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On complexity and motion planning for co-rank one sub-Riemannian metrics

Published online by Cambridge University Press:  15 October 2004

Cutberto Romero-Meléndez ,
Jean Paul Gauthier  and
Felipe Monroy-Pérez
Cutberto Romero-Meléndez
Affiliation:
Laboratoire d'Analyse Appliquée et Optimisation, Département de Mathématiques, Université de Bourgogne, 21078 Dijon, France.
Jean Paul Gauthier
Affiliation:
Departement Maths, Lab. LE2I, UMR CNRS 5158, Université de Bourgogne, BP 47870, 21078 Dijon, France.
Felipe Monroy-Pérez
Affiliation:
Basic Sciences Department, UAM-Azcapotzalco, 02200, México D.F., Mexico; fmp@correo.azc.uam.mx.
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Abstract

In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [CITE]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C ∞ case, we study some non-generic generalizations in the analytic case.

Keywords

Motion planning problemmetric complexitynormal formsasymptotic optimal synthesis.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 4 , October 2004 , pp. 634 - 655
Copyright
© EDP Sciences, SMAI, 2004

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