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

Erscheinungsjahr 2014
ISBN: 978-3-319-08689-7
Verlag: Springer

Buch, Englisch, 104 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1883 g

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Jean, Frédéric

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik

Inhaltsverzeichnis

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.