Variational point-obstacle avoidance on Riemannian manifolds

2019/09/26 by Anthony Bloch, Bloch, Anthony, Margarida Camarinha +3
Computer Science · Engineering · Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC

paper · pdf · doi:10.48550/arxiv.1909.12321

arxiv created 2019/09/26 · arxiv updated 2019/09/30

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.

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