Motion Planning in Dynamic Environments

189 Pages·1991·8.002 MB·English

by  Prof. Dr. Kikuo Fujimura (auth.)

Computer Science Workbench
Editor: Tosiyasu L. Kunii
Computer Science Workbench
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K. Fujimura: Motion Planning in Dynamic Environments. XIII, 178 pp.,
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Kikuo Fujimura
Motion Planning
in Dynamic
Environments
With 85 Figures
Springer-Verlag Tokyo Berlin Heidelberg New York
London Paris Hong Kong Barcelona
PROF. DR. KIKUO FUJIMURA
DepaI tment of Computer and Information Science
The Ohio State University
2036 Neil Avenue Mall
Columbus, OH 43210, USA
Series Editor:
PROF. DR. ToslYASU L. KUNII
Department of Information Science
Faculty of Science
The University of Tokyo
7-3-1 Hongo, Bunkyo-ku
Tokyo, 113 Japan
ISBN-13:978-4-431-68167-0 e-ISBN-13:978-4-431-68165-6
001: 10.1 007/978-4-431-68165-6
© Springer-Verlag Tokyo 1991
Softcover reprint of the hardcover 1s t edition 1991
This work is subject to copyright. All rights are reserved, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of
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and storage in data banks.
The use of registered names, trademarks, etc. in this publication does not imply, even
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Series Preface
Computer Science Workbench is a monograph series which will
provide you with an in-depth working knowledge of current
developments in computer technology. Every volume in this series
will deal with a topic of importance in computer science and
elaborate on how you yourself can build systems related to the
main theme. You will be able to develop a variety of systems,
including computer software tools, computer graphics, computer
animation, database management systems, and computer-aided
design and manufacturing systems. Computer Science Workbench
represents an important new contribution in the field of practical
computer technology.
TOSIYASU L. KUNII
To my parents
Kenjiro and Nori Fujimura
Preface
Motion planning is an area in robotics that has received much
attention recently. Much of the past research focuses on static
environments - various methods have been developed and their
characteristics have been well investigated. Although it is essential
for autonomous intelligent robots to be able to navigate within
dynamic worlds, the problem of motion planning in dynamic
domains is relatively little understood compared with static
problems.
This research monograph is the first book dedicated to
algorithmic and computational aspects of motion planning in
dynamic environments. Chapter 1 is an introduction. Chapter 2
contains a brief survey of motion planning problems and
preliminaries. In Chaps. 3 through 5, various properties of time
minimal motions are derived and proved which are of fundamental
importance in the study of motion planning among dynamic
obstacles. Chapter 6 is independent of the previous three chapters
and treats the problem from a different perspective. Chapter 7
contains an investigation of a challenging problem on distributed
mobile agents.
Research on the subject of this monograph has just begun and
there are many important issues which remain to be investigated.
It is my hope that the research contained in this monograph will
serve as a basis for further studies and motivate more research on
related subjects.
July 1991
Kikuo Fujimura
Acknowledgements
I am grateful to all the people who helped me in writing this
volume at various stages. Special thanks go to Dr. Fran«ois
G. Pin of the Oak Ridge National Laboratory who supported
and encouraged the work. Drs. Reinhold C. Mann, Fred C.
Maienschein, and Robert C. Ward have provided an excellent
research environment at the Oak Ridge National Laboratory,
where completion of this volume was possible.
Some chapters of the monograph are based on my PhD thesis
written at the University of Maryland. I would like to express my
sincere thanks to Professor Hanan Samet, my thesis advisor, for
his support and understanding in my work at the University of
Maryland. I greatly benefited from his detailed comments which
helped me clarify my ideas and present the materials in a suitable
way. Without his help, my thesis could not have been completed.
It has been truly a privilege to work with him.
I am deeply indebted to Professor Azriel Rosenfeld who
proofread my thesis carefully. He gave me technical as well as
stylistic suggestions on nearly all paragraphs of earlier drafts of
my thesis. Professor Gary Knott made keen observations on
my formulations of motion planning problems. Discussions with
Professor David M. Mount were extremely helpful for putting the
problems in a proper perspective. Professors James H. Duncan
and Larry S. Davis also gave me helpful comments.
I received insightful comments from Professors Mickael
Dillencourt and Kenichi Kanatani. They affected the way
I presented the materials in various ways. Drs. Vladimir
Protopopescu, Philip F. Spelt, and Michael A. Unseren gave
me valuable comments on various parts of this monograph.
Dr. Gerard de Saussure read earlier drafts carefully and gave
me many suggestions for improvement. Professor Joseph S. B.
Mitchell provided me with some references. Karen Harber helped
x Acknow ledgements
me in TEX formatting. I discussed motion planning problems
with the following colleagues at the University of Maryland: John
Aloimonos, Anup Basu, John Canning, Jean-Yves Herve, and
Rajeev Sharma.
Professor Tosiyasu L. Kunii of the University of Tokyo
extended to me the opportunity to write this research monograph.
I would like to thank him for his invaluable advice and for being
always supportive of my research in the past.
At the University of Maryland, the research was supported
by the National Science Foundation under Grant IRI-88-02457.
At the Oak Ridge National Laboratory, the work is supported
in part by an appointment to the U.S. Department of Energy
Postgraduate Research Program administered by Oak Ridge
Associated Universities and in part by the Office of Engineering
Research Program, Basic Energy Sciences, of the U.S. Department
of Energy, under contract No. DE-AC05-840R21400 with Martin
Marietta Energy Systems, Inc. The grants are gratefully
acknowledged.
Table of Contents
1 Introduction ............................................................ 1
1.1 Dynamic environments ............................................. 1
1.2 Statement of the problem .......................................... 4
1.3 Scope of the monograph ........................................... 6
2 Background ............................................................ 9
2.1 Stationary obstacles .............................................. 10
2.1.1 Configuration spaces ...................................... 10
2.1.2 Shortest path problems ................................... 12
2.1.3 General problems ......................................... 14
2.2 Dynamic obstacles ............................................... 17
2.2.1 Hardness results .......................................... 17
2.2.2 Space-time formulations ................................... 18
2.2.3 Divide-and-conquere fomulations .......................... 22
2.2.4 Collision avoidance with moving obstacles ................. 22
2.2.5 Collision detection among moving objects ................. 23
2.3 Summary ........................................................ 23
3 Time-Minimal Motion: Basics ....................................... 26
3.1 Introduction ...................................................... 24
3.2 Accessibility graphs ............................................... 27
3.3 Planning and motion ............................................. 31
3.4 Time-minimal motion theorem .................................... 32
3.5 Analysis.................................... . .................... 44
3.6 Discussions ....................................................... 50
3.7 Summary ......................................................... 55
4 Time-Minimal Motion: Applications ............................... 57
4.1 Concave obstacles ................................................ 57
4.2 Convex obstacles ................................................ 59