Monographs in Computer Science

Geometrical Methods in Robotics

Authors: Selig, J.M.

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About this Textbook

The main aim of this book is to introduce Lie groups and allied algebraic and geometric concepts to a robotics audience. These topics seem to be quite fashionable at the moment, but most of the robotics books that touch on these topics tend to treat Lie groups as little more than a fancy notation. I hope to show the power and elegance of these methods as they apply to problems in robotics. A subsidiary aim of the book is to reintroduce some old ideas by describing them in modem notation, particularly Study's Quadric-a description of the group of rigid motions in three dimensions as an algebraic variety (well, actually an open subset in an algebraic variety)-as well as some of the less well known aspects of Ball's theory of screws. In the first four chapters, a careful exposition of the theory of Lie groups and their Lie algebras is given. Except for the simplest examples, all examples used to illustrate these ideas are taken from robotics. So, unlike most standard texts on Lie groups, emphasis is placed on a group that is not semi-simple-the group of proper Euclidean motions in three dimensions. In particular, the continuous subgroups of this group are found, and the elements of its Lie algebra are identified with the surfaces of the lower Reuleaux pairs. These surfaces were first identified by Reuleaux in the latter half of the 19th century.

Reviews

"Where rigorous analysis is needed, this book will certainly be a standard work of reference for a long time to come..." - Robotica

Table of contents (13 chapters)

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4757-2484-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Geometrical Methods in Robotics
Authors
Series Title
Monographs in Computer Science
Copyright
1996
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-2484-4
DOI
10.1007/978-1-4757-2484-4
Series ISSN
0172-603X
Edition Number
1
Number of Pages
XIV, 269
Number of Illustrations and Tables
1 b/w illustrations
Topics