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

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Springer, Jul 17, 2014 - Science - 104 pages
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.
 

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Contents

1 Geometry of Nonholonomic Systems
1
2 FirstOrder Theory
14
3 Nonholonomic Motion Planning
59
Appendix A Composition of Flows of Vector Fields
93
Appendix B The Different Systems of Privileged Coordinates
99
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