## Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion PlanningNonholonomic 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 | |

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 |

### Other editions - View all

Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning Frédéric Jean No preview available - 2014 |

Control of Nonholonomic Systems: From Sub-Riemannian Geometry to Motion Planning Frédéric Jean No preview available - 2014 |

### Common terms and phrases

adapted frame algorithm associated Ball-Box Theorem brackets Campbell-Hausdorff formula canonical coordinates canonical form Carnot-Carathéodory space Chitour choose components compute consequence constant construction continuous varying system control system converge deﬁned Deﬁnition degree of nonholonomy denote Desingularization diffeomorphism dimension Euclidean exist ﬁnite ﬁrst first-order frequencies function global growth vector Hausdorff Hausdorff measures implies inequality integer iterated Lemma Lie brackets Lie group local diffeomorphism manifold mapping AppSteer metric space metric tangent space motion planning problem neighbourhood nilpotent approximation nilpotent Lie algebra nilpotent systems nonholonomic derivatives nonholonomic order nonholonomic system nonzero obtain ordp ordp(f polynomial privileged coordinates proof real number regular point Riemannian distance Riemannian metric satisﬁes Sect sequence singular point smooth solution SpringerBriefs in Mathematics steering law sub-Riemannian distance sub-Riemannian geometry sub-Riemannian manifolds subset system of privileged tangent space trajectory of 1.3 vector ﬁelds vector ﬁelds X1 weighted degree xfinal xinitial