
actuators can be thought of as an unfolded bimorph actuator, which explains why the
weight difference between these two types of actuation microdevices is of 3 mg only
(the analogous bimorph actuator is 3 mg lighter). In total, Bee
+
is 20 mg heavier than
the RoboBee due to other additional structural weight; this is not an issue, however,
as Bee
+
is able to generate sufficient thrust and aerodynamic moments for flying and
control.
Because the two pairs of twinned unimorph actuators are fabricated from the
same composite stack and employing exactly the same process, their mechanical
11
properties, functionalities and achieved performances are very similar. This fab-
rication methodology is simpler and more precise than pairing actuators as done
in the case in (1). Also, the use of twinned components eliminates the possibility
of misalignment due to assembly errors on each side of the robot’s body as each
pair of unimorph actuators is a monolithic piece; thus, we only need to enforce the
symmetry of the left side with respect to the right side. To power Bee
+
, a minimum
of five wires is required: two for the driving signals of each pair of twinned actuators
and one for the common ground.
2.1.2 Aerodynamic design and analysis
Bee
+
has superior controllability capabilities compared to those exhibit by two-
winged robots. However, there are two adverse factors that must be considered: the
increased total weight of the robot; and the fact that each wing is constrained to
flap with amplitudes equal or smaller than 90
due to the geometry of the design,
which limits the maximum thrust that each wing can generate. Namely, it is not a
trivial task to guarantee the generation of sufficient thrust and moments to enable
the robot to take off, stabilize itself and maneuver. For a wing flapping according to
a sinusoidal pattern, the aerodynamic force, which depends on the velocity of the
local flow and the corresponding angle of attack (25), is the main contribution to the
cycle-averaged lift
¯
f
L
= C
L
( ¯ )
1
2
(2
0
r
ref
)
2
S = C
1
( ¯ )
2
2
0
S (2.1)
where C
L
is the cycle-averaged lift coefficient as a function of the aerodynamic mean
angle of attack ¯ ; is the density of the air;
0
is the end-to-end amplitude of the
flapping angle; is the flapping frequency; r
ref
is the characteristic distance used to
12
estimate the local velocity of the flow interacting with the wing; S is the area of the
wing; and C
1
is a lumped coefficient that simplifies the expression.
The form of (2.1) indicates that, for control purposes,
¯
f
L
can be modulated by
either varying the frequency or the amplitude
0
. Note, however, that this formula
provides a quick estimation only and, therefore, we employ the numerical fluid-
structure interaction method in (26) and the instantaneous aerodynamic models
in (25) to compute the forces produced by the four wings of the robot and the cor-
responding total lift in Table 2.1. For the purpose of design, we select = 100 Hz,
0
= 65
, the limit for the wing pitching angles to be 70
and the hinge stiffness to be
1.4µNm. For these parameters and the wing geometry shown in Fig. 2.2A, the com-
puted cycle-averaged total lift produced by the four wings is approximately 1.4 mN
and the corresponding lift-to-weight ratio is approximately 1.4; hence, based on this
estimations, Bee
+
is capable of generating sufficient lift for taking off, stabilizing itself
and maneuvering.
Experiments have shown that two-winged robots are not well suited to passively
resist rotational disturbances and actively steer their bodies about the yaw axis
b
3
(16); phenomena that here we analyze using the cycle-averaged damping force,
¯
f
D
. This approach is reasonable because for insect-scale microrobots, the flapping
frequency is significantly higher than the frequencies of the body oscillations (25,
16). Thus, for the upstroke and downstroke of a sinusoidal flapping pattern with a
symmetrical profile, the cycle-averaged damping force (27, 25) is estimated as
¯
f
D
= C
2
( ¯ )
0
!
b
S + C
3
( ¯ ) ˙ !
b
S (2.2)
where C
2
and C
3
are coefficients derived from the models in (25), and!
b
is the
angular velocity associated with the yaw rotation. In (2.1),
¯
f
L
is proportional to
2
0
2
S; therefore, given similar robot weights and a constant!
b
, from (2.2) it follows
13
that Bee
+
can generate at least
p
2 times the damping force produced by a two-winged
robot of a similar size. This fact explains the enhanced yaw-stability properties of
Bee
+
when compared with the two-winged counterparts.
In this discussion, we select the yaw steering plane to be theb
1
-b
2
body plane
in Fig. 2.2. Thus, to enable yaw steering capabilities, each wing must be able to
actively generate a non-zero net force f
S
in theb
1
-b
2
plane during one flapping cycle.
From the conceptual design perspective, there are three feasible strategies available
to generate a non-zero f
S
. The first is split-cycle. From simple analyses (18) and
experimental data obtained using the Four-wings prototype (16), it follows that this
strategy requires a high actuation bandwidth for both frequency modulation and
yaw-torque amplification, which is costly and difficult to achieve from the design
and fabrication perspective. The second is asymmetric angle of attack. This is the
method employed by the DelFly Nimble in (22), which uses an actuator to actively
control the wing root; in this way, the angles of attack of the wing during the up and
down strokes can be set to different values. The third is inclined stroke-plane (ISP),
which is employed in this case to control the yaw DOF of Bee
+
. This method consists
in pre-setting the stroke plane to have an inclination ( in Fig. 2.2B) with respect
to the steering plane. Specifically, the stroke planes of the front pair of wingsf2, 4g
are tilted backward while that of the back pair if wingsf1, 3g are tilted forward. In
this way, the aerodynamic force produced by a wing projects a non-zero component
onto the steering plane.
According to the ISP scheme, the diagonal pairf1, 4g can produce yaw torques
in the counter-clockwise direction while the other diagonal pairf2, 3g can generate
clockwise yaw torques. Thus, by adjusting the flapping amplitudes of the two diago-
nal pairs of wings, the robot can actively modulate the production of yaw torque. In
specific, the active yaw torque generated by the projection of the cycle-averaged lift
14
produced by a single wing onto the steering plane can be estimated as
¯
f
S
=
¯
f
L
sin = C
4
( ¯ )
2
2
0
(2.3)
¯
S
= r
S
¯
f
S
= C
5
( ¯ )
2
2
0
(2.4)
where r
S
is the distance from the pressure center of the wing to theb
3
axis, and C
4
and C
5
are lumped coefficients derived from the models for instantaneous forces
described in (25). Note that unlike in the two-winged case, by diagonally pairing
the four wings, the modulation of the yaw torque does not introduce significant
undesirable roll torques as they stay approximately balanced.
Since the torques about the three axes of the body frame can be controlled by
varying the flapping amplitudes of the four wings (see Fig. 2.2B), the robot can be
controlled during flight employing methods already developed for quadrotors (28, 29).
Unfortunately, since ¯ can vary along with
0
in a highly nonlinear manner, the
models specified by (2.1)–(2.4) cannot be used directly; with proper identification,
however, they can be approximated with constant-coefficient linear models, as done
in Section 2.3.4 for flight controller synthesis. Finally in this section, it is important
to state that compared to the case of two-winged robots, the wing-loading on Bee
+
is
reduced by 34 %. Lower wing-loading not only reduces the demands on the actuators
but also induces smaller deformations of the wings and enables the generation
of larger maximum flapping amplitudes, which is desirable for both power and
control purposes. For example, in the two-winged case, the typical operating flapping
amplitudes oscillate around 110
while the designed value of
0
for Bee
+
can be
chosen to be significantly larger than 55
. In static experiments (see Movie S1), the
maximum observed amplitudes achieve values of approximately 75
.
15
Gel-Pak
FR4
PZT
Alumina
Carbon fiber×2
Release film
FR4
Gel-Pak
Alumina
Copper-clad FR4
Carbon fiber
C. Release cut
First stack
B. Second cure cycle A. First cure cycle
D. Driving method
Second stack
Extension
Base
Bridge
Connection pad
M2
Figure 2.3: Fabrication process of a batch of twinned piezoelectric unimorph ac-
tuators. A. During the first cure cycle, rectangular laminates of PZT (127µm) and
alumina (127µm) are bonded to two layers of high-modulus carbon fiber composite
(63µm each) by applying heat (180
C) and pressure (15 psi) to the stack, which is
pin-aligned. An additional bottom layer of alumina serves as a substrate that main-
tains the stack flat; between this piece of alumina and the double layer of carbon
fiber we place a sheet of release film to prevent undesired bonding. B. During the
second cure cycle, the cured unimorph stack produced in the first step is bonded to
an additional layer of carbon fiber composite (27µm) and a layer of copper-clad FR4
(137µm) using the same temperature and pressure than in the first cycle. C. During
the final release cut, four pairs of twinned actuators are released from one unimorph
stack. D. The driving method employs two independent voltages per each pair of
unimorph actuators. In this case, we use positive sinusoidal signals with maximum
magnitudes of 260 V; accordingly, the two unimorphs bend upwards (as indicated by
the arrows), generating maximum tip displacements of 300µm. The total length of a
twinned pair is 13 mm.
2.2 Fabrication of the robot
2.2.1 Fabrication of twinned unimorph actuators
The proposed twinned unimorph actuators are the most important components
of the mechanisms that flap the four wings of the robot (Fig. 2.2A). The fabrication
of actuators of this type is not feasible employing the methods invented to create
the bimorph actuators used to drive the RoboBee in (1). Here, we introduce a new
technique that is based on a modification of the pre-stack technology described
in (24). This approach not only significantly improves the quality and consistency of
16
the fabrication process but also enables the physical realization of almost any planar
design. The specific process employed in the construction of the unimorph actuators
of the Bee
+
prototype in Fig. 2.1 is depicted in Fig. 2.3, which consists of two cure
cycles (Figs. 2.3A and 2.3B) and one laser release cut (Fig. 2.3C). We use piezoelectric
ceramics PZT-5H (T105-H4NO-2929, Piezo.com) as the active layer to create the
unimorph structure because of its high-modulus and piezoelectric coefficient, and
two layers of high-modulus carbon fiber composite as the passive surface constraint
in order to obtain an equivalent stiffness similar to that of a bimorph actuator of the
same size. The tip extension and base are made of alumina ceramics.
Before the first cure cycle starts, we cut all the pieces of laminated materials
required to assemble the first stack in Fig. 2.3 using a precision diode-pumped solid-
state (DPSS) laser (Photonics Industries DC150-355). The pieces of PZT and alumina
are first cut into rectangles, and then cleaned with isopropyl alcohol using a sonicator
in order to improve the adhesion between layers during curing. Sheets of FR4 are
machined as jigs to hold the pieces of PZT and alumina in position, thus forming
two layers of the pin-aligned stack as shown in Fig. 2.3A. Here, the lower FR4 jig
is placed on a layer of Gel-Pak (lightly tacky film) that is used to stick the piece of
alumina in place. Similarly, the upper FR4 jig, which holds the pieces of PZT in place,
is covered with a layer of Gel-Pak. As shown in Fig. 2.3A, from the bottom up, the
stack also contains a layer of release film and two layers of carbon fiber. Through
the application of heat (180
C) and pressure (15 psi) for two hours, the epoxy resin
impregnated in the two layers of carbon fiber cures and bonds these pieces together,
and them with the layer composed of PZT, alumina and FR4, thus forming the first
cured stack employed to assemble the second stack that is shown in Fig. 2.3B. Note
that the lower layer of the first stack serves only as a rigid substrate that maintains the
configuration flat; therefore, it does not bond to the carbon fiber pieces as a layer of
17
release film isolates them from each other. During the second cure cycle (Fig. 2.3B),
we apply the same temperature and pressure patterns to bond the first cured stack
with an additional layer of carbon fiber and a copper-clad FR4 sheet. This last layer
of carbon fiber structurally bridges the interfaces between the pieces of PZT and
alumina, thus increasing the rigidity of the actuator. The layer of copper-clad FR4 is
necessary to make the electrical connection pads.
Finally in the fabrication process, the unimorph actuators are released from the
second cured stack through a final laser cut. As the final stack has only one layer of
PZT at the top and one layer of carbon fiber at the bottom, during the final release
procedure, we simply cut all the layers at once from the top as shown in Fig. 2.3C.
This simpler laser cut reduces the releasing time by half compared to that required to
release bimorph actuators, as the final fabrication step of bimorphs consists of one
cut from the top and another cut from the bottom of the corresponding stack. The
one-single-cut-based final release procedure of the unimorph fabrication method
significantly improves the yield of actuators per stack. This observation is explained,
to some extent, by the fact that the final release of bimorphs requires the flipping of
the cured stack and its realignment in between the top and bottom laser cuts, which
increases the likelihood of introducing manufacturing errors such as the induction
of cracks in the PZT ceramics.
In this case, we apply the fabrication method in such a way that from one stack,
the final release cut yields a total of four pairs of twinned actuators. One twinned pair
is depicted in Fig. 2.3D. As seen in this illustration, two identical unimorphs located
side by side share the same structural base and electrical ground. At the base, there
is a clearance of 50µm that separates the bottom edges of the PZT layers of both
twined unimorphs. In contrast, their passive carbon fiber layers are connected at
the bottom, thus creating a common electrical ground. Consistently, to drive the
18
actuator pair, we can employ the simple circuitry shown in Fig. 2.3D. In this electrical
configuration, two independent voltage signals drive the two unimorphs, whose
bending directions when excited are indicated with blue arrows. To connect the
electrical copper pads with the PZT layers, we employ conductive epoxy.
2.2.2 Robotic assembly
The airframe, wings, hinges, transmissions, protective spars and legs are fabricated
using smart composite microstructures process (3). While detailed fabrication pro-
cesses will not be discussed here, the specific assembling process should be explained
because it is crucial for achieving the desired assembly relationships among all com-
ponents. To begin with, three types of sub-assemblies are assembled separately. First
one is airframe, including three pieces of carbon fiber and five pieces of FR4. Assem-
bly relationships of these pieces are uniquely defined by their tab-and-slot features,
where cyanoacrylate (CA) glue is also applied to create firm adhesion. Second one
includes four wing-hinge sub-assemblies. Wings are attached to hinges with the
toothed mating features (M1, highlighted in the detailed view of Fig. 2.2A) using
CA glue respectively. Third one includes two actuator-transmission sub-assemblies.
Four transmissions are installed on the raised mating features of extension tips (M2,
highlighted in Fig. 2.3D) of two pairs of twinned unimorph actuators as the orienta-
tions shown in Fig. 2.2A. Next, the actuator-transmission sub-assemblies are firmly
glued onto the base of the airframe. We use orthogonal contact surfaces among the
actuators and the base as constraints to guarantee the precision of assembling. Also,
ground linkages of the transmissions are affixed to the airframe using glue. The last
step is attaching the wing-hinge sub-assemblies to the transmissions. Their assem-
bly relationships are less constrained, allowing final adjustments for compensating
19
errors caused by previous steps.
2.3 Flight controller design
2.3.1 System dynamics
To describe the dynamics of the robot, we define the body-fixed frameb
1
-b
2
-b
3
B
and the inertial framen
1
-n
2
-n
3
N
, as shown in Fig. 2.2. Because the direction of
the thrust force is assumed to be aligned with theb
3
axis and the number of actuators
is less than the total number of the DOF of the system, Bee
+
is essentially a thrust-
propelled underactuated system. Thus, it can be thought of as a rigid body with its
dynamics given by
m ¨ r =mgn
3
+ fb
3
(2.5)
J ˙ !=!J!+ (2.6)
˙
¯
q =
1
2 ¯
q
¯
p (2.7)
where m is the total mass of the robot; r = [r
1
r
2
r
3
]
T
indicates the location of the
robot’ s center of mass measured from the origin ofN ; f is the magnitude of the total
thrust force generated by the four flapping wings; J denotes the robot’s moment of
the inertia, written with respect toB;! is the flyer’s angular velocity with respect to
N , expressed inB;=[
1
2
3
]
T
is the torque generated by the flapping wings; the
quaternion
¯
q describes the attitude of the robot relative toN ;
¯
p =
0!
T
T
; and the
symbol denotes the standard quaternion multiplication.
Note that the model specified by (2.5)–(2.7) assumes that the direction of the
thrust force is aligned withb
3
; that the projection of the total aerodynamic force
generated by the four flapping wings onto the steering plane is zero during one
20
flapping cycle, which implies that fb
3
is the only external actuation force acting on
the system; that the aerodynamic disturbances affecting the flyer are negligible; and
that the gyroscopic effect resulting from the interaction of the flapping wings with
the rotating body is also negligible.
2.3.2 Attitude control
Here, we describe the desired attitude dynamics of the robot with the quaternion
equation
˙
¯
q
d
=
1
2 ¯
q
d
¯
p
d
(2.8)
where
¯
q
d
is the quaternion employed to represent the desired attitude of the flyer
during flight; and
¯
p
d
=
0 ˆ !
T
d
T
, in which ˆ !
d
denotes the desired angular velocity
expressed in the desired frame of reference, whose orientation coincides exactly with
that of
¯
q
d
(see (29) for further details). Consistently, it follows that the attitude error
between
¯
q
d
and
¯
q , described by the quaternion
¯
q
e
=
m
e
n
T
e
T
, is given by
¯
q
e
=
¯
q
1
d
¯
q . (2.9)
In this case, we regulate the attitude of the flyer employing the control law
=K
1
sgn(m
e
)n
e
K
2
(!!
d
) (2.10)
in whichK
1
andK
2
are positive definite diagonal gain matrices; sgn() denotes the
sign function; and!
d
is the desired angular velocity with exactly the same compo-
nents as those of ˆ !
d
but expressed in the body frame instead of the desired frame
with the same orientation as that of
¯
q
d
. We represent the axis of the rotation from
¯
q
to
¯
q
d
with the unit vectora
e
and we use
e
to denote the associated rotation angle,
with 0¶
e
<. Thus, note that the termsgn(m
e
)n
e
is geometrically identical to
21
sin(
e
=2)a
e
and that we use the multiplier sgn(m
e
) to remove the ambiguity associ-
ated with the quaternion notation according to which both
¯
q
e
and
¯
q
e
represent the
same rotation.
2.3.3 Position control
To control the position of the robot in space, we employ as control signals the mag-
nitude and direction of the total thrust generated by the flapping wings. According
to this approach, the magnitude of the total thrust force, f , is modulated by jointly
varying the flapping speed of the four wings and the corresponding force direction
is modulated by varying the attitude of the robot. As described in Section 2.3.2,
the flyer’s attitude is controlled with the feedback law specified by (2.10), which is
physically realized by flapping the wings asymmetrically according to the patterns
depicted in Fig. 2.2B. In this case, the desired instantaneous total thrust force required
to track a desired position of the flyer’s center of mass,r
d
, is generated according to
the proportional-integral-derivative (PID) structure
f
d
=K
p
(rr
d
)K
d
( ˙ r ˙ r
d
)
K
i
Z
(rr
d
)d t + mgn
3
+ m ¨ r
d
(2.11)
where K
p
, K
d
and K
i
are positive definite diagonal gain matrices. Note that the
magnitude of f
d
to be tracked using direct feedback control is simply given by
f
d
=f
T
d
b
3
. (2.12)
The set of all the flyer’s attitudes compatible with the direction of f
d
can be readily
computed as
i
3
=
f
d
f
d
2
(2.13)
22
which is chosen to be the desired yaw axis of the robot during flight. We compute
the other two axes defining the desired attitude of the robot in terms of the desired
instantaneous yaw rotation angle,
d
, andi
3
, according to
i
1
=
i
d
i
3
i
d
i
3
2
, i
2
=i
3
i
1
(2.14)
wherei
d
=
sin
d
cos
d
0
T
. In the implementation of the algorithms for sig-
nal processing and control, i
1
, i
2
, i
3
and i
d
are expressed in the inertial frame.
To implement the controller specified by (2.10), we compute the desired attitude
quaternion
¯
q
d
from the desired rotation matrixS
d
=[i
1
i
2
i
3
], employing standard
quaternion algebra.
2.3.4 Actuator command generation
As discussed in Section 2.1.2, each actuator generates a sinusoidal output with a
constant pre-specified frequency (100 Hz in this specific case) and an adjustable am-
plitude used to generate the flapping patterns in Fig. 2.2B. By simplifying the models
described by (2.1)–(2.4), we estimate the magnitude of the thrust force produced by
each flapping wing j =f1, 2, 3, 4g, according to f
j
= k
f
v
j
, where v
j
is the amplitude of
the sinusoidal command signal generated by the jth unimorph actuator and k
f
is a
lumped thrust force coefficient. As illustrated in Fig. 2.2B, yaw torques in the steering
plane can be generated by employing the ISP strategy discussed in Section 2.1.2.
Consistently, we estimate the component of the i th aerodynamic force projected on
the steering plane as f
s j
= k
s
v
j
, where k
s
is also a lumped force coefficient.
Thereby, the mapping that relates the amplitudes of the actuators’ outputs, as
inputs, with the total thrust force and control torques, as outputs, is given by
u =v (2.15)
23
with
u =
h
f
1
2
3
i
T
=
2
6
6
6
6
6
6
4
k
f
k
f
k
f
k
f
k
f
d
1
k
f
d
1
k
f
d
1
k
f
d
1
k
f
d
2
k
f
d
2
k
f
d
2
k
f
d
2
k
s
d
3
k
s
d
3
k
s
d
3
k
s
d
3
3
7
7
7
7
7
7
5
and v =
h
v
1
v
2
v
3
v
4
i
T
where d
j
, for j =f1, 2, 3g, is the equivalent lever-arm associated with the correspond-
ing torque component
j
, employed to model, in an extremely simplified manner,
the transmission mechanism that connects the actuators’s output with the flapping
angle of the j th wing. Thus, for a known set of control signals
f ,
1
,
2
,
3
, the
corresponding set of instantaneous actuator commands is straightforwardly com-
puted asv =
1
u . Note that, simply due to its four-winged design, Bee
+
has better
control capabilities than those of two-winged prototypes, because the thrust force
and control torques are generated by four wings rather than two.
2.4 Experimental results
2.4.1 Experimental setup
The main components of the experimental setup are a Bee
+
prototype, four piezo-
actuator drivers (PiezoMaster VP7206), a Vicon motion capture (VMC) system and a
ground target–host Mathworks Simulink Real-Time system that is used to process
sensor measurements and generate the control signals. The control algorithms are
run at a frequency of 2 kHz and the VMC system measures the robot’s position and
24
attitude at a rate of 500 Hz. The robot’s angular velocity cannot be directly measured
with the VMC system, thereby we estimate it according to
2
4
0
!
3
5
= 2
¯
q
1
s
s +
¯
q (2.16)
where s is the differential operator; the bracketed function on the right side represents
a low-pass filter that operates on the signal
¯
q ; and is tuned filter parameter. To
estimate the translational velocities, we employ a simple discrete-time differentiator
in combination with a low-pass derivative filter similar to that in (2.16). Note that,
in the case of Bee
+
, the use of low-pass filters is necessary to clean the measured
signals because the forces generated by the flapping wings induce high-frequency
oscillations on the robot’s body.
Furthermore, the open-loop trimming flight tests required for controller tuning
in the case of two-winged robots (13, 30), are not necessary in the case of Bee
+
proto-
types. This fact demonstrates that the proposed actuation and control methods do
not require the fine tuning of the control signals and the zeroing of the biases affect-
ing the actuation torques. This advantage has significantly improved the efficiency
of flight experiments at the insect-scale.
2.4.2 Simultaneous control of altitude and attitude
The objective of the controller tested through this experiment is to enable the robot
to fly at a desired altitude and with the direction of the thrust force remaining perpen-
dicular to then
1
-n
2
plane. In this case, yaw feedback control is not employed in order
to alleviate the actuation burden on the flapping wings and, also, to demonstrate that
the proposed four-wing design significantly increases the aerodynamic damping
along the yaw angular motion, which improves the open-loop stability of the yaw
25
degree of freedom, as discussed in Section 2.1.2. Theoretically, in the control of the
thrust force direction, which coincides with theb
3
axis, the Euler yaw angle can be
ignored. Therefore, to simultaneously control the robot’s altitude and attitude, we
regulate the vertical coordinate of the body’s center of mass to a desired constant,
and we regulate the robot’s roll and pitch angles to zero.
Accordingly, it follows that the attitude quaternion required to achieve the si-
multaneous experimental control of the robot’s altitude and attitude is given by
¯
q
d
=
cos( =2) 0 0 sin( =2)
T
, where is the actual Euler yaw angle according to
the Z-Y-X convention. In addition, the altitude controller can be simply derived from
(2.11) and (2.12). In specific, under the assumption thatb
3
i
3
, we immediately
obtain that
f =k
p
(r
3
r
d3
) k
d
˙ r
3
k
i
Z
(r
3
r
d3
)d t + mg (2.17)
where r
3
is the measured altitude of the robot; r
d3
is the desired altitude of the robot;
and k
p
, k
d
and k
i
are controller gains found through classical control methods.
A set of results obtained from an experiment in which the robot’s altitude and
attitude are simultaneously controlled is shown in Fig. 2.4. Here, Fig. 2.4-A compares
the desired and measured altitudes, and Fig. 2.4-B shows the measured roll and
pitch angles of the robot for references equal to zero. From these data, it is clear
that the algorithm specified by (2.10) is effective in controlling the robot’s attitude
as the experimental direction of the thrust force is approximately perpendicular to
then
1
-n
2
plane. In this case, the angular oscillations stay mostly inside the range
[10
: 10
], which is acceptable in the sense that the magnitude of the lift force is
not greatly degraded, as can be deduced from Fig. 2.4A. In specific, the robot rapidly
reaches a value close to that of the desired altitude, even though the steady-state
error does not seem to approach zero, probably due to an insufficient integral action.
26
A: Reference r
d3
and measured altitude r
3
.
B: Measured Euler roll and pitch angles.
Figure 2.4: Simultaneous real-time control of altitude and attitude. A. This plot shows
that the measured altitude signal, r
3
, tracks the main trend of the reference signal,
r
d3
; however, significant transient and steady-state errors can be observed. B. This
plot shows that the Euler roll and pitch angles oscillate approximately between=10
and 10
, which is partially caused by the vibration of the robot’s body that is induced
by the flapping of the wings. The entire experiment lasts for approximately 5 s; then,
the robot leaves the volume of operation and the power is automatically turned off.
Furthermore, the time lapse of the experiment in Fig. 2.5A (also shown in Movie S1)
indicates that the four flapping wings generate a lift force sufficient for the robot
to take off and maintain its body in the upright orientation for a significant period
of time. The observed drifting phenomenon is expected due to the lack of control
action in then
1
-n
2
plane. Overall, the data in Fig. 2.4 and photographic sequence in
Fig. 2.5A provide compelling evidence demonstrating the effectiveness of the design,
fabrication, actuation and control methods developed to create Bee
+
.
27
Figure 2.5: Controlled flight experiments. A. Photographic sequence of a flight experi-
ment during which the altitude and altitude of the Bee
+
prototype are simultaneously
controlled. The corresponding altitude and Euler angles are shown in Fig. 2.4. During
the experiment, the direction of the thrust force is controlled to remain approximately
perpendicular to then
1
-n
2
plane. The cable tethered to the robot provides the power
and transmits the control signals. The robot drifts on then
1
-n
2
plane due to the lack
of control actions along the horizontal inertial axes. After 2 s, the robot flies outside
the focus area of the camera. B. Photographic sequence of the position control exper-
iment. The corresponding position and Euler angles of this experiment are shown in
Fig. 2.6. The complete set of experiments is shown in Movie S1.
2.4.3 Position control experiment
In this experiment, a Bee
+
prototype is commanded to hover at a desired position in
space while driven by the attitude controller specified by (2.10) and the position con-
troller described by (2.11) and (2.12). As in the experiment described in Section 2.4.2,
the desired and true yaw angles are assumed to be identical to each other, i.e.
d
= ,
which does not affect, in any way, the computation of position control signals as
the direction of the total thrust force does not depend on the yaw angle. A photo-
graphic sequence of the experiment, with the corresponding time-lapse information,
is shown in Fig. 2.5B; the associated experimental data is shown in Fig. 2.6. Here,
Fig. 2.6A shows the measured controlled position of the robot along with the corre-
sponding reference signals. These data show that the robot approximately tracks the
reference signals during the first second of the test; then, the position error along the
28
A: Reference and measured position of the center of
mass.
B: References and measured roll and pitch angles.
Figure 2.6: Position control experimental results. A. The dash lines show the desired
position of the center of mass and the solid lines show the measured position of the
center of mass. B. The dash lines show the desired Euler angles derived from (2.13)
and (2.14); the solid lines show the measured Euler angles.
n
1
axis gradually increases. Fig. 2.6B shows that during the first second of the test,
the measured roll and pitch angles approximately track the references and that the
low-frequency content is tracked accurately; then, the pitch tracking error gradually
becomes significant, which is consistent with the increasing position error along the
n
1
axis shown in Fig. 2.6A. We hypothesize that the oscillation about the pitch axis
is caused by actuator saturation. This problem will be addressed by improving the
robotic design in order to generate more thrust for position regulation and trajectory
following. The complete set of experiments is presented in Movie S1.
29
2.5 Discussion
We presented Bee
+
, a new 95-mg four-winged insect-sized flying robot with an ex-
tremely compact configuration, and the associated design and fabrication process.
The proposed approach has numerous advantages in terms of weight, dimensions,
aerodynamics, control and fabrication. The key innovation, and core component,
that enabled the development of Bee
+
is a new actuation technique based on the
use of pairs of twinned unimorph actuators. By employing instantaneous and time-
averaged quasi-steady analyses, we estimated the main aerodynamic characteris-
tics of the robotic design, including ranges for thrust forces, damping and steering
torques. Also, three different strategies for yaw-torque generation were discussed
and we determined that the inclined stroke-plane method is the most appropriated
for the control of the four-winged Bee
+
. Finally, we presented a method for controller
synthesis based on techniques developed for quadrotors and real-time control ex-
periments. In the future, the process of thrust-force generation will be improved by
employing the method in (31) and we expect to achieve lift-to-weight ratios as high
as 3. These developments will enable Bee
+
to increase its available thrust force in
order to perform aerobatic maneuvers and other complex flight tasks. In addition,
the clap-and-fling phenomenon observed in Movie S1 will be investigated as this
aerodynamic mechanism can lead to a lift increase.
30
Chapter 3
Catalytic artificial muscle
3.1 Mechanism of catalytic artificial muscles
External-energy-dependency is one factor that prevents microrobots, like Bee
+
and
RoboBee, from progressing towards full autonomy. Microrobots have yet to be
equipped with on-board power sources and compatible actuators capable of support-
ing flight or even long-duration ground-based missions. In other words, microrobots
long for more powerful, longer-lasting muscles.
For animals, the most energy-demanding activity is muscle contraction (32, 33).
Muscle cells are able to produce enough adenosine triphosphates (ATP) from carbo-
hydrates through biochemical processes, and convert the chemical energy stored in
the ATP into mechanical work used directly for muscle contractions. Carbohydrates’
HED makes them an ideal source of energy as they can sustain long periods of intense
activities for animals. For example, insects’ flight muscles can propel their wings to
flap continuously at high frequencies (50 to 200 Hz) for many minutes during flights.
Similarly, for autonomous bioinspired microrobots, limb or wing actuation usually
consumes most of the energy. Therefore, we believe adopting actuation methods
31
that utilize HED sources is the key to achieving energy autonomy in microrobots.
In recent years, a wide variety of novel micro actuation technologies have been
developed and tested (34), including piezoelectric ceramics and polymers, electroac-
tive polymers (35), electrostatic actuators (10), shape-memory alloys (SMAs) (36, 37),
self-contained soft composites (38), twisted polymer-based fibers (39), deformable
elastomer modules (40, 41), and carbon nanotubes (42, 43). Most of these actuators
are electrically powered. Presently, to solve power supply issue for millimeter-scale
robots employing these actuation technologies requires them to be tethered to ex-
ternal power supplies. For example, a family of flying microrobots (1, 44, 45) are
actuated by piezoelectric ceramics attached to high-voltage drivers. Tanaka et al.
presents a quadruped micro-electromechanical systems (MEMS) microrobot that em-
ploys electrically heated SMA actuators, and is also connected to an external power
station. The state-of-the-art lithium battery is not yet a viable power option at this
scale as it suffers from the crucial drawback of its low energy density (0.5 MJ/kg) (47),
and even more importantly, the low maximum power density, about 200 W/kg.
In comparison, the energy density of hydrocarbon fuels is 40-50 MJ/kg and hy-
drogen is 120 MJ/kg (48), which are at least two orders of magnitude higher than that
of batteries. This deciding advantage has motivated researchers to explore methods
of powering artificial muscles using hydrocarbon fuels. Ebron et al. introduced a
platinum-coated (Pt-coated) nanotube electrode of a fuel cell, for which to work,
the actuator has to be submerged in an electrolyte and the chemical energy of the
fuel needs to be converted to electricity first in order to produce bending motion.
Ebron et al. also looked into the possibility of directly harvesting and utilizing thermal
energy generated from the flameless catalytic combustion to power a catalyst-coated
Nickel-Titanium (NiTi) SMA wire. Limited by the coating technique, fuel delivery
rate and lack of a controller, the system was experimentally shown to actuate at a rate
32
slower than 0.002 Hz. Tadesse et al. created a robotic jellyfish (164 mm in diameter)
actuated by catalytic combustion powered SMA actuators. However, the jellyfish was
tested in open loop and could only generate bell stroke less than one third of that
found in its natural counterpart at a frequency of 0.1 Hz. Recently, a soft autonomous
octopus robot has been reported that can lift its arms alternately using pressurized
bubbles generated from catalytic reaction of hydrogen peroxide (51).
In this chapter, I introduce a method to realize closed-loop control of fast catalytic
combustion on a millimeter-scale SMA-based artificial muscle. This innovation will
enable the application of catalytic artificial muscles (CAMs) to microrobotic actuation
once the fuel storage and supply system is scaled down accordingly. Coated with
Pt catalyst, the CAM directly utilizes chemical energy of hydrocarbon fuels through
exothermic catalytic reaction to generate mechanical outputs. Due to the inherent
nonlinearity of the catalytic reactions and the hysteretic behavior of SMAs, CAM
actuation is a complex thermomechanical process. To characterize and investigate
the performance of the CAM, we built an experimental setup that can precisely
control the fuel supply, and simultaneously measure the temperature, strain and
stress of the CAM during reaction. Through an identification process, we obtained
a set of experimental parameters that makes possible the synthesis of the closed-
loop controller capable of controlling the catalytic reaction. Specifically, we report
the first successful employment of a fuzzy-logic-based control strategy to regulate
the temperature profile of the CAM. In addition, we developed a reliable coating
method to ensure the micrometrical precision of the catalyst layer on the CAM. As
an example, we controlled a 10-mm CAM to produce a peak-to-peak displacement
of 120µm at 1 Hz using the described control scheme. Furthermore, we fabricated a
micrometer-scale four-bar transmission mechanism using the SCM method (52) to
demonstrate the possible application of this type of actuator.
33
H
2
O
2
H
2
O
Heating Cooling
Pt catalyst SMA
A B C D
E
100μm
10μm
F
50μm
Figure 3.1: NiTi-Pt-based composite artificial muscles driven by catalytic combustion.
A. A schematic diagram of a CAM. This catalyst(Pt)-coated SMA wire will heat up and
contract upon heterogeneous catalytic reaction occurring on its surface. After the
reaction finishes, the wire cools down and extends to original length. B. Scanning
electron microscope (SEM) image of an SMA wire coated using Pt black with an overall
diameter of 105µm. C. An SMA wire coated using Pt foil with an overall diameter
of 77.8µm. The foil is a 0.12µm thick Pt leaf used for gilding (W&B Gold Leaf, LLC).
D. A bare NiTi SMA wire, 76.2µm in diameter. E and F. SEM images of the detailed
surface structure of the Pt black coating of the SMA wire. The fine Pt black particles
agglomerate and form a rough and porous 3D micro structure with large surface
area.
3.1.1 Heterogeneous catalytic reactions
We choose hydrogen as the fuel in this study because of its associated low ignition
temperature, a property discussed in the later paragraphs. The overall heteroge-
neous catalytic combustion contains three elementary steps in the following order:
adsorption of reactants, surface reactions and desorption of products (53, 54). First,
as gas phase H
2
and O
2
molecules arrive at the catalyst, a layer of these reactants
34
are adsorbed on the surface by the Pt particles (in Fig. 3.1A). Then, the presence of
the catalyst provides a reaction pathway with much lower energy barriers for the
adsorbed species to dissociate and form the products. The surface reaction step
accounts for most of the energy converted in the catalytic combustion, generating
sufficient amount of energy to raise the temperature of the CAM. During the final
step, reaction products desorb from the catalyst surface into the gas phase. The
overall reaction is
H
2
(g)+
1
2
O
2
(g)
Pt
! H
2
O(g).
The enthalpy changeH is=241.8 kJ/mol (55), meaning one mole of H
2
releases
241.8 kJ thermal energy. Exothermic catalytic reactions have two distinct attributes,
an induction period and a thermal runaway (Fig. 3.2). The induction period is the
initial stage of the reaction, during which the reaction temperature is low. Since reac-
tion rates generally increase rapidly with temperature according to the Arrhenius law,
the induction period is also characterized by its low reaction rate. Following the in-
duction period, the reaction typically accelerates with the rising temperature until it
becomes transport-rate-limited rather than reaction-rate-limited. Thus, the temper-
ature response of catalytic reactions typically follows the curve of a sigmoid function.
Sometimes, however, the temperature may rise beyond the material limitation before
reaching steady-state. Owing to these two features, the catalytic combustion is a
nonlinear phenomenon. For such an inherently unstable process to produce reliable
and precise temperature profiles applicable to SMA actuation, we implemented a
special control strategy discussed in results section.
In addition, we have experimentally identified two other factors that can charac-
terize the behaviors of CAMs in heterogeneous catalytic reactions. The first one is
the ignition temperature T
ig
, the temperature threshold upon reaching when rapid
35
0 0.5 1 1.5 2
Time (s)
20
40
60
80
100
120
140
Temperature (°C)
Ignites
Thermal runaway
Induction period
Figure 3.2: Induction period and thermal runaway of catalytic reaction on the CAM.
catalytic reactions start, which is considered equivalent to the temperature recorded
at the end of the induction period. This temperature depends on both the fuel
selection and activity of the surface catalyst. A Pt-foil-coated SMA wire needs to
be preheated up to approximately 100
C before the catalytic reaction begins. In
comparison, when tested with the same fuel mixture, an SMA wire coated using Pt
black (fine powder of platinum) can readily start reacting at room temperature 20
C,
eliminating the preheating process. Low T
ig
is desirable also because it allows for
low-transition-temperature SMA wires to go through full phase transition during
reaction, maximizing their strain outputs. The second feature is the activation of
the catalyst coating. It has been observed that the temperature response of a freshly
coated CAM can evolve significantly after the first catalytic reaction takes place over
its surface before settling into a consistent profile. Such phenomenon has also been
noted in the Refs. (56, 57), which can partly be explained by the fact that oxide layer
tends to improve the activity of the Pt catalyst.
36
Strain (%)
T
mf
T
ms
T
af
T
as
Temperature (°C)
Major loop
Minor loop
A B Stress (MPa)
Temperature (°C)
Strain (%)
Shape memory
eect
Superelasticity
Detwinned Martensite
Twinned Martensite
Austenite
Detwinned Martensite
Forward
transformation
Reverse
transformation
ε
L
T
mf
0
T
ms
0
T
as
0 T
af
0
Cycle 2
Cycle 1
Figure 3.3: Characteristics of SMAs. A. A general stress-temperature-strain diagram
of SMAs. The schematic representations of crystal structure orientations of austenite,
detwinned martensite and twinned martensite are described accordingly. Herein,"
L
stands for the residual strain of SME and is the uniaxial stress applied on the SMA
wire. B. Strain-temperature characteristics of SMAs under constant loading stress.
3.1.2 Mechanism of shape-memory alloys
A loaded SMA is able to memorize its original shape, and recover when thermally
triggered. This property is possible because SMAs can exhibit both high-symmetry
cubic and low-symmetry (e.g. monoclinic in NiTi alloys) crystal structures. The
former corresponds to SMA ’s parent phase—austenite and the latter is associated
with its product phase—martensite. Phase transformation between austenite and
martensite allows SMAs to generate robust and repeatable deformation. Specifically,
starting from the high temperature austenitic phase, an SMA wire will transform to
detwinned martensite and extend upon cooling or loading, following the forward
transformation path described in Fig. 3.3A marked with blue arrows. Conversely,
the original austenitic phase can be recovered from the martensitic phase by either
heating or unloading, following the reverse transformation path outlined in Fig. 3.3A
marked with red arrows. Thermally- and mechanically-induced SMA phase transfor-
mation are known as the shape-memory effect (SME) and superelasticity, respectively.
Both transformations clearly display hysteresis as shown in Fig. 3.3A.
37
According to the constitutive model of SMAs (58), the transformation process
and hysteresis can be outlined by four temperatures. They are, from low to high,
martensitic finish T
Mf
and start temperature T
Ms
, austenitic start T
As
and finish tem-
perature T
Af
, each marking a critical stage during SMA ’s phase transformation process.
Furthermore, these four transition temperatures are approximately linearly corre-
lated with stress as illustrated by the stress-temperature curves in Fig. 3.3A. This
relationship can be expressed by
T
Mf
= T
o
Mf
+
C
M
, T
Ms
= T
o
Ms
+
C
M
, T
As
= T
o
As
+
C
A
, T
Af
= T
o
Af
+
C
A
,
in which T
o
s are transformation temperatures at zero stress level, and C
M
and C
A
are the stress influence coefficients (59). However, the convoluted effect of SME and
superelasticity makes identification of SMA ’s phase transformation a complex nonlin-
ear problem. Different heating and loading conditions will lead to an infinite amount
of possible phase transition paths. To view this from a 3D perspective, the four transi-
tion stress-temperature curves are swept along the strain axis to form four transition
planes as shown in Fig. 3.3A. During forward transformation, austenite-to-martensite
transition initiates above T
Ms
plane (light yellow) and completes above T
Mf
plane
(light blue). In comparison, during reverse transformation, martensite-to-austenite
transition begins beneath T
As
plane (light orange) and concludes under T
Af
plane
(light red).
In the presented work, we focus on controlling the strain while maintaining a
constant loading stress on the CAM. Therefore, a constant stress strain-temperature
curve presented in Fig. 3.3B describes the strain dynamics we address in this study.
The hysteresis loop associated with the largest possible strain is termed the major
loop while all smaller hysteresis loops enclosed within the major loop are known as
minor loops. The major loop is usually confined between T
Mf
and T
Af
. It is clear from
38
1 2 3 4 5
Figure 3.4: CAM fabrication method. A bare SMA wire is crimped with two cable ring
terminals using a hand-held hydraulic crimper (Step 1). The wire segment between
two terminals is 10 mm so the wire can be properly held straight on a bracket (Step 2)
during the coating process. Afterwards, a layer of thermally conductive paste (Omega
OT-201) is uniformly brushed onto the wire with micrometrical precision under a
microscope to minimize the layer thickness (Step 3). The thermal paste layer serves
as an adhesion agency that bonds the Pt black powder to the SMA wire and does not
cure. Subsequently, the wire is immersed into Pt black powder laid out on a right
angle stand (Step 4). Such process is repeated while the coated wire is speculated
using a microscope to control for coating quality. The finished CAM (Step 5) is placed
onto the burner for actuation experiment. A CAM has an average diameter of 105µm
(Fig. 3.1 E and F).
the diagram that the additional strain in the major loop corresponds to a dispropor-
tionately large increase in the temperature spectrum. Meanwhile, if the reaction
is set to oscillate within the range of T
Ms
and T
As
, the resulting strain is ineffectual.
Conclusively, following the heating trajectory of a properly selected minor loop can
be much more efficient than adopting the major loop, as it can reduce energy cost
and increase actuation frequency. To actuate the proposed CAM, we experimentally
identified a temperature profile leading to a minor loop that optimizes both strain
and actuation speed. In addition, the condition T
ig
< T
Mf
needs to be satisfied for the
reaction, otherwise the CAM can no longer transform to martensite completely once
ignited, significantly reducing the attainable strain.
39
3.2 Fabrication of catalytic artificial muscles
Reliable, consistently repeatable and controllable catalytic reactions can only be
achieved on actuators with properly coated Pt surfaces. Specifically, the quality of
the coating is determined by four characteristic: uniformity, thickness, mechanical
robustness and capacity for catalytic activity. A uniformly coated catalytic layer allows
for an evenly distributed heat profile along the entire length of the wire and reduces
the chances of the appearance of local hot spots. A thin coating layer is required to
obtain a small total thermal mass, and therefore, to achieve a fast thermal response
rate of the NiTi-Pt composite. Mechanical robustness is required because during
periodic actuation, the Pt catalyst layer continuously undergoes rapid contractions
and extensions as the length of the NiTi wire oscillates according to the hysteretic
dynamic behavior described in Section 3.1.2. Therefore, to attain reliable actuation
patterns it is crucial that the Pt coating layer remains firmly bonded with the NiTi wire
for all the temperature–stress conditions endured by the actuator, i.e., the catalytic
layer neither peels off nor fissures during sustained operation of the actuator.
The capacity for catalytic activity positively depends on the total Pt surface area in
contact with the reactants (57, 60, 61). This notion directly follows from the observa-
tion that the larger the active catalytic surface, the shorter the induction period and
faster the reaction conversion rate. In this work, through an exhaustive experimental
search, we devised a coating method that produces a surface with characteristics that
make controlled catalytic combustion feasible. The proposed fabrication technique
is based on the use of fine powder (Pt black, HiSPEC 1000 from Alfa Aesar). The pro-
cess starts by applying a layer of thermally conductive paste (OMEGATHERM OT-201
from Omega), with a thickness of approximately 5µm, to the surface of the NiTi wire;
then, particles of Pt black are spread over the epoxy layer and agglutinated to create
40
the 3D porous structures shown in Fig. 3.1E. In this configuration, the attachment
between the SMA material and the first sublayer of Pt catalyst is created by the glue;
however, the adhesion between particles in the upper sublayers of the coating is
created by intermolecular van der Waals forces. Employing the information provided
by the manufacturer (62), we estimate that for the SMA wire employed here with
a specific surface area of 8.16 10
=3
m
2
/g, the resulting active catalytic surface has
a specific surface area of 27 m
2
/g, corresponding to a factor of approximately 3300
times. The details of the fabrication process are described in Fig. 3.4.
As mentioned in Section 3.1.1, additionally to the NiTi-Pt composite actuator in
Fig. 3.1B, we tested the actuator shown in Fig. 3.1C which is composed of an NiTi wire
and a thin coating Pt foil. As expected from the notion that the capacity for catalytic
activity depends on the total surface area of the Pt coating exposed to the reactants,
the experimental performance of the actuator in Fig. 3.1B is significantly better than
that obtained with the actuator in Fig. 3.1C. For example, the ignition temperature
for the former is 20
C and for the latter is 100
C; and sustained catalytic combustion
is achieved with an H
2
flow of 2 ml/min for the former and 30 ml/min for the latter.
3.3 Experimental setup
The experimental setup was designed to control temperature and measure the strain
as well as the stress of CAMs during actuation driven by flameless catalytic com-
bustion. A 10-mm SMA wire (76.2µm in diameter, 90
C Nitinol from Dynalloy) is
first crimped and coated using Pt catalyst (Pt black, HiSPEC 1000 from Alpha Aesar)
with micrometrical precision. Pt black was experimentally proven to provide a more
catalytically active surface (Fig. 3.1 (D-F)). The detailed coating process is described
in Section 3.2. As shown in Fig. 3.5A, the finished CAM is held 4 mm above a burner.
41
1 2
3 4 5 6 7
8
9
A B
Figure 3.5: Experimental setup. A. Computer-aided design (CAD) diagram of the
experimental setup. (1) Solenoid proportional valve; (2) Cross union fitting; (3)
10-mm CAM; (4) Burner; (5) Thermocouple and its connector; (6) Linear rail and
its cartridge. The flapping-wing mechanism and target plate are installed on the
cartridge; (7) Laser displacement sensor; (8) Load cell; (9) Dead weight. B. A zoomed-
in view photo of the experimental setup.
One end of the CAM is anchored to a bracket, while the other end is connected to a
linear rail that tracks the CAM’s deformation during reaction. A laser displacement
sensor (Keyence LK-031) is installed parallel to the rail, measuring the CAM’s strain
by tracking a specially designed target plate that extends from the linear rail car-
tridge. In order to apply a constant stress to the CAM, a dead weight is hung from
the cartridge through a pulley mechanism. A load cell (Futek LSB200) is employed to
measure the real-time stress during actuation. To measure the temperature of the
CAM, one 51µm diameter bare wire thermocouple (Omega type K, CHAL-002) is
installed onto the SMA wire. Given the dimension and characteristics of the CAM,
the Biot number (63) of the heat transfer process is approximately 6 10
=4
, implying
that its interior temperature variation during the heat transfer process is negligible.
This property allows us to assume uniform temperature distribution within the CAM
at any instance during the catalytic reaction.
In this work, the reaction rate of the catalytic combustion is controlled by regulat-
42
ing the flow rate and proportion of each component of the fuel mixture. Moreover,
according to the dimensions and heat transfer properties of the NiTi SMA wire, the
estimated thermal time constant (63) of the catalytic reaction on the CAM is in the
order of milliseconds. Therefore the fuel delivery system must be able to respond
rapidly and accurately. One of the key contributions presented in this work is the fuel
delivery apparatus that we developed which enabled us to characterize the CAM’s
thermomechanical properties, optimize reaction parameters, as well as control the
thermal profile of the CAM during reactions. The apparatus consists of fast flow
controllers, flow control valves, pressure regulators, a fuel-mixing junction, a burner
and in-line filters. One flow controller is composed of a flow sensor (Honeywell
airflow sensor, HAFBLF0200C4AX5) with a response time of 1 ms, and a solenoid
proportional valve (Kelly Pneumatics Inc., KPI-VP-20-09-25-V) with a response time
between 3 and 5 ms. Three such systems are installed to individually control the flow
of hydrocarbon, oxidant and diluent into the burner. Using system identification and
controller design methods in (64, 65), we then synthesized a linear-time-invariant
(LTI) controller to realize closed-loop feedback control of the gas flow rate, achieving a
response rate of 20 ms. In comparison, most commercially-available flow controllers
have response times in the order of seconds. A cross union fitting then connects
the output of each flow controller to the burner. To further reduce the response
time, we minimized the gas tubing volume between the flow controllers and the
burner outlet. Because according to the formula t = V=q , under a constant flow rate
q , the traveling time t is proportional to volume V the fluid has to travel through.
Accordingly, a pressure regulator, flow control valve and in-line filter are installed
upstream from each flow controller for the purposes of setting maximum flow rate,
adjusting pressure and purifying gas input from its reservoir, respectively. In addition,
a honeycomb panel (Carolina metals, Hastelloy-X) is embedded in the outlet of the
43
burner to deliver evenly distributed gas flow to the CAM placed above. Moreover,
since the cell dimension of the honeycomb (0.79 mm) is smaller than the quench
distance at which explosions can propagate, we can safely conduct experiments with
any hazardous fuel mixtures (57).
3.3.1 Fast controlled flow actuator
Achieving a fast controlled actuation of the CAM requires the fuel supply system to
have a large bandwidth (10 Hz) for rapid responses and accurate control in low-
flow-rate range (200 ml/min). However, most commercial-available CFAs have
response times in the order of seconds, and their flow rate ranges are not suitable for
our application.
Therefore, we developed a custom-built fast CFA in this work for the fuel sup-
ply system. The solenoid-proportional valve and airflow sensor we employed are
amongst the fastest off-the-shelf valves and flow sensors, respectively. In addition, to
design a high-performance controller for the CFA, we regarded the solenoid valve as a
black-box and obtained a model through system identification. One main advantage
of this method is that the derivation of a first-principle-model of the valve is not
required for the controller design. We applied the parametric-system-identification
method described in Refs. 65, 64. According to this method, the order and form of
the model is assumed a priori, which can be described with following structure:
y
k
=
n
X
i=1
y
ki
A
i
+
n
X
i=0
u
ki
B
i
, k = 0, 1, 2, ... (3.1)
where the output y
k
and the input u
k
could be either scalars or row vectors. The
formula be written as y
k
=
k
, where
k
= (y
k1
... y
kn
u
k
... u
kn
) and
T
= (A
T
1
A
T
2
... A
T
n
B
T
0
B
T
1
... B
T
n
). Thus, the problem can be formulated as a
44
0 0.05 0.1 0.15 0.2 0.25 0.3
0
0.5
1
Model (14)
Experiment
Time (s)
Amplitude
-100
-50
0
50
Magnitude (dB)
10
-1
10
0
10
1
10
2
10
3
-1800
-1440
-1080
-720
-360
0
Phase (deg)
Models
Frequency (Hz)
Model (100)
Model (14)
-80
-60
-40
-20
0
Magnitude (dB)
10
-1
10
0
10
1
10
2
10
3
-2880
-2160
-1440
-720
0
Phase (deg)
Closed-loop Bode Diagram
Frequency (Hz)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (s)
-1
-0.5
0
0.5
1
Amplitude
Output
Input
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (s)
-1
-0.5
0
0.5
1
Amplitude
Model (14)
Experiment
A
B
C
D
E
Figure 3.6: System identification and LTI controller design for CFA. A. White noise
input signal and the response signal for system identification. B. Bode diagrams
for identified 100th-order model and 14th-order model obtained using balanced
truncation model reduction method. C. Validation for the identified 14th-order
model. D. Closed-loop Bode diagram for CFA system with LTI feedback controller. E.
Theoretical and experimental step responses for the closed-loop CFA system.
multiple-input/multiple-output least-squares (MIMO-LS) problem:
min
kY
N
N
k
F
(3.2)
wherekk
F
denotes the matrix Frobenius norm. The solution to this problem can be
45
found using least-squares method:
ˆ
=
+
N
Y
N
(3.3)
in which
+
N
is the pseudoinverse of
N
, Y
T
N
=(y
T
0
y
T
1
... y
T
N
),
T
N
=(
T
0
T
1
...
T
N
)
and N is the number of times the system is sampled. Here, it is clear that
ˆ
is unique
and (3.3) holds, since in practical application N has magnitude of various thousands,
meanwhile the input signal to the system is chosen to be white noise, which can
excite the system over the entire sampled frequency spectrum, from 0 Hz to 500 Hz,
the Nyquist frequency of the system (66). The system was excited by the white noise
for ten minutes, and the last 500 seconds signals are used for system identification.
A segment of the input and output signal (2 s) are plotted in Fig. 3.6A. The model of
the system identified through this process is a 100th-order model.
To reduce the order of the system, a state-space realization of the identified 100th-
order model was balanced, and a certain number of states, relatively less observable
and controllable than the others, were discarded, as explained in Ref. 68. The final
model obtained has an order of 14th and matches the model originally identified
well within a bandwidth (0 Hz to 100 Hz) that is large enough for our application,
as shown in Fig. 3.6B. In addition, this model was validated by exciting the system
with a new set of the white noise signal, and the output of 14th-order model, in a
large extent, agrees with the measured output of the system (Fig. 3.6C), implying the
identified model is a satisfactory estimation of the true model of the system.
Based on this identified model, we designed an LTI controller using the feedback
control techniques. The corresponding Bode diagram of the closed-loop system is
presented in Fig. 3.6D. It is evident that the controller improves the high-frequency
performance of the system (at 10 Hz). The gain and phase margins, estimated from
the Bode plot, are approximately 9 dB and 60
, respectively, indicating that the re-
46
sulting closed-loop system is robustly stable. Furthermore, the controller design
was validated by comparing its step response in numerical simulation with that of
the experimental result. As shown in Fig. 3.6E, the trend of step responses have a
satisfactory agreement, despite some small discrepancies. From the plot, the esti-
mated rise time and settling time of the built-in-house CFA are 11.4 ms and 23.6 ms,
respectively.
3.3.2 Temperature measurement
To rapidly and accurately measure the temperature of a 105-µm-thick CAM wire is
a nontrivial challenge, and critical for the control experiment. Various sensors can
be used to measure temperature of substances, such as infrared sensor, thermistors
and thermocouples etc. However, the response performance of all these sensors
are limited by the rate of heat radiation or rate of heat transfer. To increase the
rate of heat transfer between sensor and measured object, the thermal mass and
resistance of the sensor should be as small as possible (69). Here, a fine gage bare
wire thermocouple is applied to measure the temperature of the CAM. The diameter
of the bead, the sensing part of thermocouple, is only 0.0508 mm. This is the thinnest
applicable thermocouple for our experiment. In addition, increasing the contact
surface between the thermocouple and the CAM also can improve heat transfer
condition between them (36). Therefore, the thermocouple is installed on the CAM
by wrapping the lead wires close to the bead several rounds for further improving
the response time and disturbance rejection in temperature measurement.
47
Figure 3.7: Measurement and processing of the temperature on the surface of the NiTi-
Pt composite. Here, T
t
(t) is the true temperature; T
m
(t) is the measured temperature;
the sequence T
m
(k) is the sampled measured temperature; [F T
m
](k) is the low-pass
filtered measured temperature; and
ˆ
T
t
(t) is the estimate of T
t
(t).
-100
-50
0
50
100
Magnitude (dB)
10
-1
10
0
10
1
10
2
10
3
10
4
-90
-45
0
45
90
Phase (deg)
Models and Filters
Frequency (Hz)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Time (s)
20
30
40
50
60
70
80
90
Temperature (C
°
)
Measured and Corrected Temperature Signals B A
Figure 3.8: Filters and signal correction. A. Bode plots of the systems in Fig. 3.7. Here,
H(s) describes the continuous-time dynamics of the thermocouple for
0
= 18.18;
H
d
(z) is the discretized version of H(s), found employing the Tustin method; N(z) is
the stabilized version of the inverse of H
d
(z); and M(z) is the almost-all-pass filter
resulting from multiplying H
d
(z) and N(z), thus demonstrating that in steady-state
N(z) can be employed to compensate the distortion introduced by the thermocouple.
B. Comparison of the measured sampled temperature T
m
(k) with the corrected signal
ˆ
T
t
(t)
Temperature sensor model The thermocouple employed in this research can be
modeled as a normalized (DC Gain= 0 dB) first-order system with the form
H(s)=
0
s +
0
(3.4)
associated with the impulse response h(t)=
0
e
0
t
1(t), where
0
=
1
0
,
0
is the
time constant of the system and 1(t) is the standard Heaviside step function. In
principle,
0
can be identified from the step response s(t) =
1 e
1
0
t
1(t). The
main difficulty with the characterization of this system is that
0
is different for
48
different media and Reynolds numbers. Here, we use
0
=0.055 s, estimated in the
work presented in Ref. (69), for a thermocouple of the same diameter operating in
air.
Latency compensation strategy The filter H(s) introduces a significant phase de-
lay to non-constant signals. Thus, the raw measurements of temperature must be
processed in order to cancel the distortion introduced by the thermocouple sensor.
This process is performed using a discrete-time inverse filter. To begin with, we find
a discretized version of H(s) for the sampling period T
s
= 10
3
s, computed according
to the Tustin method, which yields
H
d
(z)=
0.009008z + 0.009008
z 0.982
(3.5)
This filter is non-minimum phase; therefore non-invertible. This issue is corrected
by replacing the unstable zero 1 with 0.96, which allows us to compute the stable
inverse predictive filter
N(z)=
z 0.982
0.009008z + 0.008648
(3.6)
This is a lightly damped high-pass filter that amplifies high-frequency noise; for this
reason, during post processing, we filter the data with a zero-phase FIR
1
low-pass
filter of order 12, F(z). This leads to the measurement and signal processing scheme
in Fig. 3.7. The corresponding Bode plots are shown in Fig 3.8. Here, it can be seen
that, in the range 0.1 Hz to 200 Hz, the frequency response of the stabilized discrete-
time filter H
d
(z) perfectly matches that of H
d
(s), which indicates that H
d
(z) accurately
captures the dynamics of H
d
(s) over of the operational range of the actuator; also, the
frequency response of the operator M(z)= H
d
(z) N(z) is very close to 1 in the range
1
Finite impulse response.
49
CAM
Pulse wave
generator
Flow
sensor
Fuzzy logic
controller
Valve
LTI
controller
T
ε
T
r
-
+
+
-
CFA 3
Amplitude
Thermocouple
CFA 2 CFA 1
q
1
q
2
q
3
q
1r
q
2r
q
3r
Figure 3.9: Temperature control scheme. Outputs of the plant, composed of flow con-
troller and CAM, are strain" and reaction temperature T . The fuzzy logic controller
compares the errors between T and reference temperature T
r
, and generates the
corresponding amplitude of square pulse wave signal as input to the flow controller
based on prescribed logic rules.
0.1 Hz to 200 Hz, which indicates that in steady state N(z) effectively compensates
the distortion introduced by the thermocouple. The suitability of the proposed
correction method (scheme in Fig. 3.7) is demonstrated in Fig. 3.8B, which compares
the raw temperature measurement, T
m
(k), with the corrected signal,
ˆ
T
t
(k), which is
used in the characterization of the actuator dynamics discussed in Section 3.4.1
3.3.3 Real-time controller synthesis
Fuzzy-logic-based controller The block diagram of overall control experiment is
exhibited in Fig. 3.9. The CAM is regarded as a subsystem as its input the vector
composed by the flow rates of H
2
, air and N
2
and as its output the temperature
on the surface of the NiTi-Pt composite and strain. In this case, the underlying
open-loop dynamics of the combustion process is nonlinear and unstable, which is
evidenced by the runaway effect described in Ref. (57). Therefore, in order to generate
50
reliable periodic actuation, the use of a stabilizing feedback controller is essential.
To control this process we employ the feedback scheme in Fig. 3.9, where the output
is measured with a high-speed thermocouple and the flow rates of the oxidant and
diluent are controlled to track the same constant values employed during the system
identification process (i.e., 200 ml/min and 750 ml/min), while the flow rate of H
2
is used to induce changes in the output of the system. In this way, the catalytic
combustion process becomes a SISO
2
mapping that relates the flow rate of H
2
with
temperature. As illustrated in Fig. 3.9, in order to achieve a periodic smooth output
"(t) with fundamental frequency f
r
, the control signal q
3r
(t) is chosen to be a train of
positive pulses with fundamental frequency f
r
, constant duty cycle P
d
and height a
0
(t).
Accordingly, f
r
determines the speed of actuation and P
d
dictates the heating and
cooling times during an actuation cycle. In this structure, the signal a
0
(t) is generated
according to a heuristically tuned fuzzy-logic-based control law defined in terms of
the fuzzy sets high, medium and low. The defining values associated with the high
and low fuzzy sets are experimentally determined through an iterative tuning process,
and the values associated with the medium fuzzy set are chosen to be the averages
of those associated with the other two fuzzy sets. The details regarding the selection
of the fuzzy logic output values are described in next section. Generally speaking,
during catalytic-combustion-driven operation, when the measured temperature Tm
is within an a-priori-defined reference range, the fuzzy controller outputs a medium-
valued a
0
(t). If the measured temperature drifts above an a-priori-defined upper
limit, the fuzzy controller switches its output to a low-valued a
0
(t); conversely, if
the measured temperature drifts below an a-priori-defined lower limit, the fuzzy
controller switches its output to a high-valued a
0
(t).
2
Single-input-single-output.
51
0 0.5 1
error
0
0.2
0.4
0.6
0.8
1
Degree of membership
low medium high
0 0.5 1
gain
0
0.2
0.4
0.6
0.8
1
Degree of membership
small medium large
-0.5 0 0.5 1 1.5
error
0
0.2
0.4
0.6
0.8
1
gain
A B C
Figure 3.10: Fuzzy-logic-based controller. A. Input membership functions; B. Output
membership functions; C. Controller input–output surface.
Fuzzy-logic rules and parameter selection A Mamdani-Type fuzzy controller (70)
is chosen here for synthesizing the controller based on experience obtained from real
time tuning. The input and output membership functions are shown in Fig. 3.10 A
and B. The input and output for the controller are error and gain respectively, noting
that they are all normalized here. The fuzzy sets for error are low, medium and high,
corresponding to T
m
> T
r
, T
m
= T
r
and T
m
< T
r
. And the fuzzy sets of gain are defined
as small, medium and large, corresponding to three amplitude values of a
0
(t). The
heuristic logic rules for input and output fuzzy sets are summarized as:
1: i f error i s low, t he n gain i s small; (3.7)
2: i f error i s medium, t he n gain i s medium; (3.8)
3: i f error i s high, t he n gain i s large. (3.9)
Thus, based on these fuzzy rules, the resulting input–output surface of the synthe-
sized controller is shown in Fig.3.10C. The essential function of this controller can
be understood in an intuitive way that when the reaction temperature is too high
(T
m
> T
r
), the controller generate small gain signal to reduce the flow rate of H
2
, as
a result the reaction will be mitigated and temperature decreases; when the CAM
operate in the desired range, the controller maintains the flow rate of H
2
to sustain
52
the actuation; if the scenario is T
m
< T
r
, large flow rate signal will be produced by
the controller to boost the catalytic reaction, then the temperature recovers to the
operating range again. The effectiveness of this controller is demonstrated in the
experimental result section, meanwhile the performance of such controller could be
further improved by tuning the membership functions and introducing extra input,
e.g.
˙
T
m
. The advantage of fuzzy-logic control strategy is that such a high-level algo-
rithm can be easily exploited on an actuator-level mechanical controller with passive
feedback mechanism, which make the down-scaling of such system to insect-size
very feasible.
The system characterization process provides the reference temperature range
optimized for CAM actuation, and the object of the fuzzy-logic-based controller is to
regulate the temperature of CAM to oscillate within the reference range. The input to
the fuzzy logic is the measured temperature and the output is the amplitude of the
H
2
flow rate to the flow controller which consists of three values: high, medium and
low. To obtain the high flow rate value, a constant-amplitude pulse signal is fed into
the flow controller in open loop. We adjusted the amplitude value until the minor
loop in the strain-temperature diagram was observed to be oscillating consistently
between T
Af
and T
Ms
. We then recorded the corresponding pulse magnitude as the
high value. Similarly, we selected the low value to be the pulse magnitude that led
the minor loop to oscillate consistently between T
As
and T
Mf
. The medium value was
then taken as the average of the high and low values.
3.3.4 Wing-flapping mechanism
When the CAM is implemented on a microrobot, its strain output needs to be ampli-
fied for producing applicable mechanical output for locomotion and other activities.
53
A C
500μm
B
δ
θ
Carbon Fiber
Polyimide Film
Adhesive
l
Figure 3.11: Micro four-bar transmission mechanism. A. Schematic diagram of
the working principle of four-bar transmission. B. SEM image of the micrometer-
scale transmission mechanism. A diode-pumped solid-state (DPSS) laser is used
for micromachining in-plane features for each layer of materials. The diameter of
the laser beam is about 10µm. All layers of different materials are then bonded
together under pressure and proper heating condition, creating this 3D structure.
The smallest laser-machined feature, the clearance between carbon fiber bars, is
70µm in this mechanism. The thicknesses of carbon fiber, polyimide film, adhesive
sheet are 90µm, 7.5µm and 12.5µm, respectively. C. An artificial butterfly wing is
installed on the transmission mechanism. The design has a wingspan of 67 mm and
is inspired by a species of butterfly named Troides rhadamantus. The spars of the
wing are 90µm carbon fiber, and the membrane is made from polyester film (2.5µm
in thickness). The inset is an enlarged view of the installed transmission mechanism,
of which the top layer is secured to a tweezer (held on a third hand) using a piece of
Gel-Pak, and its bottom layer is fixed to the T-bracket on a linear rail cartridge.
Therefore, we installed a millimeter-scale four-bar transmission mechanism in the
experimental setup, through which the CAM is able to drive an artificial butterfly
wing to flap as shown in Fig. 3.11. The transmission system is essentially inspired by
the design utilized in flapping-wing insect-sized flying robots (1, 44). The working
principle of the transmission is illustrated in Fig. 3.11A. The rigid linkages of the trans-
mission are made of carbon fiber, while the compliant joints of these linkages are
made of thin flexure film. The transmission ratio M of such mechanism is mainly de-
termined by the thickness l of the middle layer carbon fiber, obeying the relationship
described by the following equation:
M == 1=l .
54
For current transmission design, l is approximately 110µm, leading to a transmission
ratio of 9 10
3
rad/m. This means 1.2 % strain (120µm) of the CAM can theoretically
generate up to 62.5
of rotation at the distal end of the transmission. An SEM image
(Fig. 3.11B) shows the detailed view of the fabricated transmission mechanism. The
top linkage of the transmission is held stationary with respect to the floor using a pair
of cross-lock tweezers, and the bottom linkage is fixed to an T-bracket connected to
the CAM. Therefore, actuation of the CAM during operation will cause linear motion
of the bottom linkage. Accordingly, the artificial butterfly wing attached to the distal
end of the transmission will be driven to flap (Fig. 3.11C).
3.4 Experimental results
3.4.1 System characterization
In this study, the fuel, oxidant and diluent employed are H
2
, air and N
2
, respectively.
The identification of the thermomechanical behavior of the CAM under constant
stress is conducted first. A 76 g loading weight plus the load cell (9.9 g) are attached
to the linear rail, translating to approximately 185 MPa of stress applied to the wire.
Data acquisition and signal processing are performed with a DAQ board (National
Instruments PCI-6229) mounted on a target PC which communicates with a host PC
via xPC Target 5.5.
Through trial and error, we set the flow rates of H
2
, air and N
2
to be 2, 200 and
750 ml/min, respectively, for the identification process. Since air and N
2
serve as
carriers of H
2
during heating, high constant flow rates ensure that the fuel is smoothly
and swiftly delivered to the CAM while preventing potential thermal runaway. During
cooling, they can also enhance the cooling effects. The CAM is then heated up to
55
20 40 60 80 100 120 140 160
Temperature (°C)
0
1
2
3
4
5
Strain (%)
Austenite
Martensite
T
mf
T
ms
T
as
T
af
Figure 3.12: Experimentally identified hysteresis major loop of the SMA wire. Four
transformation temperatures are marked with four colored lines, from which a hys-
teresis of about 40
C can be identified. The heating/cooling cycle follows the reverse
and forward transformation path as indicated by the arrows.
160
C using this fuel mixture before naturally cooling back down to room tempera-
ture (20
C). The corresponding strain-temperature curve is presented in Fig. 3.12. A
maximum strain of 5 % is achieved and the four characteristic transition tempera-
tures T
Mf
, T
Ms
, T
As
, T
Af
are estimated and highlighted. According to the diagram, the
martensite-to-austenite transformation mostly occurs when the CAM is heated from
90
C to 100
C and significant austenite-to-martensite transition takes place when
it is cooled from 70
C to 60
C. This result agrees with the transition temperatures
provided by Dynalloy (71), which implies that the coating we applied does not cause
critical change in the SMA ’s characteristics. Furthermore, this identification result
leads us to select 60
C and 100
C as lower and upper temperature limits for the
following control experiments because of the substantial amount of strain attainable
56
0 20 40 60 80 100
Time (s)
20
40
60
80
100
Temperature (°C)
Temperature response A
60 62 64
Time (s)
60
80
100
Temperature (°C)
0 20 40 60 80 100
Time (s)
3
4
5
Strain (%)
Strain response B
60 62 64
Time (s)
0.3
0.35
0.4
0.45
Displacement (mm)
20 40 60 80 100 120
Temperature (°C)
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
Strain (%)
Strain-temperature curves C
Figure 3.13: Experimental controlled operation and thermomechanical character-
istics of the catalytic artificial muscle. A. Controlled temperature response of the
actuator operating at 1 Hz (left) and zoomed-in view of the temperature response
between 60 s and 64 s (right). B. Controlled strain response of the actuator operating
at 1 Hz (left) and corresponding enlarged view of the output displacement response
in mm between 60 s and 64 s (right). C. Temperature–strain hysteretic relationship
over the entire time-span of the experiment. The minor loops at the beginning of the
experiment evolve and settle into a regular hysteretic pattern once the temperature
reaches steady state within the operating temperature range.
within this range.
3.4.2 Fuzzy-logic-controlled fast actuation
In order to control the temperature of the CAM to oscillate within desired range,
we proposed a fuzzy-logic-based regulation scheme. Here, the flow rates of oxidant
and diluent are still set to the same constant values adopted in the identification
process. The flow rate of H
2
however, takes the form of an on/off square pulse wave
signal, the period of which is determined by the prescribed heating/cooling cycle
period. The duty cycle of the H
2
pulse signal is experimentally selected to minimize
flow rate tracking error and provide an adequate cooling period. Accordingly, the
catalytic reaction is then simplified to a SISO system, of which the input is the pulse
amplitude of the H
2
flow rate signal and the output is the reaction temperature
57
(Fig. 3.9). The output of the fuzzy controller is the amplitude of H
2
flow rate and
toggles between three values: high, medium and low. The high and low values are
experimentally determined through an iterative tuning process, and the medium
value is taken as the average of the two. The details on selecting the fuzzy logic output
values are described in Section 3.3.3. During the reaction, when the temperature
measurement is within the reference range, the fuzzy controller outputs medium
flow rate. Once the temperature drifts above the upper temperature limit, the fuzzy
controller switches to output the low flow rate. Conversely, it produces the high flow
rate if the temperature drops below the lower limit. To our best knowledge, this is
the first time that a fuzzy-logic-based control strategy has been successfully adopted
to control catalytic reactions.
Through trial and error, we set the pulse period of the H
2
signal to be 1 s and the
pulse duration to be 100 ms while we selected the high, medium and low flow rate
values to be 17.50, 16.65 and 15.80 ml/min, respectively. Using this set of parameters,
for instance, the catalytic reaction was controlled to produce a peak-to-peak displace-
ment of 120µm (1.2 % strain) at 1 Hz under a constant loading stress of 185 MPa on
the CAM. The corresponding specific work is 597.7 W/kg , about 11 times larger than
that of mammalian skeletal muscles (50 W/kg) (72). As a comparison, the flight mus-
cles of Drosophila can typically generate 1 % strain, producing 0.04 MPa of stress and
39.9 W/kg of specific work (73). Clearly, the proposed artificial muscle can generate
comparable strain with that of insect muscles while enabling significantly higher
level of stress that leads to superior specific work.
The temperature-time diagram (Fig. 3.13A) exhibits a transient period of around
10 s before the temperature settles into the stable operating range. This transient
period is not the induction period because the CAM’s temperature (initially at room
temperature) clearly begins oscillating once the reaction starts, an indication of a
58
controlled catalytic reaction. In addition, this fact verifies that the Pt black coating
was highly active. Figure 3.13A also offers an enlarged view of the stabilized tem-
perature response. The temperature profile closely resembles a sinusoidal curve,
exhibiting similar heating and cooling times within each cycle. However, the duty
cycle of the signal controlling H
2
flow is only 10 %, which logically would produce
an asymmetric temperature profile characterized by swift heating but prolonged
cooling. This phenomenon can be partly explained by two possible reasons. First, H
2
is delivered to the CAM mixed with its carriers (air and N
2
). This might cause H
2
to
diffuse spatially so the concentration of the H
2
portion within the delivered fuel may
no longer maintain its pulse wave form, i.e. the square pulse may be rounded off. Sec-
ond, the pulse response of the CAM system, including the catalytic reaction and heat
transfer process, can be approximately treated as the response of a first-order plus
dead time (FOPDT) system commonly used in chemical process modeling (61, 74).
Figure 3.13B captures the strain behavior of the same experiment. It can be ob-
served that the strain closely follows the heating-cooling cycle once the reaction
temperature has exceeded 50
C. No substantial strain was generated at lower temper-
ature. This finding further validates the transition characteristics we have previously
identified. The enlarged view of the displacement-time diagram clearly shows a
consistent peak-to-peak displacement of around 120µm. Figure 3.13C records the
progression of the strain-temperature behavior during the experiment. Starting
from room temperature, the strain slowly started increasing and began oscillating
during the transition phase, described by the growing hysteresis minor loops moving
upwards in the diagram. Once the temperature has stabilized within the prescribed
operating range, strain-temperature behavior settled into a stably repeating minor
loop.
59
0s 0.2s 0.4s
0.6s 0.8s 1s
Figure 3.14: Flapping sequences and thermal images of CAM during one cycle (1 s)
of actuation. At time zero, the inset displays the enlarged view of a 10-mm CAM.
The two lead wires are the thermocouple wrapped around CAM. The position of
the artificial butterfly wing is indicated by a red arrow in each frame. The blue and
red wing-sweeping areas represent flapping motion associated with the cooling and
heating process, respectively. In the thermal images, the heated CAM over the burner
appears as a glowing yellow strip and its surroundings at room temperature are
shown in purple.
3.4.3 Wing-flapping motion driven by the artificial muscle
Figure 3.14 captures the CAM-driven wing flapping sequence during one complete
cooling-heating cycle. The full recording of the flapping sequence can be found in
Movie S2. The CAM was at its peak operating temperature at time zero. Between 0 and
0.6 s, the CAM cooled down and extended. The linear rail moved rightwards, leading
the transmission to drive the wing (indicated by a red arrow) to flap counterclockwise
(downward). The CAM was then heated between 0.6 and 1 s and its consequent
contraction pulled the linear rail leftwards. Reciprocally, the wing flapped clockwise
before returning to its time zero position. The thermal images of the CAM reaction
were also recorded using a thermal camera (FLIR ONE Pro) at each captured flapping
frame. The CAM is shown as a yellow strip in these figures while the surroundings, at
60
room temperature, are shown in purple. The higher the temperature, the brighter and
thicker the strip appears, and vice versa. Movie S2 also offers a clear view of the CAM’s
thermal profile during actuation. No hot spot is observed, implying a uniformly
coated catalyst layer. The maximum flapping angle is estimated to be about 52
from
the video, smaller than the magnitude predicted by the transmission ratio (62.5
).
This discrepancy is likely caused by fabrication error as well as mechanical losses
of the flapping-wing mechanism. In conclusion, the CAM demonstrates promising
potential for actuating microrobots.
3.5 Discussion
We presented a controlled-catalytic-combustion driven artificial muscle made of
an SMA wire. The wire was coated with catalytic Pt black with micrometrical preci-
sion and powered using a fuel mixture composed of hydrogen, air and nitrogen. To
achieve controlled catalytic reaction, we built an experimental setup that includes a
fast and accurate fuel-delivery system. We first experimentally identified the thermo-
mechanical characteristics of the CAM before adopting a fuzzy-logic-based control
strategy to control the temperature of the CAM during catalytic reactions. As an
example, a robust peak-to-peak displacement of 120µm (1.2 % strain) was realized
at 1 Hz. Additionally, to demonstrate its applications to microrobotic actuation,
we employed the CAM to drive the flapping motion of an artificial butterfly wing
through a micrometer-scale transmission mechanism. We showed that a 120µm
displacement in CAM can generate about 52
rotational movement at the attached
wing through this transmission system. From an energy-utilization perspective, this
work provided a method for directly harnessing energy generated from chemical
reactions to actuate robotic locomotions.
61
The actuation frequency of the CAM is mostly limited by its cooling rate. Though
the cooling period of SMA based actuators can be reduced by adopting a cooling agent
(water or air) and heat sink (75) or by increasing surface area (76), these methods are
yet to be realized at the scale in accordance with microrobots. However, one feasible
solution is to use high temperature SMAs (HTSMAs) (77), whose high operating
temperature can enhance convective and radiative cooling without an additional
apparatus. In addition, a recent study introduced a bending SMA actuator with
an actuation bandwidth of 35 Hz, which is composed of multiple thin SMA wires
(38µm in diameter) arranged in a laminate composite structure (78). This finding
suggests that actuation rates of SMA based actuators can be improved substantially
by adopting thinner wires and improving their mechanical layouts.
The CAM presented in this work is a critical step towards achieving power auton-
omy for microrobots. Our research provided reliable fabrication methods of CAMs,
proper reactant composition, and effective control strategy applicable to catalytic
reactions, all of which could be extended to the micrometer scale by coupling the
periodic actuation of CAM with an on/off fuel delivery method. This mechanism will
enable the creation of a compact and controllable binary oscillating system and at
the same time, eliminate the need for the flow control apparatus. Therefore, we are
currently working on developing portable fuel storage technology (79). In addition,
the nonlinear hysteretic behavior exhibited in the CAM needs to be properly charac-
terized and modeled. A well-established understanding of the thermomechanical
characteristics of CAMs combined with advancement in micro robotic system design
and fabrication will allow for the synthesis of long envisioned fully autonomous
microrobots in the next stage.
62
Chapter 4
RoBeetle
4.1 Introduction
Biological machines still surpass their robotic counterparts in almost every aspect,
including power conversion, actuation, sensing and control. The most advanced
insect-scale microrobots, for instance, are yet to achieve the capabilities observed
in honeybees and beetles. In fact, no sub-gram robot has been reported to au-
tonomously complete tasks that are challenging or useful for humans, and the vision
of creating truly autonomous artificial insects will become a reality only once several
of the long-standing grand challenges in robotics are overcome (80). Namely, new
methods for microfabrication, actuation and control must be developed along with
the introduction of new sources of power, mechanisms, structural micro-components
and actuation materials (80, 81). Here, we understand autonomy as the capability of
a robot to perform sustained and periodic operations without being tethered to exter-
nal power sources or controllers through cables or wireless fields. Form this perspec-
tive, despite impressive recent progress (13, 16, 82), autonomy at the sub-gram scale
has been hindered by the lack actuation methods capable of utilizing high-energy-
63
density sources of power. This issue arises because electricity is the most common
type of power employed to drive microrobots (44, 83, 84, 10, 85, 86, 87, 88, 89) and,
therefore, for which the only path to autonomy is the use of batteries. The limita-
tions of state-of-the-art batteries (e.g., Li-metal) become evident when their specific
energy (1.8 MJ/kg;4.3 MJ/kg) is compared to that of the fat metabolized by insects
(38 MJ/kg).
Most insects have strong muscles for intense activities (90) and stout bodies for
energy storage in the form of fat and glycogen (91); inspired by the metabolism of
these animals, we introduce a new actuation method that enables the creation of
artificial muscles with both high work-density (HWD) and the capability of utilizing
high-energy-density (HED) sources of power (2H). To demonstrate the method, we
developed RoBeetle, an 88-mg crawling robot that is autonomous from the power
and control perspectives. The principal innovation that enabled this breakthrough is
the use of controlled catalytic combustion to thermally excite, according to a periodic
pattern, a wire composite with an NiTi shape-memory alloy (SMA) core and a surface
made of platinum (Pt) that acts as a catalyst. This technique can be implemented
using different fuels, including hydrogen (H
2
), methanol (CH
3
OH), propane (C
3
H
8
)
and butane (C
4
H
10
). In this case, we employ methanol, which has a specific energy
of approximately 21 MJ/kg and can be stored as a liquid at the atmospheric pressure.
A key element that makes the proposed approach possible is feedback control
of the catalytic combustion process, according to a scheme in which the periodic
deformation of the SMA material is employed to indirectly sense temperature by using
an identified model of the wire’s hysteretic dynamics and, also, to synchronously
open and close the micro-valves that modulate the flow of fuel. Thus, the controller
is implemented onboard employing only mechanical components embedded in the
artificial muscle mechanism. This control technique enables the full autonomy of
64
RoBeetle, which is the most distinct characteristic of this system with respect to other
mechanisms powered by HED sources (51, 92, 93). Also, the notion of harnessing
the heat released by catalytic reactions to drive thermally-excitable materials has
been discussed in the past. For example, (39) discusses the use of chemically-driven
twisted nylon fibers as actuators and the work in (49), employing a highly complex
experimental apparatus, demonstrates that the catalytic combustion of H
2
can be
used to excite the strain response of a catalyst-coated SMA wire; however, in both
these cases, the fundamental issue of feedback control for sustained actuation is
entirely overlooked.
The idea of integrating power, actuation, sensing and control into self-contained
mechanical systems is centuries old and this approach was employed in numerous
cases before the advent of the electronics era; the most notable example being the
centrifugal governor (94). In the case of RoBeetle, a main innovation is the design
and fabrication method that enabled the embedding of an entire electronics-free
mechanical control mechanism (MCM) into the microrobot, thus satisfying stringent
size, weight and energy constraints that are not achievable using micro-batteries (95,
96) or other thermomechanical-based techniques such as those in (51) and (97). As
in the cases of other recently-developed microrobots (11, 13, 82), RoBeetle is entirely
fabricated using the SCM method in (3).
4.2 Catalytic NiTi-Pt artificial muscle for microrobot
4.2.1 Mechanism
To create 2H micro-actuators capable of driving insect-scale robots, we combine
the high energy-densities of fuels (Fig. 4.1A) with the high work-densities of SMAs
65
0 100
Specic energy (MJ/kg)
0
10
20
30
40
Energy density (MJ/L)
Fat
Gasoline
H2
Propane
Butane
Methanol
Lithium-ion battery
Lithium metal battery
10
3
10
4
10
5
Power density (kW/m
3
)
10
1
10
2
10
3
10
4
Work density (kJ/m
3
)
SMA
Hydraulic
Pneumatic
Piezoceramic
Muscle
Dielectric elastomer
Carbon nanotube
A B
Figure 4.1: Energy sources and actuation methods for micro-actuation. (A) Energy
densities and specific energies of various power sources (see Table S1 for detailed
data). The red dots indicate potential energy sources to power the proposed NiTi-Pt-
based artificial muscles as these fuels can be used in exothermic reactions catalyzed
by Pt. Fat, the type of energy utilized by animals is represented with a yellow dot.
(B) Work and power densities of different actuation methods (see Table S2 for detailed
data). The red dots indicate the actuators that have been employed in microrobotic
applications; the yellow dot indicates the properties of animal muscle.
(Fig. 4.1B). The main component of the actuation mechanism is the artificial muscle
depicted in Fig. 4.2A, which is composed of an NiTi core and an outer catalytic layer
of agglutinated Pt powder. During operation, the SMA core of the composite wire is
excited by the heat produced by the controlled catalytic combustion of fuel on the
catalytic surface; for example, in Fig. 4.2A, the catalytic combustion of methanol
CH
3
OH(g)+ 3=2O
2
(g)
Pt
! 2H
2
O(g)+ CO
2
is facilitated by the Pt catalyst in order to produce the heat required to excite the SMA
material according to the shape-memory effect (SME) depicted in Fig. 4.2B. Namely,
the catalytic combustion of CH
3
OH raises the temperature of the NiTi material be-
yond the point required to transition from the martensite to the austenite phase
when fuel is delivered to the catalytic surface of the NiTi-Pt composite wire, and
contraction occurs. Analogously, when the flow of fuel is stopped and the chemical
reaction is suspended, the SMA material cools down and the wire extends, thus tran-
66
O 2
H 2 O
CH 3 OH
CO 2
NiTi
Pt catalyst
B A
50 100 150
Temperature (°C)
0
1
2
3
Strain (%)
Tmf Taf Tas
Major loop
Minor loop
Tms
C
D E
Stess (MPa)
Reverse
transformation
Detwinned Martensite
Superelasticity
Detwinned
Martensite
Twinned Martensite
SME
Strain (%) Temperature (ºC)
Forward
transformation
Austenite
Taf
0
Tas
0
Tms
0
Tmf
0
ε L
F
Figure 4.2: Catalytic artificial muscle. A. Diagram of the NiTi-Pt composite wire.
As the wire is exposed to the reactants, CH
3
OH and O
2
, it heats up and contracts
due to the exothermic reaction facilitated by the Pt catalyst; when the fuel supply is
stopped and the reaction suspended, the wire cools down and extends back to its
original length. Periodic actuation is generated by repeating this process. B. Generic
strain–temperature–stress diagram of an NiTi SMA wire. This representation of the
austenite, detwinned martensite and twinned martensite states follows the constitu-
tive model (58, 59). In this drawing,"
L
denotes the residual strain associated with the
SME. C to E. SEM images of the surface of an NiTi-Pt composite wire with an overall
diameter of 87m. The rough and porous catalytic layer (Pt black) has a thickness of
18.1m. The magnifications of the images are 350, 1200, 6500; and scale bars
represent 100m, 30m, 5m, respectively. F. Experimental strain–temperature
hysteretic relationship of the wire under a constant loading stress. Here, we show
a major loop and two eccentric minor loops. The corresponding temperature and
strain signals are shown in Fig. 4.3.
sitioning from the austenite to the martensite phase. Thus, by regulating the flow of
fuel according to a periodic pattern and simultaneously maintaining an appropriate
tension, the composite wire produces a periodic actuation output. An SEM image of
the surface of an NiTi-Pt wire, fabricated using the method described in Section 4.2.2
and Fig. 4.3, is shown in Fig. 4.2, C, D and E. As seen, the catalytic surface at the
microscopic level is inhomogeneous as the fabrication method creates 3D structures
composed of particles randomly adhered together. This surface pattern creates a
catalytically active area which is approximately 2200 times larger than that of the
bare NiTi wire, which is essential to achieve sustainable and controllable catalytic
combustion. In specific, using the information provided by the manufacturer of the
Pt black, we estimate that the resulting catalytic area is27 m
2
/g. Consistent with our
67
own experimental observations, published research indicates that Pt-coating based
on the agglutination of particles produces highly active catalytic surfaces (56, 57).
To characterize the thermomechanical behavior of the NiTi-Pt-based artificial
muscle for the purpose of controller synthesis, we constructed an experimental
setup capable of precisely controlling the flow and delivery of gases to the catalytic
surface, sensing the temperature of the outer layer of the composite wire, precisely
measuring the strain output and regulating the total load applied to the SMA material
(further details are presented in Section 4.2.3). Obtaining an accurate model of the
complex nonlinear strain–temperature–stress dynamical behavior of an artificial
muscle, including the interactions between the superelastic and SME (99), is difficult.
Therefore, employing the methods in (100, 101), we identify the temperature–strain
hysteresis behavior of the artificial muscles under the constant stress of 164 MPa, a
value close to the average stress experienced by the actuator that drives the RoBeetle
prototype during operation. This process of system identification is an essential
component of the robotic design procedure as the transition temperatures of the SMA
material are among the most important parameters that determine the dynamics of
the system; details are provided in robotic design section.
Fig. 4.2F shows the identified major loop and two eccentric minor loops, for a
stress of 164 MPa, associated with the 9.8-mm-long NiTi-Pt wire employed to drive
the RoBeetle prototype. A major loop refers to the heating–cooling cycle during which
the SMA material undergoes a complete phase transition from the martensitic state to
the austenitic state and, then, completely back to the martensitic state. Consistently,
a minor loop refers to the heating–cooling cycle during which the SMA material
undergoes a partial phase transition from a martensitic state to a austenitic tate and,
then, back to the initial martensitic state. From the hysteretic temperature–strain
curve of the major loop, it is clear that the artificial muscle is capable of producing a
68
maximum strain of approximately 3 % when heated up to 154.5
C; then, it recovers
its original length when cooled down to the room temperature (25
C). According
to widely-used constitutive models (58, 59), constant-stress major loops can be
characterized by four critical transition temperatures. Namely, from low to high:
T
Mf
=58
C, T
Ms
=70
C, T
As
=87
C and T
Af
=99
C, as indicated in Fig. 4.2F .
The sequential completion of major loops generates a periodic output strain
with the maximum amplitude achievable by the wire at a given constant stress.
Note, however, that to operate following the trajectory of a major hysteretic cycle
is not necessarily optimal from the speed and energy perspectives. For example,
as shown in Fig. 4.2F , comparatively large output strains can be obtained, with the
same reaction rates as those employed to induce a major loop, by exciting the SMA
material with temperatures inside a relatively narrow range. Accordingly, we can
make the actuation of a RoBeetle prototype efficient by controlling the catalytic
reactions on the surface of the NiTi-Pt wire so that the corresponding temperature
oscillates between T
Mf
and T
Af
, which corresponds to a wisely-chosen minor loop.
Consistently, in this case, a main control objective is to design a tunable MCM that
enables a stable oscillation of the surface temperature and, therefore, of the output
strain produced by the artificial muscle.
4.2.2 Fabrication method
The artificial muscles are fabricated by coating a thin rough layer of Pt, which acts
as a catalyst for the flameless combustion of fuel, on the surface of an SMA wire
with a diameter of 50.8m. In this case, the thermally-excitable SMA material is
90
C Nitinol, a Ni
50%
Ti
50%
compound produced by Dynalloy. The homogeneity and
structural robustness of the resulting catalyst layer are of critical importance to
69
A
B
C
D
E
F
G
H
I J
K
Figure 4.3: Fabrication method of the NiTi-Pt composite artificial muscles. A. A NiTi
wire is threaded into an 8-mm-long 316 stainless steel tubing. B. We use a hand-held
crimper to crimp the wire. C. Install the leaf spring. D. The NiTi wire is threaded into
the second tubing. The length of the wire between two tubings is accurately set as
9.8 mm by using a fixture tool. E. Crimp the second tubing. F. The crimped tubings
are truncated to 2 mm with a flush cutter. Scale bar, 5 mm for (A to F). G. Use a micro
brush to uniformly apply a thin layer of thermally conductive paste on the NiTi wire.
H. SEM image of the NiTi wire with a layer of thermal paste, whose thickness is about
0.6m. Scale bar, 100m. I. Immerse the wire into Pt powder laid out on a right
angle bracket. J. The finished NiTi-Pt composite artificial muscle. Scale bar, 5 mm for
(G, I and J). K. SEM image of the Pt-coated artificial muscle with an overall diameter
of 87m. Thickness of the coating layer is 18.1m. Scale bar, 100m.
achieve reliable, repeatable and controllable catalytic reactions. As depicted in
Fig. 4.3 (A to K), the first step in the fabrication process is to crimp the NiTi wire at two
locations with compressible tubes (McMaster-Carr 89875K85 with an outer diameter
of 0.635 mm and a wall-thickness of 0.152 mm) using a 10-ton hand-held hydraulic
crimping tool. Then, the tubes are cut to have a length of 2 mm using a flush cutter.
The resulting interior length of the crimped NiTi wire is exactly 9.8 mm; a length
precisely ensured by using a fixture tool (Fig. 4.3, D and E).
As shown in Fig. 4.3H, the second step in the fabrication procedure is to ap-
ply a uniform layer of thermally conductive paste (Omega OT-201), which acts as
70
a permanently-wet adhesive, on the surface of the NiTi wire. In order to ensure
micrometric precision, the paste is applied using a micro-brush under an optical mi-
croscope; the resulting layer of conductive paste has an average thickness of 0.6m
and remains uncured at room temperature (see Fig. 4.3H). Finally, the outer layer of Pt
catalyst is added to the piece of SMA material, in order to create the final NiTi-Pt com-
posite wire, by simply immersing it into a heap of Pt powder (Pt black HiSPEC 1000,
Alfa Aesar) as shown in Fig. 4.3I. This process is repeated until the desired shapes and
configurations of the 3D structures that composed the catalyst layer are achieved (see
Fig. 4.3K); during fabrication, the quality of the coating is controlled by continually
monitoring its condition under a microscope. The finished NiTi-Pt composite wire
has an outer diameter of 87m. All them-scale images in the paper were captured
using the same scanning electron microscope (JEOL JSM-7001f-SEM).
The fixture tool employed to enforce the precise length of the wire (Fig. 4.3, D
and E) has dimensions of 9.8 mm2 mm2.36 mm and simply consists of three
pieces, which are made from a 185-m-thick carbon-fiber-polyimide composite
sheet, assembled in a 3D configuration. A diode-pumped solid-state (DPSS) laser
(DCH-355-3, Photonics Industries) with a focused beam diameter of 10m was used
to cut out, from the composite sheet, the pieces composing the small structure; then,
these parts were joint together manually by matching pre-machined tab-and-slot
assembly features.
4.2.3 Characterization experiment
To characterize the thermomechanical behavior and properties of the artificial mus-
cles when driven by flameless catalytic combustion, we utilize hydrogen (H
2
) as fuel.
Due to its low ignition temperature and because the flow rate of pressurized hydrogen
71
can be easily controlled using off-the-shelf valves. The experiments are performed
employing a built-in-house setup, which is composed of a fuel-supplying system
and a measuring apparatus. Hierarchically, the fuel-supplying system is composed
of gas-flow sensors (Honeywell HAFBLF0200C4AX5), solenoid-proportional valves
(KPI-VP-20-09-25-V , Kelly Pneumatics), and the corresponding real-time single-input–
single-output (SISO) flow controllers which are implemented and run on a Simulink
Real-Time system. Fine-gauge bare-wire thermocouples (Type K, Omega CHAL-
002) with their sensing junctions wrapped around the artificial muscles are used to
measure the temperatures of the active catalytic surfaces during operation; thermo-
couples of this type have response times of approximately 0.055 s in air (69). For a
constant pre-set loading stress, the instantaneous strains of the wires are measured
using a laser displacement sensor (Keyence LK-031). The loading stress is applied by
hanging weights and measured using a load cell (Futek LSB200). During the execu-
tion of the experiments, the measurements are acquired and the control signals are
generated at a sample-and-hold rate of 1 kHz, using a PCI-6229 National Instruments
AD/DA board. A photograph of the entire experimental setup is shown in Fig. 4.4A.
For the purposes of system characterization, the mixture of fuel used to initiate,
sustain and control the catalytic reactions on the surfaces of the artificial muscles is
composed of H
2
, air which provides oxygen (O
2
) and nitrogen (N
2
) which is used as a
diluent gas. The rates for the flows of air and N
2
are set to be constant at 200 ml/min
and 750 ml/min, respectively; the flow rate of H
2
is set to be a pulse-train signal with a
constant height of 2 ml/min and a variable width that can be used for control accord-
ing to a pulse-width modulation (PWM) scheme. A typical experiment performed
to find a constant-stress temperature-strain hysteretic loop consists of exciting the
catalytic surface of the NiTi-Pt composite wire with a fuel-mixture signal composed
of three consecutive H
2
pulses with widths of 4.16 s, 5.06 s and 6.06 s, respectively.
72
1
2
3
4
5 6
7
8
9
0 10 20 30 40 50 60
Time (s)
20
50
100
150
Temperature (°C)
0
1
2
3
Strain (%)
A B
Figure 4.4: Characterization of the NiTi-Pt composite artificial muscles. A. Computer-
aided design (CAD) diagram of the built-in-house experimental setup: (1) Solenoid-
proportional valve, (2) Cross union fitting, (3) Gas mixture outlet, (4) Catalytic artifi-
cial muscle, (5) Thermocouple and its connector, (6) Laser displacement sensor, (7)
Load cell, (8) Dead weight and (9) Optical breadboard. B. Temperature profile and
corresponding strain response for characterizing the NiTi-Pt artificial muscle.
This excitation pattern produces three consecutive triangular pulses of temperature
with respective maximum values of 113
C, 125
C and 154.5
C, as shown in Fig. 4.4B.
In this case, as seen in Fig. 4.4B, the first two pulses generate two eccentric minor
loops and the last pulse generates a major loop, or a close approximation of it, with a
maximum strain of approximately 3 %. According to the identified constitutive model
of the SMA wire’s major loop shown in Fig. 4.2F , the most pronounced transition from
the martensite phase to the austenite phase occurs when the wire is heated up from
87
C (T
As
) to 99
C (T
Af
) and the most pronounced transition from the austenite phase
to the martensite phase occurs when the wire is cooled down from 70
C (T
Ms
) to 58
C
(T
Mf
); these four critical transition temperatures are indicated by four vertical lines in
Fig. 4.2F . This experimentally-identified hysteretic dynamical description indicates
that an effective and efficient operational range of actuation is from 70
C to 99
C, as
relatively large strain outputs can be achieved by varying the surface temperature of
the artificial muscle inside this relatively narrow interval.
73
Methanol
Articial muscle
State 1
State 2
Seal groove
A
F
B
D
C
Fuel inlet
Fuel tank
Bias leaf spring
Horn
Anchor block
Hindleg
Foreleg
Articial muscle
G Laser target
M3
H
E
Transmission
M1
M2
Sliding shutter
Lid
Figure 4.5: Robotic design of the proposed 88-mg insect-scale autonomous robot
powered by fuel. A. Photograph of a RoBeetle prototype resting on a leaf. Sale bar,
10 mm. B. Schematic diagram of the RoBeetle’s actuation mechanism. C. Exploded
view of the robotic assembly. D. Exploded view of the fuel tank sub-assembly. E. Ex-
ploded view of the tank lid, transmission and sliding shutter. F. Bottom side of the
sliding shutter. G. NiTi-Pt composite artificial muscle and leaf spring. H. Forelegs
and hindlegs with bio-inspired backward-oriented claws.
4.3 Design and analysis
4.3.1 Robotic design
To demonstrate the capabilities of the proposed 2H NiTi-Pt-based actuators, we
built the autonomous RoBeetle prototype in Fig. 4.5A. This robot crawls employing
a variable-friction-based mode of locomotion; the proposed actuation approach,
however, can be employed to power a wide gamut of microrobotic platforms that
locomote by walking (88), jumping (102), swimming (103) and flying (104). The
combined mechanism for actuation, sensing and feedback control is depicted in
Fig. 4.5B; the integration of all the robot’s components required for autonomous
operation, including the NiTi-Pt composite wire, MCM, fuel tank and structural
elements, is shown in the exploded view of Fig. 4.5 (C to H).
As seen in Fig. 4.5B, during the assembly process, one end of the NiTi-Pt composite
74
wire is anchored to the fuel tank and the other end, corresponding to the actuator
output, is attached to a bias leaf spring required to maintain the SMA material under
tension. Both a transmission and a sliding shutter are connected to this spring in
order for them to be driven by the deformation of the NiTi-Pt wire. The locomotion
pattern consists of a sequence of transitions between State 1 (upper illustration of
Fig. 4.5B) and State 2 (bottom illustration of Fig. 4.5B). We employ methanol as fuel
because it can be stored in liquid form and evaporates at an approximately constant
rate at the atmospheric pressure. Accordingly, during State 1, the orifices of the
sliding shutter remain aligned with those of the fuel tank, thus allowing methanol
vapor to flow out from the container and reach the surface of the NiTi-Pt wire. As the
catalytic surface is exposed to both fuel and oxygen, the SMA material contracts as
illustrated in Fig. 4.2A and the system transitions to State 2 as predicted by the plot
in Fig. 4.2F , period during which the tank valves remain closed. Sequentially, as the
flow of fuel ceases, the SMA material expands, the shutter slides back to State 1 and
the tank valves open in order to initiate a new actuation cycle.
Inspired by the control mechanism of the centrifugal governor (94), during the
transitions from State 1 to State 2 and from State 2 to State 1, the slider shutter mech-
anism functions as a stabilizing controller for the catalytic reaction in a negative
feedback loop. Namely, the supply of fuel decreases as the catalytic reaction accel-
erates because the tank valves steadily close as the shutter slides back to State 2;
conversely, the supply of fuel increases as the catalytic reaction decelerates because
the tank valves steadily open as the shutter slides back to State 1. Note that from the
control perspective, the areas of the tank and shutter orifices, the pre-set tension
on the NiTi-Pt wire, and the stiffness of the leaf spring correspond to the parame-
ters of the feedback controller that determines the performance and stability of the
closed-loop system.
75
While a rigorous mathematical analysis of the closed-loop dynamics of the system
is beyond the scope of this paper, it is important to explain how the mechanical con-
troller parameters must be selected to ensure functionality and stability. In this case,
instability is equivalent to thermal runaway (105), a phenomenon characterized by a
rapid increase of the surface temperature until the NiTi-Pt wire melts. The literature
and experimental observations indicate that the rate of temperature variation de-
pends monotonically on the flow rate of fuel, which in this case depends on the area
of the tank and shutter orifices. Specifically, if the fuel flow surpasses a critical point
due to an excessive interface area between the tank and the catalytic surface, the
closed-loop system becomes unstable. Furthermore, note that the pre-set tension of
the wire and stiffness of the leaf spring also indirectly influence the flow rate of fuel
and, therefore, the stability of the closed-loop dynamics. On the other hand, if the in-
terface area between the tank and the catalytic surface is not sufficiently large for the
flow of fuel to initiate and sustain catalytic combustion, the correct functionality of
the actuation mechanism becomes infeasible. In this case, through an experimental
tuning process, we enabled the actuation mechanism to self-oscillates stably and
robustly while driving the locomotion of the RoBeetle prototype.
As seen in Fig. 4.5, B and C, the actuation output is transformed into a rotational
motion employing a four-bar transmission inspired by the flight muscles of Dipteran
insects (106, 44, 107) and that can be modeled as a static mapping (108, 107). As
illustrated in Fig. 4.5, B, C and E, the rotational motion produced by the transmis-
sion is transformed into locomotion through two joint active forelegs and two fixed
hindlegs, which employ anisotropic friction to sequentially slide forward and anchor
to the ground. Specifically, during the transition from State 1 to State 2, the pair of
hindlegs anchor the robot to the ground while the pair of forelegs rotate clockwise
and slide forward; analogously, during the transition from State 2 to State 1, the pair
76
of forelegs rotate counterclockwise while anchored to the ground and the pair of
hindlegs slide forward.
Now, we describe the components of the robot and the assembly process in
Fig. 4.5 (C to H); the details regarding fabrication are presented in Section 4.3.2. Based
on their functionality, the components are grouped into four categories.
i. The first category includes the parts that compose the torso of the robot, which is
also the fuel tank that stores the methanol (Fig. 4.5, C and D). The bottom and sides
of the tank are built from seven pieces made of carbon-fiber-polyimide composites
that are assembled together employing tab-and-slot features. Cyanoacrylate (CA)
glue is applied on all the clearances to seal the tank and make it liquid-tight.
ii. The second category is formed by the components of the MCM: the tank lid and
sliding shutter (Fig. 4.5E). These parts are assembled together with the transmission
during a step prior to the final assembly. As shown in the detailed view of Fig. 4.5E,
the mating fixture M1 on the lid is attached to the grounded link of the transmission
using CA glue; then, the shutter is glued to the slider input link of the transmission at
the mating fixture M2. To create the interface between the container and the NiTi-Pt
wire, a row of six 0.1 mm1.5 mm rectangular orifices are perforated on the tank lid
at regular intervals of 1 mm; correspondingly, six 0.1 mm0.5 mm rectangular are
perforated on the shutter according to the same pattern. These interacting matching
perforations function as synchronized micro-valves, which are employed to control
the flow of fuel that feeds the catalytic reaction on the surface of the NiTi-Pt wire.
Since the flow rates depend monotonically on the overlapped areas of the valve
mechanism, the shape and configuration of the matching perforations determine
the heating and cooling profiles of the SMA material. During the design process, by
performing a series of tethered tests, employing robotic prototypes with a variety of
sliding valve configurations, we identified the parameters for an MCM that enables
77
the NiTi-Pt-based artificial muscle that drives the RoBeetle prototype to operate
within desired temperature ranges. We performed an evaporation experiment to
measure the fuel flow rates for the robotic design (Section 4.3.3, Movie S3). And
the experimental result was used to calibrate a theoretical model that describes the
diffusion process of the methanol vapor (Section 4.3.4). In order to prevent leakage,
seal grease is applied to the groove carved on the bottom of the sliding shutter, as
shown in Fig. 4.5F . Lastly, the complete MCM is used to cap the tank, thus forming
the torso of the microrobot as shown in Fig. 4.5C.
iii. The third category is composed of the parts that constitute the actuation mecha-
nism, including the NiTi-Pt wire, the transmission (Fig. 4.5E), the leaf spring (Fig. 4.5, C
and G), two horn-shaped static arms that are employed to mount the leaf spring
and the anchor fixture that holds the composite wire (Fig. 4.5C). The three mounting
pieces are connected to the tank lid using socket-lock mechanisms and permanently
fixed using CA glue. The leaf spring is a stiff bar made from carbon fiber with an
orifice through which the NiTi-Pt wire is threaded (Fig. 4.5G). Then, both ends of
the wire are crimp-clamped in order to install it on the robot and set its tension. In
specific, the monolithic piece composed by the spring and the crimp-clamped wire
is attached to the robot’s torso by first inserting the rightmost end of the wire into
the slot of the anchor-block, as indicated by the red dashed line; then, the bottom
locking protrusion M3 (see Fig. 4.5G) and both sides of the spring are inserted into
the mating orifice carved on the shutter and the slots of the horns, respectively. This
configuration enables the artificial muscle to simultaneously drive the sliding shutter
and the transmission through the leaf spring. In agreement with the description in
Fig. 4.2, B and F , the SMA wire must be pre-loaded in order to function effectively
as an actuator; for this reason, the initial condition of the system is set with the leaf
spring bended and the wire in tension. This initial state is enforced by simply using
78
an NiTi-Pt wire with an unexcited length that is smaller than the distance between the
slots of the horns and the anchor block; namely, 9.8 mm at 25
C instead of 9.88 mm.
For the robot used in the locomotion experiments, the measured spring stiffness is
4.26 N/mm (See Section 4.3.5) with a corresponding loading stress of168 MPa.
Note that the proposed robotic design allows us to arbitrarily set the loading stress
acting on the NiTi-Pt wire by adjusting the location of the crimp-clamps. Similarly,
the entire artificial muscle can be easily replaced if different geometrical or catalytic
characteristics for effective operation are required.
iv. The last category is composed of the bioinspired microrobotic legs with claws that
are capable of inducing anisotropic friction, thus emulating the friction mechanism
employed by beetles of the subspecies Pachnoda marginata peregrina (109). As seen
in Fig. 4.5, C and H, the two forelegs are installed at the distal end of the transmission
and the two hindlegs at the bottom of the tank, employing tab-and-slot features.
The overall design and limb configuration enable RoBeetle prototypes to locomote
unidirectionally using the simple proposed two-anchor crawl gait, which is similar
to the scheme observed in some types of inchworms; for example, the patterns of
caterpillars of the species Manduca sexta (110), which conceptually also resemble
the locomotion method employed by the soft robot in (111). All the fundamental
parameters of the RoBeetle prototype employed in the experiments are summarized
in Table S3.
4.3.2 Fabrication of the robotic prototypes
With the exception of the artificial muscles, all the mechanisms and structural compo-
nents of the RoBeetle prototypes are designed and fabricated using the SCM method,
especially some of the techniques described in (112). In specific, the fuel tank, lid,
79
legs, sliding shutter and horns are made from 185-m-thick composite laminates
composed of two 80-m-thick carbon fiber layers (top and bottom) and one central
7.5-m-thick polyimide film layer (Kapton HN 30 gauge, DuPont); the transmission
and anchor block are made from 380-m-thick composite laminates, which are
fabricated by bonding two layers of 185-m-thick composite laminates together
using a 12.5-m-thick adhesive film (Pyralux FR1500, DuPont); and the leaf spring is
made from a 190-m-thick carbon fiber laminate. In this case, following the SCM
method, all the 3D micro-parts are created by assembling and folding featured 2D
components that are cut from the composite sheets using the DPSS laser. During
3D assembly, the 2D parts are connected to each other by matching tab-and-slot
features; then, the connections and corners are rigidized and strengthen using CA
glue (Loctite 416, Henkel). To gas-tight-seal the interface between the tank lid and
sliding shutter, a thin layer of grease (Parker O-ring lubricant) into the 80-m-deep
seal groove described in Fig. 4.5F .
4.3.3 Evaporation of methanol experiment
In order to measure the evaporation rate of the methanol inside the fuel tank, a
bare NiTi wire is installed on the robot to maintain the sliding shutter permanently
open. During these tests, the robot is fixed horizontally on a 3D-printed pillar using
a piece of double-sided tape, as shown in Fig. 4.6. Then, using a 0.3-cc syringe,
120l of methanol are injected into the fuel tank. It takes approximately 155 min
for this amount of methanol to evaporate into the atmosphere at room temperature
(25
C) and the relative humidity of 48 %. Consistently, the mean evaporation rate
is 0.013l/s, which is used to calibrate the evaporation model in Section 4.3.4. A
time-lapse video of a representative experiment, composed of frames taken at 30-s
80
Methanol
0
h
Air
0min 155min A
B
0 50 100 150
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Evaporation rate (μl/s)
0
20
40
60
80
100
120
140
160
Fuel volume (μl)
Time (min)
C
Figure 4.6: Evaporation rate of methanol inside the fuel tank. A. Image sequence of
evaporation experiment. Scale bar, 10 mm. B. Schematic of the diffusion of methanol
vapor inside the fuel tank. The distance between tank outlet and methanol surface is
denoted by h. C. The evaporation rate and volume of methanol versus time, which
were obtained using an experimentally-calibrated model derived from Stefan’s law.
The mean evaporation rate of this model equals that of the available experimental
data. See Section 4.3.3 and 4.3.4 for further details.
intervals, is shown in Movie S3.
4.3.4 Diffusion of methanol vapor model
To analyze the performance of RoBeetle from the energy perspective, it is important
to obtain a model for calculating the amount of methanol vapor flowing out from the
tank, through the sliding shutter, per unit time. A diffusion model for this specific
container with multiple small openings is not currently available, hence this problem
must be addressed. Here we derive a model in two steps. The first step is to calculate
the molar evaporation rate
˙
N
tank
without considering the effect of the shutter, i.e.
the tank is assumed to be fully open to the atmosphere. With this assumption, it is
straightforward to employ a general diffusion description, the Stefan flow model (63),
to obtain the evaporation rate
˙
N
tank
using following formulas,
˙
N
tank
A
tank
=
C D
h
ln
1 y
m,h
1 y
m,0
, (4.1)
h = h
tank
1
A
tank
V
m0
M
m
˙
N
tank
t
m
, (4.2)
81
where A
tank
is the bottom area of the fuel tank; D is the diffusion coefficient of
methanol in air (1.610
-5
m
2
/s); h is the height from the methanol-air interface
to the top opening of the tank, as shown in Fig. 4.6B; y
m,0
and y
m,h
denote the mole
fractions of methanol vapor at these two positions, respectively; h
tank
is the height
of the tank; V
m0
is the initial volume of methanol (120l); M
m
is the molar mass
of methanol (32.04 kg/kmol); t is time; and
m
is the density of liquid methanol
(792 kg/m
3
). The ideal gas relationship can be used to obtain the total molar density
as
C =
P
R
u
T
r
, (4.3)
where P is the atmosphere pressure (101.325 kPa); R
u
is the universal gas constant
(8.314 kJ/kmolK); and T
r
denotes operating temperature (298 K). In addition, the
mole fraction at the top opening, y
m,h
, is assumed to be zero, while y
m,0
at the interface
can be calculated according to
y
m,0
=
P
m,0
P
, (4.4)
where P
m,0
is the vapor pressure of methanol at 25
C (16.96 kPa).
The second step is to introduce a coefficient
ss
to calculate a corrected molar
evaporation rate
˙
N
c
, under the assumption that the effect of the sliding shutter on
the evaporation rate can be approximated with a linear model as
˙
N
c
=
ss
˙
N
tank
. (4.5)
The coefficient
ss
needs to be calibrated to satisfy the condition that the average
evaporation rate of model must equal that of the experiment measurement, i.e,
M
m
¯
˙
N
c
m
=
¯
˙
V
exp
. (4.6)
82
B
0.0 0.1 0.2 0.3
Displacement (mm)
0.00
0.25
0.50
0.75
1.00
Force (N)
F
A
Laser sensor
Weight
Load cell
Figure 4.7: Experimental estimation of the leaf-spring stiffness coefficient. A. Illus-
tration of the experimental setup (not to scale). B. Force-versus-displacement plot
for the leaf spring. The static behavior of the leaf spring can be approximated by a
linear spring model with a constant of 4.26 N/mm.
As the
¯
˙
V
exp
is measured to be 0.013l/s, the corresponding
ss
coefficient is deter-
minated to be 0.11, a value that can be explained by the fact that the sliding shutter
openings allow only approximately 11 % of the vaporized methanol to flow through
during the evaporation process.
4.3.5 Determination of the leaf-spring stiffness coefficient
The stiffness of the leaf spring is experimentally determined by measuring the result-
ing deflections at its center under different loading stresses. During these tests, the
robot is firmly fixed to an optical table in the orthogonal position depicted in Fig. 4.7A.
In this case, to measure the spring deformation, the Keyence laser displacement
sensor is placed above the robot and the Futek load cell (9.9 g) is connected to the
lower end of the NiTi-Pt composite wire to measure the applied stress. To obtain
a sufficient number of data points, various calibration weights (8-piece 1000-gram
calibration weight set, Neewer) with different values, including 20 g, 50 g, 70 g and
100 g, are hung from the load cell and, then, the corresponding deflections of the
83
spring are recorded. For each weight, the measuring process is repeated five times;
consistently, in Fig. 4.7B, each solid blue dot indicates the average of five measure-
ments while each bar indicates the associated measurement range. As shown in the
plot, employing the least-squares method, we found a linear fitting of the empirical
data from which we extract the spring constant; namely, 4.26 N/mm.
The spring is made from a carbon fiber composite laminate with a thickness of
190m that is fabricated by curing a stack of eight layers of unidirectional prepreg
with the 0-90-0-90-0-90-0-90 configuration. As illustrated in Fig. 4.7B, the spring can
be modeled as a simply-supported bending beam loaded with a central force. Thus,
we can compute the equivalent stiffness of the spring employing basic Euler-Bernoulli
beam theory; namely,
K
e
=
F
=
48E I
l
3
, (4.7)
in which is the beam deflection at the midpoint; F is the magnitude of the force
acting of the spring; E denotes the Young’ s modulus of cured laminates composed of
carbon fiber and epoxy (80 GPa); and I = w h
3
=12 is the moment of inertia defined
in terms of the width w and high h of the piece. In this case, the dimensions of the
spring are l w h = 8.48 mm 1.2 mm 0.19 mm, which from (4.7) corresponds to
a stiffness of 4.32 N/mm; a very close match with that estimated experimentally.
4.4 Tethered stationary experiments
4.4.1 Experimental results
To obtain adequate parameters for the design of the MCM, we conducted a series of
tethered experiments using several RoBeetle prototypes. Specifically, we measured
the most relevant variables associated with the operation of the microrobot, including
84
the surface temperature of the NiTi-Pt wire and the resulting self-oscillatory actuation
strain, as shown in Fig. 4.8 and Movie S4. Due to limitations in miniaturization,
installation and signal transmission, the use of on-board wireless sensors to measure
physical variables in a moving insect-sized robot is still infeasible, which justifies the
stationary experimental approach in Fig. 4.8A. During these tests, one hindleg of the
robot is held in place using a pair of cross-lock tweezers while the other three legs
are left to freely dangle in the air; the deformation of the NiTi-Pt wire is measured
with a laser displacement sensor (Keyence LK-031) that is installed in front of the
robot so that the emitted laser beam hits the target area of the leaf spring shown in
Fig. 4.5G. To measure the temperature of the catalytic reaction, a Pt-black-coated
thermocouple (type K, Omega CHAL-002) is installed next to the NiTi-Pt wire. Note
that this thermocouple measures the temperature close to a single point of the
catalytic surface and that thermocouples exhibit dynamics that delay and filter the
high-frequency content of the true signals. Therefore, the signal obtained as in
Fig. 4.8A is a reasonable estimation but not the true temperature of the SMA material.
Further details regarding the experimental setup are presented in Section 4.4.2.
Measured temperature and strain signals corresponding to a representative sta-
tionary experiment, obtained using the prototype in Fig. 4.5A, are shown in Fig. 4.8B.
In this plot, it is clear that the temperature of the catalytic reaction is mechanically
controlled to continually oscillate within the desired range; accordingly, the artifi-
cial muscle produces effective periodical strain outputs. These results, therefore,
demonstrate that the robot is able to operate autonomously when controlled by the
proposed MCM. In this case, the measured temperature is composed of a main oscil-
latory signal and a set of components with higher frequencies resembling random
patterns. Despite the disturbances affecting the system, the principal oscillatory
component remains bounded within the range[37 : 100]
C and is sufficiently regular
85
0 20 40 60 80 100 120 140 160 180 200
50
100
Temperature (°C)
0
0.05
0.1
Displacement (mm)
Time (s)
Thermocouple
Laser sensor
4 6 8 10 12 14
50
100
Temperature (°C)
0
0.05
0.1
Displacement (mm)
Time (s)
Closed
Open
Closed Open
0s 1.9s
A B
D C
Figure 4.8: Tethered stationary experiments employed to characterize the RoBeetle
prototype. A. Schematic diagram of the experimental setup (not to scale). B and
C. Temperature and displacement responses generated by the NiTi-Pt composite
artificial muscle during operation and associated zoomed-in view. The top and
bottom dashed lines indicate the closed and open positions of the sliding shutter
mechanism, respectively. D. State 2 (closed values) and State 1 (open values) of the
actuation cycle (1.9 s, from State 2 to State 1). The insets show the closed and open
states of the sliding shutter mechanism. Scale bar, 10 mm.
to enable locomotion. These disturbances appear because the diffusion process of
methanol vapor from the orifices of the sliding shutter to the surface of the NiTi-Pt
wire and the catalytic reaction can be easily affected by gusts of air. These issues can
be solved by adding a protecting fixture to the design in order to make the artificial
muscle windproof. As seen in Fig. 4.8C, the general trend of the strain output is to
follow the changes in the measured temperature signal; this behavior is consistent
with the hysteretic model in Fig. 4.2, B and F .
We hypothesize that some of the observed discrepancies between the two signals
in Fig. 4.8C reflect inaccuracies of the method employed to measure temperature.
This issue is explained because, as illustrated in Fig. 4.8A, a small (0.0508 mm in
diameter) thermocouple’s bead is placed right next to the surface of the NiTi-Pt wire,
and not wrapped around its cross-section, in order to avoid mechanical interferences
with the actuation cycle. In addition to obtaining measurements as shown in Fig. 4.8A,
86
to heuristically evaluate the entire functionality of the system, we also took an infrared
thermal video of a representative tethered experiment (Movie S5). Based on the
thermodynamic model of the artificial muscle in supplementary Section 4.4.3 and
using data obtained through a tethered experiments (Fig. 4.8), we estimate that the
actual overall thermal efficiency of the RoBeetle prototype during operation has an
average value of approximately 0.16. This value comprises both fuel utilization and
the heat-transfer efficiency associated with the artificial muscle. In this case, the
heat-transfer efficiency can be improved by reducing the thickness of the layer of
Pt; the fuel-utilization efficiency can be improved by installing multiple artificial
muscles over the sliding shutter in order to capture more fuel vapor for combustion.
4.4.2 Experimental method
During the performance of these experiments, temperature and strain are measured
using the same thermocouple and laser sensor used in the characterization tests
(Section 4.2.3). As shown in Fig. 4.8D, the RoBeetle prototype is held immobile by its
left hindleg using a pair of cross-lock tweezers (HOL-165.00, Eurotool) mounted on a
third-hand station. The fuel is injected into the tank using an ultra-fine syringe (0.3 cc
& 31 gauge, Becton Dickinson) to pierce the polyimide membrane of the container
at the fuel inlet, as shown in Fig. 4.8D. In this case, we employ as fuel 20l of pure
methanol (Sigma Aldrich 179337-1L, ACS reagent,99.8 %). As the catalytic reaction
on the surface of the artificial muscle is triggered and sustained, the robot starts to
move its front legs while the actuator displacement output is measured with the laser
sensor placed at a distance of approximately 30 mm from the leaf spring, as seen in
Fig. 4.8A. The position and orientation of the robot is adjusted to ensure that the laser
beam hits the 0.5 mm0.5 mm target area in the middle of the leaf spring (Fig. 4.5G).
87
The thermocouple is also held using a third-hand station; in this way, the sensing
junction, which is coated with Pt black using the same method employed to fabricate
the NiTi-Pt composite wire, can be precisely positioned right next to the catalytic
surface during combustion in order to measure its temperature. A thermal video of
a typical tethered experiment is shown in Movie S5, which was recorded using an
entry-level infrared camera (FLIR ONE Pro, FLIR Systems).
4.4.3 Thermodynamic model of the artificial muscles
The overall heterogeneous catalytic combustion process of methanol is described by
CH
3
OH(g)+
3
2
O
2
(g)
Pt
! 2H
2
O(g)+ CO
2
(g),
where the enthalpy change of the reaction,H , is -676.49 kJ/mol (55), which implies
that one mole of methanol can theoretically release 676.49 kJ of thermal energy.
Therefore, the heat transfer process of NiTi-Pt artificial muscle during actuation is
governed by,
h
c
A
s
(T
r
T)+H
¯
˙
N
c
= m
s
c
p
˙
T (4.8)
in which the first term is the rate of heat transfered into the SMA wire due to con-
vection; h
c
is the heat transfer coefficient (200 W/m
2
K); A
s
is the cross-sectional
area of the SMA wire; T
r
and T are the room temperature and temperature of the
SMA, respectively. The second term represents the rate of the heat generated by the
catalytic reaction; is the coefficient of the overall thermal efficiency; and the mean
molar flow rate
¯
˙
N
c
is 0.0089l/s for 20l of methanol fuel, according to the evapora-
tion model presented in Fig. 4.6C. The right-hand-side term of the equation denotes
the thermal energy change in the SMA wire. Based on the results from the tethered
88
stationary experiment, this thermodynamic model yields a thermal efficiency with
an average value of 0.16.
4.5 Autonomous locomotion experiments
4.5.1 Experimental results
To validate the proposed actuation approach and study the untethered locomotion
performance of the RoBeetle prototype, we performed two types of experiments:
autonomous crawling inside a stationary atmosphere and autonomous crawling
inside a gently-moving atmosphere. These two experiments are aimed to highlight
the worst-case and best-case conditions of operation. An instance of the first type of
locomotion test is shown in Fig. 4.9A; an instance of the second type of locomotion
test is shown in Fig. 4.9B. The complete set of experiments is shown in supporting
Movie S6. From this movie, relevant locomotion data is extracted and processed using
object tracking software (see Section 4.5.5). The robot’s positions as functions of time,
corresponding to both tests in Fig. 4.9, A and B, are shown in Fig. 4.9C. The resulting
experimental gait resembles the two-anchor crawl locomotion mode employed by
inchworms (113); since during operation, the distance from the claws of the hindlegs
to the claws of the forelegs cyclically increases, as the artificial muscle contracts, and
decreases, as the artificial muscle extends (see Fig. 4.9D).
A distinguishing characteristic of the locomotion mechanism employed by RoBee-
tle, with respect to that employed by inchworms, is the utilization of anisotropic
friction. Specifically, as shown in Fig. 4.5H, the backward-oriented claws of the four
legs generate frictions with different magnitudes depending on the direction of the
89
0 50 100 150 200
Time (s)
0
20
40
60
80
Position (mm)
Crawling experiment (Fig. 5A)
Crawling experiment (Fig. 5B)
Crawling simulation (Fig. 5A)
Crawling simulation (Fig. 5B)
0s
20s
40s
60s
80s
A
0s
20s
40s
60s
80s
B
D
State 1
State 2
C
10
4
10
3
10
2
10
1
10
0
10
1
10
2
10
3
10
4
10
5
Weight (g)
10
4
10
2
10
0
10
2
Velocity (BL/s)
1
2
3
4
7
9
10
11
12
13
14 15
16
17
5
18,19
20
21
22
23
24
25,26
27
28
29
30
31
32,40
33
34
35
36
37
38
39
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59 60
61
62
63
64,69
65
66
67
68
70
71
72
6
8
Small legged robot (<100mm)
Small wheeled robot (<100mm)
Legged robot (≥100mm)
Soft robot
Insect
,
,
,
,
E
Figure 4.9: Autonomous locomotion under two atmosphere conditions. A. Pho-
tographic sequence of autonomous crawling on a flat surface inside a stationary
undisturbed atmosphere. B. Photographic sequence of autonomous crawling in-
side a gently moving atmosphere. C. Positions of the robot during the locomotion
experiments in (A) and (B); both experimental signals are compared to simulation
results obtained with the dynamic model in Section 4.5.3. D. Two states in a loco-
motion cycle. At State 1, the hindlegs of RoBeetle anchor and the forelegs start to
slide forward as the artificial muscle contracts due to the opening of the sliding shut-
ter. At State 2, the forelegs anchor to the ground using claws and the hindlegs slide
forward as the artificial muscle extends. Scale bar, 10 mm. E. Locomotion velocities
of various robots and insects in body-length (BL) per second versus body-weight in
grams. Solid symbols indicate the robots that are fully autonomous, while robots
relying on external power sources are represented with hollow symbols. See Table S4
for detailed data. The robots are numbered based on their order in the table. The
location of RoBeetle is marked with a black circle.
sliding motion. Here, we model this phenomenon quasi-statically, according to
f
+
f
=
+
f
N
l
f
N
l
= f
f
f
+
h
=
+
h
N
l
h
N
l
= f
h
+
f
=
+
h
f
=
h
, (4.9)
90
where N
l
is the normal force exerted on each leg; f
+
f
is the friction that opposes the
forward sliding motion of each of the two forelegs when the system is transitioning
from State 1 to State 2 (Fig. 4.9D); f
f
is the friction that opposes the backward sliding
motion of each of the two forelegs when the system is transitioning from State 2 to
State 1; correspondingly,
+
f
and
f
are friction coefficients satisfying
+
f
f
; f
+
h
is
the friction that opposes the forward sliding motion of each of the two hindlegs when
the system is transitioning from State 2 to State 1; f
h
is the friction that opposes the
backward sliding motion of each of the two hindlegs when the system is transitioning
from State 1 to State 2; and, correspondingly,
+
h
and
h
are friction coefficients
satisfying
+
h
h
.
In agreement with experimental observations and the model specified by (1), the
robot’s body remains immobile during the transition from State 1 to State 2 because
+
f
h
. On the other hand, the body moves forward during the transition from
State 2 to State 1 because
+
h
f
. Since obtaining kinetic models of friction and the
associated coefficients for the tiny legs of the prototype is a nontrivial experimental
task, we estimated values for
+
f
,
+
h
,
f
and
h
through the static experiments de-
scribed in Section 4.5.2. These measurements validate the anisotropic characteristic
of the friction forces induced by the interaction of the robot’s legs with the ground,
as intended by design. Furthermore, these obtained friction coefficients enable us to
validate the dynamical model for locomotion presented in Section 4.5.3.
The experiments in Fig. 4.9, A and B, were recorded while the RoBeetle prototype
crawled on a perfectly horizontal flat plane covered with a smooth paper tissue.
This surface is homogenous and moderately rough (R
a
=7.528m), which makes it
suitable for studying the robot’s crawling under two different conditions of operation.
In the first test, the robot crawls autonomously inside a static atmosphere so that the
surface of the NiTi-Pt wire passively cools down during the actuation cycle, mostly due
91
to heat conduction; the performance achieved under this condition is the expected
worst case. In the second test, the robot crawls autonomously inside a gently moving
atmosphere so that the surface of the NiTi-Pt wire passively cools down during the
actuation cycle, due to both conduction and convection; the performance achieved
under this condition is expected to be significantly better than that achieved in the
first case, due to the enhancing effect of convection. In this case, we accelerate the
airflow field surrounding the robot by simply waving a paper card with dimensions
7.62 cm12.7 cm at a distance of10 cm over the prototype.
As seen in Fig. 4.9C, in the test in Fig. 4.9A, the robot crawls in small steps with a
corresponding mean stride of1.2 mm. The irregularities observed in the crawling
pattern are caused by disturbances affecting the diffusion process of methanol va-
por, which is consistent with the results obtained through the tethered stationary
experiments in Fig. 4.8. In contrast, in the test in Fig. 4.9B, the robot exhibits a regular
crawling pattern with a corresponding mean stride of approximately 2.83 mm. This
increased operational regularity is produced by a shorter cooling time during each
actuation cycle due to convection. Interestingly, the actuation periods observed
during both experiments are very similar; namely, 3.3 s and 3.7 s, respectively. There-
fore, the better performance achieved by the robot is the result of a larger actuation
amplitude and not a faster frequency. Directly from the data in Fig. 4.9C, we estimate
that the robot’s average locomotion velocity during the experiment in Fig. 4.9A is
0.37 mm/s and that the robot’s average locomotion velocity during the experiment
in Fig. 4.9B is0.76 mm/s. We hypothesize that the mechanism that improves the
performance of the system in the second test is the removal of both residual fuel
vapor and heat from the surface of the catalytic surface by the airflow interacting
with the robot. This process induces not only a faster cooling rate but also a faster
heating rate as the forelegs fully return to their initial state, which corresponds to
92
the entirely-open position of the sliding shutter and, therefore, to the condition of
maximum fuel supply.
Simulation results obtained using the dynamical description of the friction-based
crawling mechanism presented in Section 4.5.3 are also plotted in Fig. 4.9C. Specifi-
cally, we model locomotion as a mapping for which the input is the displacement
output generated by the artificial muscle and the output is the position of the robot
along a straight line (see Fig. 4.9, A and B). Consistently, considering the hysteretic
dynamics of SMA actuators (see Fig. 4.9B), the input to the crawling mechanism
is modeled as a sequence of bell-shaped signals with identical maximum plateaus
and periods (see Section 4.5.3); the signal parameters were identified from the data
obtained through the tethered and untethered experiments already described above.
From the comparisons in Fig. 4.9C, it is clear that the model captures the main fea-
tures of the crawling process; namely, the mean locomotion speeds match almost
perfectly and the distinct staircase increments in position produced by the two-
anchor crawling are approximately replicated. The observed slight discrepancies
between the simulated and experimental signals are explained by inhomogeneities
in the locomotion path and disturbances affecting the diffusion of fuel vapor from
the valves to the catalytic surface of the wire. Note that because of the regularity of
actuation created by the enhancing effect of convection, for the test in Fig. 4.9B, the
simulated model generates a position signal that matches even some of the small-
est features of the measurement. For example, the simulation replicates the slight
backward motion of the robot produced by micrometric sliding displacements of the
hindlegs during the transition from State 1 to State 2; a phenomenon that, as seen in
Movie S6 and Fig. 4.9C, is most evident during crawling between 50 s and 80 s.
The performance of RoBeetle, compared to those of various insects and the
set of most advanced terrestrial locomoting robots, is shown in Fig. 4.9E. Here, the
93
horizontal axis indicates weight in a log
10
-scale and the vertical axis indicates the
normalized velocities of the compared systems. The velocities are normalized to
be expressed in the same units; namely, body-length (BL) per second, i.e., BL/S. We
consider five main classes of systems: insects (in yellow); soft robots (in blue); normal-
sized legged robots (in purple), characterized by lengths equal or larger than 100 mm;
small wheeled robots (in green), characterized by lengths smaller than 100 mm; and
small legged robots (in red), characterized by lengths smaller than 100 mm. In this
classification, autonomous robots are indicated with solid symbols and tethered
robots using hollow symbols; the performance of the RoBeetle prototype is indicated
with a solid red dot encircled in black. Note that RoBeetle is not only the first sub-
gram insect-sized autonomous robot created to date but also the fastest autonomous
crawling robot relative to its size.
4.5.2 Experimental estimation of the friction coefficients
To measure the friction acting under each individual leg of an insect (114), or a
robotic insect, in real time when crawling is extremely challenging. Here, we apply
the method mentioned in (9) to measure the overall static friction coefficients of the
robot taking the frictions acting under both forelegs and hindlegs into account. Then,
the experimental results are used to estimate the specific friction coefficients of the
forelegs and hindlegs to model the dynamics of the two-anchor crawling mode as
discussed in Section 4.5.3.
As shown in Fig. 4.10, the robot is placed on a flat plate which is then slowly
rotated until the robot starts to slide. The corresponding critical inclined angle
is
measured using a protractor. Based on static analyses, the balance between friction
and the projected component of gravity yields the relationship for estimating the
94
1 2
State
0
0.1
0.2
0.3
0.4
0.5
Friction coecient
Forward
Backward
A
1 2
State
0
1
2
3
4
5
Friction coecient
HDFC
FDFC
B
Forward Backward
State 2 State 1
HDFC FDFC
State 2 State 1
Figure 4.10: Static friction coefficients for the legs of the RoBeetle prototype. A. Top
bar chart: static friction coefficients for the robot on an aluminum plate with precisely
polished surface at State 1 and State 2. Bottom chart: we measure the static friction
coefficients for all legs for forward (first row) and backward (second row) locomotion
direction by slowly rotating the plate counterclockwise and clockwise respectively
until the robot starts to slip. B. Top bar chart: hindleg- and foreleg-dominated static
friction coefficients. Bottom chart: in the first column (State 1), we cover the section
of the aluminum surface under hindlegs of the robot with paper tissue (first row),
in this way the static friction coefficient
hd
, mainly attributed to hindlegs, can be
measured by rotating the plate clockwise. The coefficient
+
fd
, mainly attributed to
forelegs, is measured with the same manner (second row); in the second column
(State 2), it shows the methods for measuring HDFC
+
hd
(first row) and FDFC for
fd
(second row). Note that the arrows indicate the directions of frictions acting on the
robot, opposing to the directions of locomoting movements.
static friction coefficient as
= tan(
). (4.10)
95
This measuring process is repeated ten times in order to reduce statistical errors. The
first set of experiments is performed on a smooth surface (Mirror-like 6061 aluminum
sheet, McMaster-Carr 1655T8, R
a
=0.021m); the experimentally-estimated static
overall friction coefficients
+
and
for States 1 and 2 of the locomotion stride
are plotted in Fig. 4.10A. Consistently, the resulting
+
and
have very low values
which is expected for this smooth surface (0.24 and 0.31 for State 1 and State 2,
respectively). Also, as expected, the differences between them for each state are
negligible (<1 %).
In the second set of experiments, we artificially create larger frictions acting
under specific legs by covering half of the aluminum plate with paper tissue. In this
way, we are able to measure the hindleg-dominated friction coefficient (HDFC,
hd
)
or the foreleg-dominated friction coefficient (FDFC,
fd
) by placing the hindlegs or
the forelegs on the tissues as shown in Fig. 4.10B. Based on the measurements, at
State 1, the friction, mainly generated by the hindlegs, are greater than that mainly
generated by the forelegs (
hd
>
+
fd
), exhibiting an anisotropic friction property. This
property enables the robot to anchor its hindlegs and move the forelegs forward.
Similarly, at State 2, as
fd
>
+
hd
, the robot is able to anchor its forelegs and slide the
hindlegs forward. It is worth noting that the anisotropic property is more pronounced
at State 2 as shown in Fig. 4.10B, which implies that RoBeetle is prone to have a
better anchoring/sliding behavior at this stride state. This explains the phenomena
observed in locomotion experiments during which the hindlegs of the robot cannot
be properly anchored at some crawling steps.
96
B A
Actuation signal prole for angle θ
Stage 1 Stage 4
Time
Stage 3 Stage 2
t 1 t 2 t 3 t 4
θ max
θ 0
θ amp
0
P 2 (x 2, y 2)
P 0 (x 0, y 0)
C 1 (X 1, Y 1)
C 2 (X 2, Y 2)
l 1, m 1, J 1
c 1 l 2, m 2, J 2
f n1
f 1
l 0
c 2
f 2
f n2
x
y
P 1 (x 1, y 1)
Figure 4.11: Dynamic model of RoBeetle. A. The two-linkage simplified description of
RoBeetle. B. Input signal profile for the dynamic locomotion model (colored region
represents one complete cycle with 4 stages).
4.5.3 Dynamic model of the locomotion gait
Part I: Dynamic modeling and numerical solution
First, the input signal for the locomotion dynamics of the robot, which is also the
output of the actuation mechanism, is modeled as a uniform periodic function
which corresponds to the leg angle described in Fig. 4.11A. A typical signal profile is
illustrated in Fig. 4.11B. The actuation torque acting on the leg can be alternatively
chosen as the input signal; this signal, however, is more complex to construct and
not used in this work.
The periodic input signal represents the strain response of the artificial muscle in
tension as a result of the force applied by the leaf spring and the reacting force acting
under the legs of the robot. As depicted in Fig. 4.11B, during Stages 1 and 3, the length
of the artificial muscle remains constant due to a static equilibrium between the
actuation and restoring forces. During Stages 2 and 4, the signal is assumed to have a
sinusoidal shape. In Stage 2, the muscle is heated and contracts, which increases the
value of . In contrast, the leg angle decreases as the artificial muscle cools down
and extends at Stage 4. Consistently, the mathematical expression for the resulting
97
input signal in one cycle is
=
8
>
>
>
>
>
>
<
>
>
>
>
>
>
:
0
, 0 t< t
1
0
1
2
amp
cos(
tt
1
t
2
)+
1
2
amp
, t
1
t< t
2
0
+
amp
, t
2
t< t
3
0
+
1
2
amp
cos(
tt
1
t
2
t
3
t
4
)+
1
2
amp
, t
3
t t
4
, (4.11)
where
0
is the minimum leg angle and
amp
is the stroke amplitude. Note that
the derivative of is smooth. The selection of this simplified signal is reasonable
as its profile agrees with observations and results from the real-time locomotion
experiments (Movie S6). Also note that
0
,
amp
and t
i
can be potentially used as the
parameters of the actuation mechanism for design.
The locomotion dynamics can be described as a two-linkage mechanism (Fig. 4.11A).
For each instant, during locomotion, is determined by the input signal; therefore,
the state of the robot is uniquely determined by the contact point P
2
(x
2
, y
2
) of the
second linkage. The center of mass of the two linkages are computed based on their
geometry according to
X
1
= x
1
c
1
cos(
1
+
1
)= x
2
+ s
1
(t), (4.12a)
Y
1
= c
1
sin(
1
+
1
), (4.12b)
X
2
= x
2
+ c
2
sin(
2
+
2
)= x
2
+ s
2
(t), (4.12c)
Y
2
= c
2
sin(
2
+
2
), (4.12d)
where l
0
is the distance between the contact points of the two linkages; and x
1
= x
2
+l
0
is the location of the contact point P
1
of the first linkage. The inclined angle of each
i th linkage with respect to the ground is
i
; c
i
is the distance of the center of mass
C
i
from the contact point P
i
; the biased angle of C
i
with respect to l
i
is denoted as
i
; s
i
is defined as the function for the relative position of C
i
with respect to P
2
.
98
The dynamic equations of the translational and rotational motion of the robot
are given by
m
1
¨
X
1
+ m
2
¨
X
2
= f
1
+ f
2
, (4.13a)
m
1
¨
Y
1
+ m
2
¨
Y
2
= f
n1
+ f
n2
, (4.13b)
J
1
¨
1
+ J
2
¨
2
= f
n1
(x
1
X
2
) f
n2
(X
2
x
2
)+(f
1
+ f
2
)Y
2
+ m
1
¨
X
1
(Y
2
Y
1
) m
1
¨
Y
1
(X
1
X
2
),
(4.13c)
where f
i
is the friction acting under linkage i ; and f
ni
is the corresponding normal
force. By substituting (4.13a) and (4.13b) into (4.13c), the explicit coupling between
frictions and normal forces is converted into implicit coupling through inertial forces.
The normal force at each contact point is
f
ni
= G
i
+(1)
i
H , (4.14)
where the combined inertial terms are given by
G
1
(t)=((m
1
+ m
2
)g(X
2
x
2
) m
1
¨
Y
1
(x
2
X 2) m
2
¨
Y (x
2
X 2))=l
0
, (4.15a)
G
2
(t)=((m
1
+ m
2
)g(x
1
X
2
)+ m
1
¨
Y
1
(x
1
X 1)+ m
2
¨
Y
2
(x
1
X
2
))=l
0
, (4.15b)
H(t)=(J
1
¨
1
J
2
¨
2
+ m
1
¨
X
1
Y
1
+ m
2
¨
X
2
Y
2
)=l
0
. (4.15c)
The frictions and normal forces cannot be explicitly decoupled, because explicit
expressions for the static frictions are not available. Consistently, we model friction
according to
f
i
=
8
<
:
i
i
f
ni
, j ˙ x
i
j
f
si
, j ˙ x
i
j<
, (4.16)
in which we assume that whether the friction is static or kinetic, it depends on the
horizontal velocity ˙ x
i
at contact point;
i
is the static friction coefficient;
i
is a
99
conversion factor from the static friction coefficient to the kinetic friction coefficient.
Moreover, f
si
is the nominal static friction for small velocities as defined in (4.21);
and sets the bound for the nominal friction range (111). Note that, even though the
value of
i
of a linkage varies during anchoring and sliding, in this analysis we can
still use constant values to approximate the corresponding static and kinetic friction
coefficients, as the contact conditions of the claws in one locomotion direction
remain approximately invariant. In this case, the kinetic frictions are assumed to
be equal to the maximum values of the static frictions, i.e.
i
= 1. These modeling
choice reflects the fact that these values are typically close and that measuring the
kinetic friction acting on each leg, whose magnitude is typically less than 1 mN for
this insect-sized robot, is very challenging.
In (4.14), the frictions and normal forces are implicitly coupled through the in-
stantaneous inertia forces. In the implementation of numerical simulations, this
coupling is removed by using the acceleration from the last time step. Consistently,
for X
i
, it follows that
¨
X
i
(t
k
)= ¨ x
2
(t
k1
)+ ¨ s
i
(t
k
). (4.17)
This decoupling approach is also applied to
¨
Y
i
and
¨
i
terms. Then, the normal force
f
ni
is updated according to (4.14) as
f
ni
(t
k
)= G
i
(t
k
)+(1)
i
H(t
k
). (4.18)
Negative f
ni
may result due to numerical errors; therefore, corrections are introduced
to avoid non-physical results as
f
ni
= 0, f
n(3i)
=(m
1
+ m
2
)g + m
1
¨
Y
1
+ m
2
¨
Y
2
if f
ni
< 0. (4.19)
The acceleration terms are included in G
i
(t
k
) and H(t
k
). The time step sizet
is required to be sufficiently small in order to achieve numerical convergence. To
100
obtain the nominal static friction f
si
in (4.16), a temporary friction f
ti
is calculated as
f
ti
(t
k
)= m
1
¨
X
1
(t
k
)+ m
2
¨
X
2
(t
k
) f
3i
(t
k1
). (4.20)
Then, the f
si
, assuming small velocities, can be computed as
f
si
=
8
<
:
f
ti
,
i
f
ni
f
ti
> 0 or
i
f
ni
f
ti
< 0
i
f
ni
, else
. (4.21)
Numerical simulations of the dynamics of locomotion follow the steps resulting by
solving equation (4.18), (4.19), (4.20), (4.21) and (4.16) in sequence, then the formula
for updating the acceleration of the contact point P
2
is
¨ x
2
(t
k
)=
1
m
1
+ m
2
(f
1
(t
k
)+ f
2
(t
k
) m
1
¨ s
1
(t
k
)+ m
2
¨ s
2
(t
k
)). (4.22)
Part II: Specific friction coefficient estimation for each leg
As discussed above, the static friction coefficient for each leg in (4.16) and (4.21)
during anchoring and sliding, defined in terms of a coefficient, is considered to
be constant during dynamic simulations. We obtain these values from static mea-
surement experiments (Section 4.5.2) as follows. The coefficients for forward and
backward locomotion are denoted by
+
i
and
i
, depending on ˙ x
i
at time step t
k
, as
i
=
8
<
:
+
i
, ˙ x
i
> 0
i
, ˙ x
i
0
. (4.23)
The coefficients estimated in experiments correspond to the overall friction of the
robot. To estimate the specific friction coefficient acting under the leg, we can analyze
the equilibrium states in Fig. 4.10. When the robot is placed on the inclined plate,
the normal forces and frictions satisfy
f
ni
=(m
1
+ m
2
)g
ˆ
l
3i
cos
, (4.24a)
1
f
n1
+
2
f
n2
=(m
1
+ m
2
)g sin
, (4.24b)
101
where is ‘+’ or ‘’; and
ˆ
l
3i
=
jx
i
X
2
j
l
0
, corresponding to the length ratio that depends
on the geometry of RoBeetle prototype. For State 1,
ˆ
l
1
=
ˆ
l
2
= 0.5; for State 2,
ˆ
l
1
= 0.6
and
ˆ
l
2
= 0.4. According to (4.24), the relationship between specific and overall friction
coefficients is
1
ˆ
l
2
+
2
ˆ
l
1
= tan
=
, (4.25)
in which is ‘fd’ or ‘hd’ . Firstly, we use the overall friction coefficients of the robot on
the smooth aluminum plate measured through experiments (Fig. 4.10A) to estimate
the corresponding specific friction coefficients with following assumptions: (1) For
State 1, the friction coefficients for the forelegs and hindlegs are approximately same,
i.e.,
1
=
2
; (2) The friction coefficients of the hindlegs for State 2 is equal to that
for State 1 as
2
only varies within a small range. The second step is to calculate the
specific friction coefficients for the forelegs or hindlegs on the smooth paper tissues
by plugging the specific friction coefficients (for hindlegs or forelegs) obtained from
the first step and the overall FDFC and HDFC measured from experiments (Fig. 4.10B)
into (4.25). We summarized all calculated specific friction coefficients on this surface
used for simulation in Table S5.
Part III: Simulation results
To implement the simulation of the dynamics model, the geometric and inertial
parameters for the robot prototype are estimated from the Computer-aided design
model of the system (fuel included) as listed in Table S6. Then, the parameters of
the profiles were obtained based on analysis of the videos of locomotion experi-
ments (Movie S6) and summarized in Table S7. We applied the 4th-order Runge-Kutta
scheme to solve the equations iteratively with a time step sizet =1s in Matlab
(MathWorks, Inc.).
The totality of the simulation results corresponding to the locomotion experi-
102
0 1 2 3 4 5 6 7 8
Time (s)
-0.5
0
0.5
Force (mN)
Friction and normal force at P 2
fn2
f2
0 1 2 3 4 5 6 7 8
Time (s)
0
0.5
1
1.5
2
Angle (rad)
Inclined angles of linkages
0 1 2 3 4 5 6 7 8
Time (s)
-5
0
5
10
15
20
Position (mm)
Positions of point P 0 and P 2
x0
x2
A B
C
Figure 4.12: Numerical simulation results of autonomous crawling inside a gently-
moving atmosphere (8 s). (A) The temporal evolution of positions of linkage joint
point P
0
and contact point P
2
. (B) It shows the varyings of inclined angles of linkages
along the time. (C) Friction and normal force acting on contact point P
2
.
ments are plotted in Fig. 4.9C. We present two cycles of simulated results for the au-
tonomous crawling inside a gently-moving atmosphere in Fig. 4.12. From Fig. 4.12 A
and B, it is clear that our proposed dynamic model is able to properly capture the an-
choring and sliding condition. During the transition from State 1 to State 2, even the
slight backward slipping at the contact point P
2
of the hindleg, which is also observed
in experiments, can be reproduced in simulation results. In Fig. 4.12C, the frictions
and normal forces are processed using a zero-phase low-pass filter (designfilt func-
tion) to reduce non-physical high-frequency numerical oscillations. The dynamic
model discussed in this section provides us with a useful toolkit to numerically study
the behaviors of prototypes with different geometric designs, such as the length of
the legs and location of the center of mass.
103
4.5.4 Functional capabilities and locomotion performance
From a navigational standpoint, an autonomous terrestrial robot must be capable of
negotiating obstacles, carrying payloads, locomoting on various different surfaces,
and so on, in order to accomplish useful tasks. Thus, to assess the functionality of
RoBeetle, we performed several further experiments. The first is ramp-climbing
(Fig. 4.13, A, B and C), a test aimed to evaluate the capability of the robot to negotiate
big obstacles. In this case, we employ a tilted glass slide with a surface area of
5.08 cm7.62 cm, covered with a smooth piece of paper tissue, as the inclined plane
to be climbed by the robot. Fig. 4.13, A, B and C show the robot crawling on inclines
with slopes of 5
, 10
and 15
, respectively. Clearly, the prototype can easily climb the
ramps with slopes of 5
and 10
, and stalls while climbing the ramp with a slope of
15
; the corresponding measured velocities, compared to that of the horizontal case,
are shown in Fig. 4.13D. The complete set of experiments are shown in Movie S7. In
these tests, the crawling velocity decreases monotonically as the value of the slope
increases. This phenomenon is explained by a decrease of the normal forces exerted
by the inclined plane under the legs of the robot; as a result, the corresponding total
friction acting on the robot is reduced and there exists a critical slope for which
crawling becomes infeasible.
In a second set of experiments, we tested the crawling capabilities of the robot
on surfaces with different levels of roughness R
a
. Specifically, the smooth glass
with R
a
=0.009m (Fig. 4.13E), the already-described piece of paper tissue with
R
a
=7.528m (Fig. 4.9A), pacopad with R
a
=10.419m (Fig. 4.13F) and polyurethane
charcoal foam with R
a
=17.922m (Fig. 4.13G). The resulting velocities for these cases
are shown in Fig. 4.13H, correspondingly labeled as #1, #2, #3 and #4; clearly, with
the current claw design, the robot achieves the fastest velocity on surface #2. Details
104
#1 #2 #3 #4
Surface
0
0.1
0.2
0.3
0.4
Velocity (mm/s)
Smooth Coarse
0 5 10 15
Slope (°)
0
0.1
0.2
0.3
0.4
Velocity (mm/s)
A
B
C
D
E
F
G
I J
H
Figure 4.13: Locomotion under different conditions. A to C. The RoBeetle prototype
climbs on inclined planes with slopes of 5
, 10
and 15
respectively. The red lines
indicate the displacements from the initial to the final positions reached in 45 s, 85 s
and 45 s, respectively. Scale bars, 10 mm. D. Mean locomotion velocities versus angle
of inclination. E to G. The robot crawls on surfaces with different levels of roughness;
namely, glass, pacopad (Pacothane Technologies, Wincester, MA) and polyurethane
charcoal foam. The red line is the displacement from the initial to the final positions.
Duration, 60 s. Scale bar, 10 mm. H. Mean locomotion velocities on four surfaces
with different levels of roughness, numbered from 1 to 4, corresponding to glass,
smooth paper tissue, pacopad and polyurethane charcoal foam. I. Time-lapse image
of the robot while crawling at 0.22 mm/s and carrying a 71-mg plastic stick on its
horns. Duration, 80 s. Scale bar, 10 mm. J. Time-lapse of the robot autonomously
crawling outdoors on a concrete sideway. The mean velocity is 0.23 mm/s. Duration,
200 s. Scale bar, 10 mm.
105
are presented in Movie S8. The corresponding average locomotion velocities of the
robot are plotted in Fig. 4.13H. The trend of the relationship between roughness
and velocity reflects the fact that if the friction generated by the interaction of a
claw with the supporting surface is too small (Fig. 4.13E), traction is not feasible
as the hindlegs slide backwards during the transition from the State 1 to State 2
(Fig. 4.9D) and the forelegs slide backwards during the transition from State 2 to
State 1. On the other hand, after passing a critical level of roughness as the supporting
surface becomes coarser, the crawler moves at a slower speed because an increased
roughness facilitates the anchoring of the legs but also makes the transitions from
State 1 to State 2, and from State 2 to State 1, more difficult due to larger frictions
acting against the deformation of the artificial muscle (Fig. 4.13G). In fact, if the
aggregated value of the static friction forces acting on the system become larger
than the maximum force that the NiTi-Pt composite wire can provide to move the
forelegs, the robot would stall completely. In this set of experiment, we use a stylus
type profilometer (PCE-RT 1200, PCE Americas Inc.) is utilized to measure R
a
. For
each surface, we consecutively made ten measurements at different positions for
minimizing statistical error.
In a third set of experiments (Fig. 4.13I), the robot carries on its horns a 71-mg
cylindrical weight while crawling at a speed of 0.22 mm/s Similar tests demonstrate
that the robot can carry a maximum payload of 230 mg (2.61 the prototype’s
weight). These experiments are shown in Movie S9. Lastly, as shown in Fig. 4.13J,
in order to demonstrate RoBeetle’s ability to locomote outdoors and its potential
for real-world applications, we placed a prototype on a concrete sideway. Under
this condition, the robot is able to operate autonomously as it carries on-board
both its own power source (fuel) and MCM (see Movie S10). To our best knowledge,
this is the first experimental demonstration of fully autonomous locomotion in a
106
non-laboratory environment by a sub-gram insect-sized robot.
4.5.5 Experimental method
Several crawling experiments are performed on different surfaces as described be-
fore. The primary locomotion path, which is employed in the experiments of Fig. 4.9,
was built by tightly wrapping a 3-mm-thick acrylic sheet with laboratory tissue
(Kimtech 34155CT Kimwipes). The acrylic platform serves as a rigid and even base,
and the smooth paper tissue create an adequate roughness for sustained locomotion.
In the performance of each crawling experiment, 20l of methanol are injected into
the tank of the robot; then, the prototype in the configuration corresponding to
State 1 (Fig. 4.9D) is placed on the locomotion path using a pair of tweezers. As seen
in Fig. 4.9, A and B, a metric ruler is used to indicate the scale of the robot in relation
to the path. All the indoor tests were carried out at approximately 25
C and 48 % of
relative humidity. All the movies were recorded with a digital SLR camera (Nikon
D7200) at 30 fps. Basic post-processing of the videos, such as clipping from the raw
footages, and exportation was done using the iMovie Apple application. In order to
extract locomotion data for analysis, the exported videos were processed using Open
Source Computer Vision (OpenCV). The estimated positions over time corresponding
to the two main experiments discussed in this work are shown in Fig. 4.9C.
4.6 An application example
4.6.1 Experimental results
In previous sections, we demonstrated the capabilities of RoBeetle and discussed
the observed performance during locomotion. In this section, we demonstrate
107
A
Micro controller
Servo motor
LED
Laptop
RFID reader Gate
RFID chip
B
0s
22s
23s 60s
20s
Figure 4.14: Experiment with on-board RFID chip. A. Diagram of the experimental
setup. The scale bar inside the inset that shows the RFID chip is 2 mm. B. Photo-
graphic sequence of the experiment. Scale bars are 20 mm.
the ability of the robot to perform an automated task. Specifically, we installed
a 6-mg radio-frequency identification (RFID) chip and a booster antenna on the
robot, as shown in Fig. 4.14A, to enable simple interactions with the environment.
In general, an RFID chip is a passive sensor that works independently to collect
and transmit data, or to estimate its position (115). In the experimental example in
Fig. 4.14 and supplementary Movie S11, a RoBeetle prototype crawls along a straight
path towards a dummy gate driven by a servomotor while the on-board RFID chip
stores the opening code. Thus, when the robot enters the range of the RFID reader,
located 50 mm behind the gate, the code broadcasted by the on-board transmitter is
detected (at time 20 s in Fig. 4.14B); then, a microcontroller identifies the code and
switches an indicator LED light from red to green (at time 22 s in Fig. 4.14B). Finally,
the microcontroller sends a command to the servomotor to lift the gate in order
to allow the robot to pass through (23 s to 60 s in Fig. 4.14B). Details are discussed
in Section 4.6.2. This experiment highlights RoBeetle’s ability to interact with its
environment and potentially with other microrobots.
108
4.6.2 On-board RFID chip
The ultra-high-frequency (UHF) RFID chip (IM5-PK2525, Hitachi Chemical) em-
ployed in the experiments, which has dimensions of 2.5 mm2.5 mm0.4 mm, is
firmly attached to the tank lid of the robot (Fig. 4.14A and 4.15) using a removable
piece of transparent double-sided tape. The booster antenna for the chip is made
from a 50.8-m-thick copper wire and installed on the robot according to the con-
figuration shown in Fig. 4.15. The total length of the copper wire (L in Fig. 4.15A) is
determined by applying basic design principles for dipole antennas (116); namely,
L =
1
2
=
1
2
c
, (4.26)
where is the wavelength of radiation; c is the speed of light in a vacuum (299,792 km/s);
and is the operating frequency of the RFID chip (920 MHz). Correspondingly, we
obtain L160 mm, which is the value that we use in this case. During operation, an
RFID receiver (SparkFun Simultaneous RFID Reader M6E Nano), mounted on a Spark-
Fun RedBoard, is used to receive the tag information sent by the RFID chip. In this
scheme, once received, the RFID information is re-transmitted from the RedBoard to
an Arduino microcontroller platform that is pre-programed, using open-source code,
to control the LED light and a servo motor shown in Fig. 4.14A. The operational status
of the Arduino microcontroller chip (ATmega328, Atmel/Microchip Technology) is
continually monitored by a laptop that is connected through serial communication
to the terminal of the Arduino board.
4.7 Discussion
We presented RoBeetle, the first untethered sub-gram insect-scale robot capable of
crawling autonomously and performing simple tasks. Two main innovations made
109
L
A B
Figure 4.15: Antenna for the RFID chip and installation. A. Booster antenna design.
A thin copper wire (length L160 mm) is utilized to form a loop shape around the
RFID chip (top). Then, two ends of the wire is bended into a large circle as shown
at the bottom, creating a simple dipole antenna. Not to scale. B. Photograph of a
RoBeetle with an on-board RFID chip and an antenna installed on its back using a
clear double-sided tape. Scale bar, 10 mm.
this accomplishment possible: the development of a new type of flameless-catalytic-
combustion-driven artificial muscle that is made from a new type of NiTi-Pt com-
posite wire; and a pre-programmable mm-scale MCM. In the proposed approach,
the robot is built as an integrated system in which the actuator, sensor employed
for feedback and MCM constitute a monolithic unit. As a result of the chosen ap-
proach, the developed artificial muscles possess both the high work densities of SMA
actuators and the high energy densities of fuels.
Presently, the speed of actuation is mainly limited by the diffusion rate of the fuel
and bandwidths of the SMA wires. Therefore, in order to amplify the frequencies of
the actuator outputs, we can simply increase the speed of fuel delivery by employ-
ing liquefied fuels, stored in pressurized containers, such as butane and propane.
Furthermore, as suggested in a recent study (78), the bandwidth of SMA-based ac-
tuator can be substantially amplified (up to 35 Hz) by adopting novel mechanical
configurations of thin SMA wires (38.1m in diameter). In particular, the magnitude
110
of the mechanical output and efficiency of the proposed actuation method can be
significantly improved by arranging multiple fiber-like thin artificial muscles in hier-
archical configurations similar to those observed in sarcomere-based animal muscle.
In addition, the introduced integrated mechanical controller that employs the strain
actuator output as feedback was compellingly validated and demonstrated to enable
the autonomous electronics-free operation of the RoBeetle prototype.
In conclusion, RoBeetle is a biologically inspired system whose fuel-powered
design can serve as a paradigm for the creation of a new diverse generation of au-
tonomous microrobots capable of terrestrial, aquatic and aerial locomotion.
111
Chapter 5
Conclusions and future work
5.1 Conclusions
The contribution in this dissertation provides a convincing demonstration of the
feasibility of creating sub-gram insect-sized robots that overcome the long-standing
difficulties in microrobotics, namely, the stringent limits of the number of indepen-
dent actuation units, and the power and control dependencies on external sources. A
tethered flying robot and an untethered autonomous crawling robot were developed
correspondingly to validate the approaches we proposed.
The Bee
+
became the first four-winged flying robot weighing less than 100 mg be-
cause of the implementation of two pairs of twinned unimorph actuators. This actu-
ation scheme is advantageous in many aspects, e.g., increasing the control authority
of flight maneuver, decreasing the total weight and wing-loading, and simplifying the
microscopic assembling process. The development of Bee
+
represents a significant
improvement in the fabrication and control of state-of-the-art insect-scale flying
robots.
Furthermore, the RoBeetle, as the smallest and lightest autonomous crawling
112
robot created to date, pioneered the research on exploring alternative on-board power
sources for microrobotic applications. The creation of catalytic artificial muscles and
on-board control scheme for catalytic combustion at millimeter-scale obviates the
requirement of any external power and control sources for sub-gram robotic insects.
In the process of developing the Bee
+
and RoBeetle, we originally developed
fabrication methods for the twinned unimorph actuators and the NiTi-Pt composite
wires based on in-depth understanding and innovative exercising of related existing
technologies. Additionally, we manufactured all the functional and structural com-
ponents for the Bee
+
and RoBeetle by using the SCM process, which is a versatile
millimeter-scale composite manufacturing technique. Lastly, the proposed micro-
robots can also facilitate theoretical studies on dynamic systems at this miniature
scale, including the aerodynamics of flapping-wing at low Reynolds number, the
mass and thermal transfer phenomena, the friction-based crawling locomotion, etc.
The techniques and knowledge refined from this work will establish a new system-
atic strategy for creating sub-gram insect-scale robots with agility, autonomy, and
intelligence.
5.2 Future work
The next steps for research on the Bee
+
and RoBeetle should cover the following
work.
1. Present dynamic models of insect-scale flapping-wing robots only consider the
two-winged case, the full dynamics of the four-winged case, especially the unique
aerodynamic interaction phenomenon among wings, known as the flap-and-fling
mechanism, yet to be completely understood and modeled. Therefore, to improve
the flight control of the Bee
+
, the intricacy of this multi-body dynamic system needs
113
to be further investigated through theoretical and experimental approaches.
2. In this work, only a simple quaternion-based LTI controller was implemented
to validate the hovering performance of the Bee
+
. The design of four-winged Bee
+
shares many commons with that of quadrotors from the perspective of aerodynamics.
So the Bee
+
can potentially achieve complex aerobatic maneuvers as quadrotors,
once high-performance non-linear advanced control algorithms were applied, such
as adaptive control, model-predictive control.
3. The main factor that limits the actuation bandwidth of the catalytic artificial mus-
cle is the cooling rate of SMA wire. Improving the actuation frequency of the artificial
muscles is crucial because the locomotion performance of microrobot significantly
depends on its actuation frequency. Feasible measures include employing SMA wires
with higher phase transition temperatures, using SMA wires with thinner diameters,
enhancing the thermal convection during the cooling process, or immersing the
artificial muscle into media with higher thermal conduction rate, etc.
4. For the current version of RoBeetle, liquid methanol is used as fuel, and therefore,
the fuel supply rate is determined by the methanol evaporation rate. To substantially
increase the fuel supply rate, we can employ liquefied hydrocarbon as the fuel, e.g.,
propane or butane. The challenges of this method are developing gas-tight storage
containers at the millimeter-scale, as well as corresponding micro valves. Emerging
technologies capable of creating sophisticated three-dimensional features, for ex-
ample, the additive manufacturing, the dip-in laser lithography, can be exploited to
fabricate the millimeter-scale fuel supply components.
5. The RoBeetle has achieved autonomous operation with on-board power and con-
trol components. However, this is just the first step for creating artificial insects that
can emulate or surpass their natural counterparts. Its locomotion capability can be
further improved, for instance, increasing the actuation frequency of the artificial
114
muscle will enable faster crawling velocity; by installing two sets of actuation mecha-
nisms for its left and right forelegs, the robot can achieve steering function. Besides,
the RoBeetle has enough payload capacity for carrying on-board electronics, such as
wireless sensors, micro cameras, chips, photovoltaic cells. This capability allows the
microrobot to possess more advanced computation and perception capabilities for a
wide range of applications. Additionally, with some modifications in mechanical de-
sign, the fuel-powered scheme we proposed can be employed on developing various
robotic platforms, such as jumping, swimming, and flying insect-sized robots.
115
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Appendix
Supplementary tables
Table S1: Energy densities and specific energies of various sources of power.
Power source Energy density (MJ/L) Specific energy (MJ/kg)
Hydrogen 0.01079 143
Propane 25.3 49.6
Butane 27.7 49.1
Gasoline 34.2 46.4
Fat 35 38
Methanol 15.6 19.7
Lithium metal battery (Li-Po) 4.32 1.8
Lithium-ion battery 2.43 0.875
142
Table S2: Work densities and power densities of different actuation methods.
Actuation method Work density (kJ/m
3
) Power density (kW/m
3
)
SMAs 10000 30000
Hydraulic 5000 20000
Pneumatic 175 3500
Piezoceramic 35 175000
Muscle 35 350
Dielectric elastomer 10 5500
Carbon nanotube 40 270
Table S3: Physical parameters of the RoBeetle prototype.
Robot properties Robot geometry
Total weight 88 mg Body length 15 mm
Max velocity 0.76 mm/s Body width 10 mm
Max climbing slope 10 deg. Body hight 13 mm
Max payload 230 mg Tank volume 368 l
143
Table S4: Locomotion velocities of various robot and insects. (Values estimated from references are marked with ‘†’)
No. Robot/insect Autonomous Max velocity Weight Body length Ref.
Yes/No (BL/s) (g) (mm)
Legged small robot (BL<100 mm)
1 RoBeetle Yes 0.05 0.088 15
2 HAMR-F Yes 3.8 2.8 45 (117)
3 RoACH Yes 1 2.4 30 (118)
4 Mesoscale quadruped Yes 3 104 90 (119)
5 Kilobot Yes 0.3 36 33 (120)
6 DEAnsect Yes 0.3 1 40 (121)
7 SMA device No 0.00018 0.4 16 (122)
8 MEMS microrobot No 0.07 0.079 2.7 (88)
Continued on next page
144
Table S4 – Continued from previous page
No. Robot/insect Autonomous Max velocity Weight Body length Ref.
Yes/No (BL/s) (g) (mm)
9 Electrostatic crawling robot No 1.5 0.047 20 (123)
10 Single-legged silicon robot No 0.15 0.018 5 (10)
11 Origami robot No 3.8 0.31 17 (85)
12 Inchworm robot No 0.16 1.4 18.5 (83)
13 HAMR-2 No 4 2 57 (124)
14 Silicon micro-robot No 0.4 0.083 15 (125)
Wheeled small robot (BL<100 mm)
15 Tugs Yes 0.4 12 25 (126)
16 Colias Yes 8.75 28 40 (127)
17 R-one Yes 3 230 100 (128)
Continued on next page
145
Table S4 – Continued from previous page
No. Robot/insect Autonomous Max velocity Weight Body length Ref.
Yes/No (BL/s) (g) (mm)
18 AMiR Yes 1.5 200
†
65 (129)
19 E-puck Yes 1.7 200 75 (130)
20 Alice Yes 1.82 11 22 (131)
21 MARV Yes 0.4 28 25 (132)
22 Inchy Yes 11.8 20
†
25.4 (131)
23 Meloe Yes 0.8 17
†
24 (131)
24 MIT ants Yes 4.2 33 35 (133)
25 Kity Yes 2 19
†
25 (134)
26 MARS Yes 2 19
†
20 (135)
27 EMRoS Yes 1.2 4.3 12.4 (131)
Continued on next page
146
Table S4 – Continued from previous page
No. Robot/insect Autonomous Max velocity Weight Body length Ref.
Yes/No (BL/s) (g) (mm)
28 Pollicino No 10 19
†
10 (136)
Legged robot (BL>100 mm)
29 PAW Yes 2.4 15700 494 (137)
30 BigDog Yes 2.8 109000 1100 (138)
31 Cheetah Yes 1.1 850 235 (139)
32 Takken 2 Yes 3.16 4300 300 (140)
33 Scout II Yes 2.4 20865 552 (141)
34 Puppy 2 Yes 3.5 273 142 (142, 143)
35 Aibo RES-210A Yes 1 1400 289 (143)
36 Puppy 1 Yes 2.9 1500 170 (144, 143)
Continued on next page
147
Table S4 – Continued from previous page
No. Robot/insect Autonomous Max velocity Weight Body length Ref.
Yes/No (BL/s) (g) (mm)
37 Cheetah-cub No 6.9 1100 205 (143)
38 HyQ No 2 70000 1000 (145)
39 Tekken 1 No 4.8 3100 230 (146)
40 Rush No 3 4300 300 (147)
41 KOLT quadruped No 0.63 80000 1750 (148)
42 Tekken 1 No 2.2 3100 230 (149)
43 Quadruped running machine No 3.5 38000 1050 (150)
Soft robot
44 Quadruped soft robot Yes 0.008 5000 650 (151)
45 Elastomer robotic snake Yes 0.07 900
†
280 (152)
Continued on next page
148
Table S4 – Continued from previous page
No. Robot/insect Autonomous Max velocity Weight Body length Ref.
Yes/No (BL/s) (g) (mm)
46 Earthworm-like microrobot Yes 0.0033 9
†
50 (153)
47 Hygrobot No 0.24 0.035 25 (9)
48 Pneumatic soft robot No 0.125 7.1
†
40 (154)
49 Hexapod robot No 0.022 80 182 (155)
50 Soft SMA robot No 0.023 63 158 (156)
51 Soft robot No 0.039 63 120
†
(157)
52 Micro inchworm robot No 0.23 1.9 23 (158)
53 Hydrogel walker No 0.003 0.052 10 (159)
54 Omegabot No 0.06 1.2 150 (113)
55 Walking devices No 0.011 0.036 10 (160)
Continued on next page
149
Table S4 – Continued from previous page
No. Robot/insect Autonomous Max velocity Weight Body length Ref.
Yes/No (BL/s) (g) (mm)
56 Quadruped soft robot No 0.016 3.58
†
59 (161)
57 Inchworm-like mobile robot No 0.026 145 285 (162)
58 Underwater microrobot 1 No 0.25 17
†
33 (163)
59 Underwater microrobot 2 No 0.055 10
†
33 (164)
60 Earthworm robot No 0.056 4.7 45 (165)
61 Walker-3 No 0.2 19
†
30 (166)
62 Self-walking gel No 0.00118 0.0012 2.4 (167)
63 Ultrarobust robot No 20 0.024 10 (7)
Terrestrial insect
64 Beetle (Onymacris plana) Yes 50 0.73 22 (168)
Continued on next page
150
Table S4 – Continued from previous page
No. Robot/insect Autonomous Max velocity Weight Body length Ref.
Yes/No (BL/s) (g) (mm)
65 Beetle (Cicindela eburneola) Yes 171 0.05 10.5 (169)
66 Spider (Dolomedes plantarius) Yes 37.5 1.5 20 (168)
67 Spider (Eremobates marathoni) Yes 9.9 3.49 23.8 (170)
68 Mite (Paratarsotomus macropalpis) Yes 194 0.00025 1.025 (169, 171)
69 Cockroach (Periplaneta americana) Yes 50 0.83 40 (172)
70 Cockroach (Nauphoeta cinerea) Yes 13 0.45 27 (173)
71 Ant (Formica fusca L.) Yes 2.6 0.0047 9 (174)
72 Ant (Leptogenys schwabi) Yes 1.36 0.00896 8.6 (175)
151
Table S5: Experimentally-estimated friction coefficient of the robot’s forelegs and hindlegs.
+
1
1
+
2
2
-1.09 8.76 -0.80 1.96
Table S6: Geometric and inertial parameters of RoBeetle employed in dynamic simulation.
m
1
m
2
J
1
J
2
l
1
l
2
c
1
c
2
1
2
6.8 mg 99.1 mg 33.6 mgmm
2
2745.7 mgmm
2
7.0 mm 14.1 mm 5.9 mm 7.6 mm 7.5
11.1
Table S7: Characterized parameters of the input signal employed in dynamic simulation.
0
amp
t
1
t
2
t
3
t
4
Crawling inside a stationary undisturbed atmosphere 64.0
10.0
0.4 s 0.9 s 1.2 s 0.9 s
Crawling inside a gently-moving atmosphere 46.5
28.0
0.8 s 1.2 s 1.0 s 1.0 s
152
Supplementary movies
Movie S1. Experiments of Bee
+
.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS1.mp4
Movie S2. Controlled fast actuation of catalytic artificial muscle.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS2.mp4
Movie S3. Fuel evaporation experiment.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS3.mp4
Movie S4. Tethered stationary experiment.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS4.mp4
Movie S5. Thermal camera video.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS5.mp4
Movie S6. Autonomous and convection-enhanced crawling.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS6.mp4
Movie S7. Climbing ramps.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS7.mp4
Movie S8. Crawling on surfaces with different levels of roughness.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS8.mp4
Movie S9. Crawling with payloads.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS9.mp4
Movie S10. Outdoors crawling experiment.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS10.
mp4
153
Movie S11. Experiment with on-board RFID microchip.
https://www.uscamsl.com/resources/yangxfthesis2020/MovieS11.
mp4
154
Abstract (if available)
Abstract
Researches working on the development of mobile robots at the sub-gram millimeter scale are mostly inspired by insects surrounding us and motivated by a significant number of potential applications. Despite impressive progress in the past two decades, state-of-the-art microrobots are yet to achieve the same levels of autonomy, agility, and intelligence exhibited by their natural counterparts while completing tasks. The most fundamental difficulties lie on stringent constraints on the number of actuators, and the power and control dependences on external sources. ❧ To overcome these non-trivial challenges, in this work, we explored the fundamental and practical aspects of two micro-actuation methods, namely piezoelectric ceramics and shape-memory-alloys (SMAs). We developed two different microrobots based on them. The first insect-sized robot is a 95-mg four-winged flying robot, Bee⁺, driven by two pairs of twinned unimorph piezoelectric actuators. The second one, named RoBeetle, is an 88-mg autonomous crawling robot actuated by catalyst-coated SMA composite artificial muscles. ❧ The work in this dissertation makes the following contributions. Firstly, Bee⁺, as a significant upgrade of current flying robotic insects, is the lightest and smallest four-winged robot created to date. Its two pairs of twinned unimorph actuators enable us to increase the independent actuation units without substantially increasing the weight and the size of the robot. Compared to state-of-the-art bimorph actuators, the twinned unimorph configuration also reduces the complexity of fabrication and statistical frequency of microscopic assembly error. ❧ Secondly, we developed a radical new actuator for microrobotic applications, which is the catalytic composite artificial muscle made of nickel-titanium-alloy (Nitinol) and platinum (Pt) black. This actuator inherently possesses the high-work-density of Nitinol and can convert the chemical energy from high-energy-density (HED) fuels into applicable mechanical outputs through flameless catalytic combustion. We achieved fast controlled actuation (1 Hz) on this artificial muscle by implementing a logic-based control algorithm on a custom-made in-house thermomechanical experimental platform. ❧ Last and foremost, we developed RoBeetle, an 88-mg robot actuated by a catalytic artificial muscle, which is the first sub-gram autonomous robot created to date. An essential innovation that makes the autonomous-operation of RoBeetles possible is a feedback control scheme of the catalytic combustion process at the millimeter-scale. This on-board mechanical control mechanism indirectly utilizes as feedback the reaction temperature on the surface of the artificial muscle. Specifically, the mechanism employs the periodical actuation output according to an identified hysteric mapping, to modulate the flow of the fuel through synchronously adjusting the openings of micro-valves. The design of this bio-inspired microrobot powered by HED fuel could serve as a paradigm for the creation of a new diverse generation of autonomous robotic insects in terrestrial, aquatic, and aerial environments.
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Development of biologically-inspired sub-gram insect-scale autonomous robots
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