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

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Mathematics, Geometry, Reference & Language, Reference
Cover of the book Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning by Frédéric Jean, Springer International Publishing
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Author: Frédéric Jean ISBN: 9783319086903
Publisher: Springer International Publishing Publication: July 17, 2014
Imprint: Springer Language: English
Author: Frédéric Jean
ISBN: 9783319086903
Publisher: Springer International Publishing
Publication: July 17, 2014
Imprint: Springer
Language: English

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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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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