Volume 10, Number 4, October 2004
|Page(s)||634 - 655|
|Published online||15 October 2004|
On complexity and motion planning for co-rank one sub-Riemannian metrics
Laboratoire d'Analyse Appliquée et Optimisation,
Département de Mathématiques, Université de Bourgogne, 21078
2 Departement Maths, Lab. LE2I, UMR CNRS 5158, Université de Bourgogne, BP 47870, 21078 Dijon, France.
3 Basic Sciences Department, UAM-Azcapotzalco, 02200, México D.F., Mexico; firstname.lastname@example.org.
Revised: 26 February 2004
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.
Mathematics Subject Classification: 34H05 / 49J15 / 53C17
Key words: Motion planning problem / metric complexity / normal forms / asymptotic optimal synthesis.
© EDP Sciences, SMAI, 2004
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