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Design and control aspects of humanoid walking robots [Elektronische Ressource] / Dirk Wollherr

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Lehrstuhl fur Steuerungs- und RegelungstechnikTechnische Universit at Munc henUniv.-Prof. Dr.-Ing./Univ. Tokio Martin BussDesign and Control Aspectsof Humanoid Walking RobotsDirk WollherrVollst andiger Abdruck der von der Fakult at fur Elektrotechnik und Informationstechnikder Technischen Universit at Munc hen zur Erlangung des akademischen Grades einesDoktor-Ingenieurs (Dr.-Ing.)genehmigten Dissertation.Vorsitzender: Univ.-Prof. Dr.-Ing. Klaus DiepoldPrufer der Dissertation:1. Univ.-Prof. Dr.-Ing./Univ. Tokio Martin Buss2. Univ.-Prof. Dr.-Ing., Dr.-Ing. habil. Heinz UlbrichDie Dissertation wurde am 31.3.2005 bei der Technischen Universit at Munc hen eingereichtund durch die Fakult at fur Elektrotechnik und Infromationstechnik 23.6.2005 angenommen2ForewordThis thesis has emerged from four years of work at three di eren t Labs. Both, the intel-lectual, and the physical journey left a signi can t imprint on my personality; all throughthe wide range of emotional experiences, ranging from the joyfull kick of successanger and the crestfallen thought of giving up in times where nothing seems to work { inthe retrospective, I do not want to miss any of it.The fundaments of this work have been laid at the Control Systems Group, Techni-sche Universit at Berlin, where the main task of assembling knowledge has been accom-plished and many practical experiences could be gained.

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Published 01 January 2005
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Lehrstuhl fur Steuerungs- und Regelungstechnik
Technische Universit at Munc hen
Univ.-Prof. Dr.-Ing./Univ. Tokio Martin Buss
Design and Control Aspects
of Humanoid Walking Robots
Dirk Wollherr
Vollst andiger Abdruck der von der Fakult at fur Elektrotechnik und Informationstechnik
der Technischen Universit at Munc hen zur Erlangung des akademischen Grades eines
Doktor-Ingenieurs (Dr.-Ing.)
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr.-Ing. Klaus Diepold
Prufer der Dissertation:
1. Univ.-Prof. Dr.-Ing./Univ. Tokio Martin Buss
2. Univ.-Prof. Dr.-Ing., Dr.-Ing. habil. Heinz Ulbrich
Die Dissertation wurde am 31.3.2005 bei der Technischen Universit at Munc hen eingereicht
und durch die Fakult at fur Elektrotechnik und Infromationstechnik 23.6.2005 angenommen2Foreword
This thesis has emerged from four years of work at three di eren t Labs. Both, the intel-
lectual, and the physical journey left a signi can t imprint on my personality; all through
the wide range of emotional experiences, ranging from the joyfull kick of success
anger and the crestfallen thought of giving up in times where nothing seems to work { in
the retrospective, I do not want to miss any of it.
The fundaments of this work have been laid at the Control Systems Group, Techni-
sche Universit at Berlin, where the main task of assembling knowledge has been accom-
plished and many practical experiences could be gained. With this know-how, I was
given the chance to spend seven months at the Nakamura-Yamane-Lab, Department of
Mechano-Informatics, University of Tokyo, where the humanoid robot UT-Theta has been
1developed . This robot provided a relyable platform to experiment with walking control
algorithms. The end of my journey is the Institute of Automatic Control Engineering,
Technische Universit at Munc hen, where I found ease and comfort to structure my mind
and write down the results of my research.
First of all, I would like to thank my doctoral advisor Prof. Martin Buss, who lead me
on my way whenever I was in need of a guiding hand, and let me walk freely, where I found
the road ahead myself.
Furthermore I found an invaluable help in the cooperation with the Simulation and
Systems Optimization Group, Technische Universit at Darmstadt. With their experience
in generating gait trajectories, Prof. Oskar von Stryk, Dr. Michael Hardt, Max Stelzer and
Jutta Kiener greatly supported the construction of a rst humanoid prototype.
Prof. Yoshihiko Nakamura nally gave me the opportunity to work on a great hardware
platform in a productive environment and broadened my view in the world of robotics {
domo arigatou Nakamura-sensei.
I am also indebted to Marion Sobotka (TU Berlin/TU Munc hen), Dr. Fabio Zonfrilli
(Universit a di Roma \La Sapienza"), and Dr. Tomomichi Sugihara (University of Tokyo)
who supported me as collegues and encouraged me as friends. To all my students, Karsten
G anger, Ste en Schostan, and Thorsten Hinzmann, I thank you very much for the e orts
you took. Last but not least, I would like to mention Uwe Weidauer, who was always
happy to implement my ideas and realized the impossible.
And of course, my deepest and unconditional gratitude for my parents for their continual
and unconditioned support and patience with me { I am very lucky to have them.
Munich, 2005. Dirk Wollherr
1The reseach stay in Tokyo was generously supported by the Japanese Society for the Promotion of
Science (JSPS).
ito my parents
...
iiDesign and Control Aspects of Humanoid Walking Robots
The research presented in this dissertation discusses the development of a humanoid
biped robot from the planning stage to biped walking focusing on low level control. Con-
cepts in hardware design, posture manipulation, and hybrid joint control, that are novel in
humanoid robotics, are presented and entirely veri ed in hardware experiments. Decisive
for the future performance of the robot is a careful selection of an appropriate motor-gear-
combination during hardware design, as oversized actuators increase the total weight of the
robot, thus deteriorating the walking performance. A systematic procedure for actuator
selection based on optimal control is discussed. When replaying precalculated trajectories
with a humanoid robot, it is often desirable to modify the posture of the robot thus com-
pensating for control errors or adapting the trajectory for new situations. This task can
be accomplished by a method termed Jacobi Compensation. A walking controller based on
the inverted pendulum method is implemented on the humanoid UT-Theta. This robot is
equipped with an innovative knee joint allowing to switch between actuated motion and
free swinging. To ensure smooth and reliable operation with this joint, a hybrid, nonlinear,
time optimal knee controller has been implemented.
Betrachtungen ub er Design und Regelung humanoider Laufroboter
Die Dissertation beschreibt die Entwicklung eines humanoiden Laufroboters von der
Planungsphase bis zum zweibeinigen Gehen, wobei der Schwerpunkt bei elementaren
Regelungsaufgaben liegt. Es werden Konzepte der Hardwaregestaltung, der Anpassung
der K orperhaltung und der Regelung hybrider Gelenke vorgestellt, deren Einsatz auf
dem Gebiet humanoider Laufroboter neu ist. W ahrend der Entwicklung der Hardware
ist eine sorgf altige Auswahl einer geeigneten Motor-Getriebe-Kombination entscheidend
fur die zukunftige Leistungsf ahigkeit des Roboters, da ub erdimensionierte Antriebe das
Gesamtgewicht des Roboters erh ohen und somit die Laufeigenschaften verschlechtern. Ein
systematischer Ansatz, Antriebe auszuw ahlen, wird vorgestellt, bei dem eine geeignete
Motor-Getriebe-Kombination durch L osen eines Optimalsteuerungsproblems ermittelt
wird. Wenn im Voraus berechnete Trajektorien auf einen Humanoiden angewendet werden,
ist es nutzlic h, wenn seine Haltung modi ziert werden kann, um Regelfehler zu kompen-
sieren oder die Trajektorien neuen Gegebenheiten anzupassen. Hierzu wird ein Verfahren
mit dem Namen Jacobi Compensation vorgestellt. Ein Gangregler, der auf der Methode des
invertierten Pendels beruht, wird an dem Humanoiden UT-Theta implementiert. Dieser
Roboter verfugt ub er eine innovative Kniekonstruktion, die ein Umschalten zwischen ak-
tivem Antrieb und passivem Schwingen des Unterschenkels erm oglicht. Gleichm a iger und
zuverl assiger Betrieb dieses Gelenks wird durch einen speziellen hybriden, nichtlinearen
und zeitoptimalen Regler sichergestellt. Die Konzepte, die in dieser Dissertation vorgestellt
werden, wurden s amtlich in Hardwareexperimenten validiert.
iiiivContents
1 Introduction 1
1.1 Spade- and Groundwork in Autonomous Walking . . . . . . . . . . . . . . 3
1.2 Main Contributions and Outline of Dissertation . . . . . . . . . . . . . . . 4
2 State of the Art 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Biped Gait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Equilibrium Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 Statically and Dynamically Balanced Gait . . . . . . . . . . . . . . 12
2.3 Overview of Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Inverted Pendulum Method . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Dynamics Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3 Passive-Dynamic Walkers . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.4 Other Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.5 Lowlevel Joint Control . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Sensors for Humanoid Robots . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Joint Position and Velocity Measurement . . . . . . . . . . . . . . . 17
2.4.2 Force and Torque Measurement . . . . . . . . . . . . . . . . . . . . 17
2.4.3 Body Orientationt . . . . . . . . . . . . . . . . . . . . 18
2.5 Humanoid Biped Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.1 Waseda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.2 Honda Asimo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.3 Sony QRio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.4 HRP-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.5 Johnnie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.6 UT-Theta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Humanoid Robot Design Based on Optimal Control 25
3.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Initial Assumptions for the Kinematic Structure . . . . . . . . . . . . . . . 26
3.3 Determining of Joint Torque Requirements . . . . . . . . . . . . . . . . . . 27
3.4 Motor Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
vContents
4 Online Posture Correction 35
4.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Online Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.4.1 Qualitative Analysis of System Dynamics . . . . . . . . . . . . . . . 40
4.4.2 Lyapunov Stability of Jacobi Compensation . . . . . . . . . . . . . 43
4.5 Singularity-Robust Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.6 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6.1 Trajectory Following Using Precalculated Trajectories . . . . . . . . 47
4.6.2 Teach-in Compensation . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5 Walking Control of Humanoid Theta 51
5.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 Mechanical Design of Humanoid Theta . . . . . . . . . . . . . . . . . . . . 52
5.2.1 Double Spherical Hip Joints . . . . . . . . . . . . . . . . . . . . . . 53
5.2.2 Backlash Clutch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3 Control of the Knee Backlash Clutch . . . . . . . . . . . . . . . . . . . . . 54
5.3.1 Transition Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.2 Contact Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.3 Free Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.3.4 Experimental Evaluation of the Knee Control . . . . . . . . . . . . 58
5.4 Walking Control Exploiting Zero Dynamics . . . . . . . . . . . . . . . . . . 60
5.4.1 Inverted Pendulum Dynamics . . . . . . . . . . . . . . . . . . . . . 60
5.4.2 Walking Pattern Generator . . . . . . . . . . . . . . . . . . . . . . 62
5.4.3 Implementation on UT-Theta . . . . . . . . . . . . . . . . . . . . . 64
5.4.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6 Conclusions and Future Directions 69
6.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
A Mechanical Construction of the Humanoid Prototype 73
A.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.2 Hardware Design and Software Environment . . . . . . . . . . . . . . . . . 74
A.3 Performance of the Motion Control Board . . . . . . . . . . . . . . . . . . 76
A.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
B Gait Trajectory Generation 81
B.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
B.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
B.3 Optimized Walk of a Biped . . . . . . . . . . . . . . . . . . . . . . . . . . 82
B.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
viNotations
Abbreviations
CoM Center of Mass
CoP Center of Pressure
DoF Degrees of Freedom
GCoM Ground Projection of Center of Mass
NPCM Normal Pro of Center of Mass
PWM Pulse Width Modulation
ZMP Zero Moment Point
Conventions
Scalars, Vectors, and Matrices
Scalars are denoted by upper and lower case letters in italic type. Vectors are denoted by
lower case letters in boldface type, as the vector x is composed of elements x . Matrices arei
denoted by upper case letters in boldface type, as the matrix M is composed of elements
M (i-th row, j-th column).ij
x scalar
x vector
X matrix
f() scalar function
f() vector
2d dx_, x equivalent to x and x2dt dt
x upper bound for x
x lower bound for x
TX transposed of matrix X
1X inverse of matrix X
#X pseudoinverse of matrix X
X singularity robust (SR-) inverse of matrix X
Subscripts and Superscripts
x ; x referring to right or leftR L
d ; d ; d component of vector d in x-, y-, z-directionx y z
d , d horizontal or vertical component of vector dh v
d , d normal or tangential component of vector dN T
q , q , q angle q at sampling time k, k 1 or k + 1k k 1 k+1
viiNotations
Symbols and Abbreviations
a acceleration
a maximum acceleration during brakingmax,brake
aum accelerationmax,accel
c cost of transportationt
c t total energy consumed by systeme
c t mechanical energy consumed by systemm
d , d , d length, width and height of a bodyx y z
(t) position error
e ciency of gearbox
F gravitation forceG
F inertia forceI
F ground reaction forceR
g earth acceleration
error measure
derivative gain matrixD
proportional gain matrixP
I identity matrix
J Jacobian
J matrix for foot positionfoot
J Jacobian for foot and hip positionfoot,hip
J matrix for hip positionhip
k weighting factor
K derivative gain matrixD
K proportional gain matrixP
condition number
l length of rod
m mass
M mass matrix
M inertia momentI
n number of revolutions per time
N gear ratio
, friction coe cien tR T
p position vector
p location of center of mass (CoM)CoM
p lo of center of pressure (CoP)CoP
p location of ground projection of CoM (GCoM)GCoM
p lo of support footSF
p location of zero moment point (ZMP)ZMP
P power consumptionW
viii