SpringerBriefs in Mathematics

Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning

Authors: Jean, Frédéric

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  • Provides recent results and state-of-the-art in nonholonomic motion planning
  • Includes the description of a complete algorithm
  • It is a crash course on first-order theory in sub-Riemannian geometry
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  • ISBN 978-3-319-08690-3
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About this book

Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.

Reviews

“The main objective of the book under review is to introduce the readers to nonholonomic systems from the point of view of control theory. … the book is a concise survey of the methods for motion planning of nonholonomic control systems by means of nilpotent approximation. It contains both the theoretical background and the explicit computational algorithms for solving this problem.” (I. Zelenko, Bulletin of the American Mathematical Society, Vol. 53 (1), January, 2016)

“This book is nicely done and provides an introduction to the motion planning problem and its associated mathematical theory that should be beneficial to theorists in nonlinear control theory. The exposition is concise, but at the same time clear and carefully developed.” (Kevin A. Grasse, Mathematical Reviews, August, 2015)


Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-08690-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-08689-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-08690-3
DOI
10.1007/978-3-319-08690-3
Softcover ISBN
978-3-319-08689-7
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 104
Number of Illustrations
1 illustrations in colour
Topics