Control of nonholonomic systems from sub-Riemannian geometry to motion planning

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, th...

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Detalles Bibliográficos
Autor principal: Jean, Frédéric
Lenguaje:eng
Publicado: Springer 2014
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-08690-3
http://cds.cern.ch/record/1748042
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author Jean, Frédéric
author_facet Jean, Frédéric
author_sort Jean, Frédéric
collection CERN
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.
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spelling cern-17480422021-04-21T20:55:48Zdoi:10.1007/978-3-319-08690-3http://cds.cern.ch/record/1748042engJean, FrédéricControl of nonholonomic systems from sub-Riemannian geometry to motion planningMathematical Physics and MathematicsNonholonomic 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.Springeroai:cds.cern.ch:17480422014
spellingShingle Mathematical Physics and Mathematics
Jean, Frédéric
Control of nonholonomic systems from sub-Riemannian geometry to motion planning
title Control of nonholonomic systems from sub-Riemannian geometry to motion planning
title_full Control of nonholonomic systems from sub-Riemannian geometry to motion planning
title_fullStr Control of nonholonomic systems from sub-Riemannian geometry to motion planning
title_full_unstemmed Control of nonholonomic systems from sub-Riemannian geometry to motion planning
title_short Control of nonholonomic systems from sub-Riemannian geometry to motion planning
title_sort control of nonholonomic systems from sub-riemannian geometry to motion planning
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-08690-3
http://cds.cern.ch/record/1748042
work_keys_str_mv AT jeanfrederic controlofnonholonomicsystemsfromsubriemanniangeometrytomotionplanning

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