Variational obstacle avoidance problem on Riemannian manifolds

Autor:	Bloch, Anthony, Camarinha, Margarida, Colombo, Leonardo
Rok vydání:	2017
Předmět:	Mathematics - Optimization and Control Computer Science - Systems and Control Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy functional depending on the velocity and covariant acceleration, among a set of admissible curves, and also depending on a navigation function used to avoid an obstacle on the workspace, a Riemannian manifold. We study two different scenarios, a general one on a Riemannian manifold and, a sub-Riemannian problem. By introducing a left-invariant metric on a Lie group, we also study the variational obstacle avoidance problem on a Lie group. We apply the results to the obstacle avoidance problem of a planar rigid body and an unicycle. Comment: Paper submitted to IEEE CDC 2017 - Melbourne, Australia. This version contain a slightly modification in the computations for the application given in section 4, part B
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.04703 Zobrazit plný text záznamu View this record from Arxiv