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.
Rezensionen / Stimmen
"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)
Produkt-Info
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
1
1 farbige Abbildung
X, 104 p. 1 illus. in color.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 7 mm
Gewicht
ISBN-13
978-3-319-08689-7 (9783319086897)
DOI
10.1007/978-3-319-08690-3
Schweitzer Klassifikation
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.
