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Geometrical Methods in Robotics

  • J. M. Selig

Part of the Monographs in Computer Science book series (MCS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. J. M. Selig
    Pages 1-7
  3. J. M. Selig
    Pages 9-24
  4. J. M. Selig
    Pages 25-40
  5. J. M. Selig
    Pages 41-60
  6. J. M. Selig
    Pages 61-79
  7. J. M. Selig
    Pages 81-100
  8. J. M. Selig
    Pages 101-121
  9. J. M. Selig
    Pages 123-148
  10. J. M. Selig
    Pages 149-169
  11. J. M. Selig
    Pages 171-191
  12. J. M. Selig
    Pages 193-207
  13. J. M. Selig
    Pages 209-231
  14. J. M. Selig
    Pages 233-249
  15. Back Matter
    Pages 251-269

About this book

Introduction

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.

Keywords

Grad computing differential geometry engineering kinematics mathematics robot robotics

Authors and affiliations

  • J. M. Selig
    • 1
  1. 1.School of Electrical, Electronic, and Information EngineeringSouth Bank UniversityLondonUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2484-4
  • Copyright Information Springer-Verlag New York 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-2486-8
  • Online ISBN 978-1-4757-2484-4
  • Series Print ISSN 0172-603X
  • Buy this book on publisher's site
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