Complexity of control-affine motion planning

Abstract : In this paper we study the complexity of the motion planning problem for control- affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time- rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quanti- tative estimates on the cost of stabilizing the system near a non-equilibrium point of the drift.
Type de document :
Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.816-844. <10.1137/130950793>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00909748
Contributeur : Dario Prandi <>
Soumis le : mardi 26 novembre 2013 - 17:41:48
Dernière modification le : vendredi 17 février 2017 - 16:13:47

Identifiants

Citation

Frédéric Jean, Dario Prandi. Complexity of control-affine motion planning. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.816-844. <10.1137/130950793>. <hal-00909748>

Partager

Métriques

Consultations de la notice

393