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

Autor:	F. Monroy-Pérez, Jean-Paul Gauthier, Cutberto Romero-Meléndez
Rok vydání:	2004
Předmět:	Combinatorics Algebra Computational Mathematics Control and Optimization Rank (linear algebra) Control and Systems Engineering Metric (mathematics) Motion planning Construct (python library) Mathematics
Zdroj:	ESAIM: Control, Optimisation and Calculus of Variations. 10:634-655
ISSN:	1262-3377 1292-8119
DOI:	10.1051/cocv:2004024
Popis:	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 (10,11)), 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::70faced8ddb8152302e8badc78a7af5d https://doi.org/10.1051/cocv:2004024 Zobrazit plný text záznamu