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

Description: Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning by Frédéric Jean 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Back Cover 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. Table 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. Review "The main objective of the book under review is tointroduce the readers to nonholonomic systems from the point of view of controltheory. … the book is a concise survey of the methods for motion planning ofnonholonomic control systems by means of nilpotent approximation. It containsboth the theoretical background and the explicit computational algorithms forsolving this problem." (I. Zelenko, Bulletin of the American MathematicalSociety, 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) Review Quote "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) Feature 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 Details ISBN3319086898 Year 2014 ISBN-10 3319086898 ISBN-13 9783319086897 Format Paperback Short Title CONTROL OF NONHOLONOMIC SYSTEM Language English Media Book DEWEY 004 Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Edition 2014th Illustrations 1 Illustrations, color; X, 104 p. 1 illus. in color. Pages 104 DOI 10.1007/978-3-319-08690-3 Author Frédéric Jean Publisher Springer International Publishing AG Edition Description 2014 ed. Series SpringerBriefs in Mathematics Publication Date 2014-07-30 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96291181;

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