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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.
List of contents
1 Geometry of nonholonomic systems.- 2 First-order theory.- 3 Nonholonomic motion planning.- 4 Appendix A: Composition of flows of vector fields.- 5 Appendix B: The different systems of privileged coordinates.
Summary
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.
Additional text
“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)
Report
"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)
