Variational point-obstacle avoidance on Riemannian manifolds
Systems and Control
2019-09-30 v1 Systems and Control
Optimization and Control
Abstract
In this letter we study variational obstacle avoidance problems on complete Riemannian manifolds. The problem consists of minimizing an energy functional depending on the velocity, covariant acceleration and a repulsive potential function used to avoid a static obstacle on the manifold, among a set of admissible curves. We derive the dynamical equations for extrema of the variational problem, in particular on compact connected Lie groups and Riemannian symmetric spaces. Numerical examples are presented to illustrate the proposed method.
Cite
@article{arxiv.1909.12321,
title = {Variational point-obstacle avoidance on Riemannian manifolds},
author = {Anthony Bloch and Margarida Camarinha and Leonardo Colombo},
journal= {arXiv preprint arXiv:1909.12321},
year = {2019}
}