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

  • Frédéric Jean

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Frédéric Jean
    Pages 1-13
  3. Frédéric Jean
    Pages 15-57
  4. Frédéric Jean
    Pages 59-92
  5. Back Matter
    Pages 93-104

About this book

Introduction

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.

Keywords

Control theory Motion planning Nilpotent systems Nonholonomic systems Sub-Riemannian geometry

Authors and affiliations

  • Frédéric Jean
    • 1
  1. 1.UMAENSTA ParisTechPalaiseauFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-08690-3
  • Copyright Information The Author(s) 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-08689-7
  • Online ISBN 978-3-319-08690-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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