Reduction by Symmetry in Obstacle Avoidance Problems on Riemannian Manifolds

Autor:	Goodman, Jacob R., Colombo, Leonardo J.
Rok vydání:	2022
Předmět:	Mathematics - Optimization and Control Electrical Engineering and Systems Science - Systems and Control Mathematics - Dynamical Systems Mathematics - Metric Geometry
Druh dokumentu:	Working Paper
Popis:	This paper studies the reduction by symmetry of a variational obstacle avoidance problem. We derive the reduced necessary conditions in the case of Lie groups endowed with a left-invariant metric, and for its corresponding Riemannian homogeneous spaces by considering an alternative variational problem written in terms of a connection on the horizontal bundle of the Lie group. A number of special cases where the obstacle avoidance potential can be computed explicitly are studied in detail, and these ideas are applied to the obstacle avoidance task for a rigid body evolving on SO$(3)$ and for the unit sphere $S^2$. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.13574 Zobrazit plný text záznamu View this record from Arxiv