Geometrical Methods in Robotics

1. Front Matter

   Pages i-xiii

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2. Introduction

   • J. M. Selig

   Pages 1-7

3. Lie Groups

   • J. M. Selig

   Pages 9-24

4. Subgroups

   • J. M. Selig

   Pages 25-40

5. Lie Algebra

   • J. M. Selig

   Pages 41-60

6. A Little Kinematics

   • J. M. Selig

   Pages 61-79

7. Line Geometry

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   Pages 81-100

8. Representation Theory

   • J. M. Selig

   Pages 101-121

9. Screw Systems

   • J. M. Selig

   Pages 123-148

10. Clifford Algebra

    • J. M. Selig

    Pages 149-169

11. The Study Quadric

    • J. M. Selig

    Pages 171-191

12. Statics

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    Pages 193-207

13. Dynamics

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    Pages 209-231

14. Differential Geometry

    • J. M. Selig

    Pages 233-249

15. Back Matter

    Pages 251-269

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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.

• Grad
• computing
• differential geometry
• engineering
• kinematics
• mathematics
• robot
• robotics

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

• School of Electrical, Electronic, and Information Engineering, South Bank University, London, UK

  J. M. Selig

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