XXVI International Fall Workshop on Geometry and Physics

Braga, 4-7 September 2017

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. In particular, we study the case when the workspace is a Lie group endowed with a left-invariant Riemannian metric. We apply the results to the obstacle avoidance problem of a planar rigid body and a unicycle.