Advances in Robot Kinematics and Computational Geometry

504 Pages·1994·18.905 MB·English

by  Bernard Roth (auth.), Jadran Lenarčič, Bahram Ravani (eds.)

ADVANCES IN ROBOT KINEMATICS AND COMPUTATIONAL GEOMETRY
ADVANCES IN
ROBOT KINEMATICS AND
COMPUTATIONAL GEOMETRY
Edited by
I adran Lenareic
"Jozef Stefan" Institute,
University of Ljubljana,
Slovenia
and
Bahram Ravani
University of California,
Davis, California, U.SA.
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-4434-1 ISBN 978-94-015-8348-0 (eBook)
DOI 10.1007/978-94-015-8348-0
Printed on acid-free paper
AU Rights Reserved
© 1994 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1994
Softcover reprint ofthe hardcover 1st edition 1994
No part of the material protected by this copyright notice may be fepfoduced Of
utilized in any fofm Of by any means, electronic of mechanical,
including photocopying, fecofding Of by any information stofage and
fetrieval system, without written permission from the copyright ownef.
Preface
Recently, research in robot kinematics has attracted researchers with different theoretical
profiles and backgrounds, such as mechanical and electrica! engineering, computer science,
and mathematics. It includes topics and problems that are typical for this area and cannot
easily be met elsewhere. As a result, a specialised scientific community has developed
concentrating its interest in a broad class of problems in this area and representing a
conglomeration of disciplines including mechanics, theory of systems, algebra, and others.
Usually, kinematics is referred to as the branch of mechanics which treats motion of a
body without regard to the forces and moments that cause it. In robotics, kinematics studies
the motion of robots for programming, control and design purposes. It deals with the spatial
positions, orientations, velocities and accelerations of the robotic mechanisms and objects to
be manipulated in a robot workspace. The objective is to find the most effective
mathematical forms for mapping between various types of coordinate systems, methods to
minimise the numerical complexity of algorithms for real-time control schemes, and to
discover and visualise analytical tools for understanding and evaluation of motion
properties ofvarious mechanisms used in a robotic system.
The purpose of the book is to present the recent advances in robot kinematics and
computational geometry in kinematics. The articles were submitted by authors from sixteen
countries. Among these, the reader will find the most outstanding names in the field. Ali of
the fifty three articles were peer reviewed by at least two independent reviewers. They each
represent an original contribution that hasn't been published elsewhere. The book is divided
into twelve sections that were identified as the prevalent areas of the contemporary research
in kinematics and computational geometry applied to robots and mechanisms. The
introductory article is written by Professor Bemard Roth from Stanford University, USA.
The articles of this book were reported and discussed at the fourth workshop on
Advances in Robot Kinematics in conjunction with the first workshop on Computational
Geometry in Kinematics organised by the Institute "Jozef Stefan" in Ljubljana (Slovenia),
July 4-6, 1994, under patronage ofthe International Federation for the Theory ofMachines
and Mechanisms. It should be emphasised that, since the first submission of the articles, the
whole procedure of reviewing, preparing the final manuscripts, editing and publishing took
approximately six months. We trust, therefore, that this book presents the actual state of the
art in the fields of robot kinematics and computational geometry in kinematics. In various
articles on the current research, the reader will find interesting personal views, scientific
conclusions, as well as speculations and attempts to foresee new scientific problems and
research directions. We are grateful to the authors of the articles for their collaboration in
this project and their valuable contributions. We are also indebted to the reviewers for their
timely review of the articles, and to the personnel at Kluwer Academic Publishers for their
excellent technical and editorial support.
J. Lenarcic and B. Ravani, Editors
V
Table of Contents
Introduction 5
B. Roth: Computational Advances in Robot Kinematics 7
1. Workspace and Trajectory Analysis 17
A.P. Murray, J.M. McCarthy: Characterizing the Workspace ofthe Spherical
/mage of Cooperat ing Robots 19
P. Wenger, J. Elornri: On the Kinematics of Nonsingular and Singular Posture
Changing Manipulators 29
M. Ceccarelli: Determination of the Workspace Boundary of a General
n-Revolute Manipulator 39
C.G. Gibson, W. Hawes, C.A. Hobbs: Local Picturesfor General
Two-Parameter Planar Motions 49
V. Milenkovic, P.H. Milenkovic: Limited Existence ofThree-Dimensional
Conforma[ Mapping in Robots 59
2. Computational Geometry in Kinematics 69
J.R. Dooley, B. Ravani: Geometric Analysis of Spatial Rigid-Body Dynamics
with Multiple Friction Contacts 71
Q.J. Ge: An Inverse Design Algorithmfor a (;2 Interpolating Spline
Motion 81
A.S. Rao: Geometry of Parallel-Jaw Gripper Grasps in the Plane 91
J. Phillips: Computational Geometry in the Synthesis of Skew
Gear Teeth 101
3. Kinematic Errors and Calibration 109
S. Illiano, G. Iodice, B. Siciliano: A CAD Toolfor Remote Calibration
of Space Station Robotic Test Bed 111
F.C. Park, K Okamura: Kinematic Calibration and the Product of
Exponentials Formula 119
M. Vineze, K.M. Filz, H. Gander, J.P. Prenninger, G. Zeichen: A Systematic
Approach ta Model Arbitrary Non Geometric Kinematic Errors 129
4. Kinematics of Mobile Robots 139
S.V. Sreenivasan, P.K. Dutta, K.J. Waldron: The Wheeled Actively Articulated
Vehicle (WAA V): An Advanced Off-Road Mobility Concept 141
F.D. Boyden, S.A. Velinsky: Limitations of Kinematic Modelsfor Wheeled
Mobile Robots 151
A. Kecskemethy: A Spatial Leg Mechanism With Anthropomorphic Properties
for Ambulatory Robots 161
A. Preumont: An lnvestigation of the Kinematic Control of a Six-Legged
Walking Robot 171
2
5. Kinematic Performance 179
M.L. Husty, J. Angeles: Kinematic Isotropy in 3R Positioning
Manipulators 181
J. Rastegar, S.Z. Zhang, K. Kazerouninan: An Object Shape Dependent
Kinematic Manipulability Measure for Path Planning and
Shape Optimization 191
B. Imcaoudene, C.M. Gosselin: Application of Dexterity Indices to Spatial
Articulated Hands 201
N.P. Belfiore, E.Pennestri: Characterization of Kinematic and Static
Performances of Robotic Geared Wrists 209
6. Kinematics in Control 219
K.S. Chang, O. Khatib: A Dynamically Consistent Strategy for Manipulator
Controlat Singularities 221
S.J. Lorenc, M.M. Stanisic: Third-Order Control of a Planar System
Tracking Constant Curvature Paths 229
F. Boyer, P. Coiffet: Control of Manipulators With Flexible Joints
and Links by Non Linear Inversion, Modal Damping and
Joints Stiffening 239
A. Ait Mohamed, C. Chevallereau: Inverse Kinematic Solution and Mixed
Control Law for Redundant Robot in the Cartesian Space 249
7. Force and Elasticity Analysis 259
P. Dietmaier: An Inverse Force Analysis of a Spatial Three-Spring
System 261
Y. Bouffard-Vercelli, P. Dauchez, F. Pierrot: A Two-Arm Robot Can Be
Stronger Than Two Arms- Experiments on Optimal Force
Distribution in Two-Arm Robot 271
J. Lenarcic: Minimum Joint Torque Configurations of Planar Multiple-Link
Manipulator 281
8. Inverse Kinematics 289
F. Thomas, C. Torras: Positionalinverse Kinematic Problems in T'x,JK"
Solved in 'J'2!n+m) 291
R. Featherstone: Explicit Modelling of General Task Spaces for Inverse
Kinematics 301
W. Khalil, D. Murareci: On the General Solution of the Inverse Kinematics
of Six-Degrees-of-Freedom Manipulators 309
P. Chiacchio, S. Chiaverini: Coping with Joint Velocity Limits in First-Order
Inverse Kinematics Algorithms 319
M.H. Ang, Jr.: Hybrid Position-Orientation Decoupling in Robot
Manipulators 329
C. Bidard: Dual Basis of Screw-Vectors for Inverse Kinestatic Problems
in Robotics 339
3
9. Kinematic Design 349
S.J. Remis, M.M. Stani§it: A Comparison of Two Minimally-Singular
Articulated Arm-Subassemblies 351
V. Hayward, J. Choksi, G. Lanvin, C. Ramstein: Design and MultiObjective
Optimization of a Linkage for a Haptic Inteiface 359
Y.J. Ou, L.W.Tsai: Design of a Three-dofTendon-driven Manipulator
with the Characteristics of Equal Maximum Tensions 369
G. Quaglia, M. Sodi: Spherical3 d.o.f. Geared Wrist with no Aligned
Singularity 379
10. Kinematic Analysis 389
E. Celaya: ls There a Most General Kinematic Chain? 391
I.A. Parkin: Zero-Magnitude Screws in a 3-System of Finite Displacement
&n~ ~1
E.A. Dijksman: True Straight-line Linkages Having a Rectilinear
Translating Bar 411
K. Dobrovodsky: On the Reduction of Parameters in Kinematic Equations 421
11. Parallel Manipulators 427
C. Innocenti, V. Parenti-Castelli: Symbolic-Form Forward Kinematics
of a 5-4 Fully-Parallel Manipulator 429
L. Tancredi, J.P. Merlet: Evaluation of the Errors When Solving the Direct
Kinematics of Parallel Manipulators With Extra Sensors 439
M.L. Husty, P. Zsombor-Murray: A Special Type of Singular
Stewart-Gough Platform 449
M. Griffis, C. Crane, J. Duffy: A Smart Kinestatic Interactive Platform 459
12. Task and Motion Planning 465
P. Alison, M.J. Gilmartin, P. Urwin: Strategic Collision A voidance of
Two Robot Arms in the Same Work Cell 461
A.C. Nearchou, N.A. Aspragathos: A Collision-Detection Scheme Based on
Convex-Hulls Concept for Generating Kinematically Feasible
Robot Trajectories 471
F. Valero, J.I. Cuadrado, V. Mata, M. Ceccarelli: Collision-Avoidance
Robot Path Planning Using Fully Cartesian Coordinates 485
P. Dietmaier, J.M. McCarthy: Planning Grasp Points and Base Locations
of Single Robots and Cooperating Robot Systems 495
A. Ude, R. Dillmann: Vision-Based Robot Path Planning 505
Author Index 513
Introduction
B.Roth
Computational Advances in Robot Kinematics
Computational Advances in Robot Kinematics
BemardRoth
Department of Mechanical Engineering
Stanford University
Stanford, CA 94305-4021, USA
Abstract - This paper presents an overview of the current state-of-the-art in solving the sets of
nonlinear equations which arise in robot kinematics. It reviews some recent results and the history
and fundamental concepts of the most widely used computational methods. The paper deals mainly
with equations with numerica! coefficients, since for such equations methods have been developed
which, in principle, will allow for the determination of ali solutions.
1. lntroduction
Computations arise in robot kinematics in connection with the analysis, design and
control of robot devices. The computations that are usually considered tobe interesting, rather
than mundane, are the ones which involve sets of nonlinear equations. This paper deals with
the solution of sets of nonlinear equations which arise in robot kinematics. It reviews recent
advances in numerica! methods applied to the solution of problems in robot kinematics, and
assess the methods' past achievements, current utility and fu ture potential.
The basic kinematic equations come from either loop closure equations or joint constraint
equations. In either case the results are inherently nonlinear, since kinematic joints and
constraints lead to mathematical descriptions in terms of trigonometric functions and their
products. Interestingly, it is the variables themselves, and not their derivatives, that cause the
nonlinearities. In kinematics, the derivatives of the motion variables are inherently linear.
This fact accounts for the reason that, computationally, it is much easier to study a robotic
device's velocities, accelerations and force/torque transmissions ata given position than it is
to determine the position itself.
From the beginning, it was clear to researchers that the problems associated with
determining the position kinematics were the most challenging from a computational point of
view. The position kinematics problems divide into easy and hard ones. In general the easy
problems are the ones which have one or two solutions, while the hard ones involve four or
more solutions. For the easy ones the only interesting questions have to do with minimizing
computer time; we will not discuss such questions here. The hard problems are the inverse
kinematics of series chains, the direct kinematics of the in-parallel chains, and both the direct
and inverse kinematics of some hybrid chains. There are also design problems in robot
kinematics that are hard in the sense that they involve finding multiple solutions, since they
are described by sets of nonlinear equations.
This paper touches on several of the basic issues involved in solving the hard problems.
Primarily, the paper reviews the use of continuation and elimination methods. It then
provides a summery of the stat~f-the-art in solving the (hard) robot position kinematics
problems.
7
A. J. Lenareic and B. B. Ravani (eds.), Advances in Robot Kinematics and Computationed Geometry, 7-16.
© 1994 Kluwer Academic Publishers.