Variational point-obstacle avoidance on Riemannian manifolds

Anthony Bloch; Margarida Camarinha; Leonardo Colombo

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arXiv · 1909.12321

Variational point-obstacle avoidance on Riemannian manifolds

Anthony Bloch·Margarida Camarinha·Leonardo Colombo

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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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Anthony Bloch, Margarida Camarinha, Leonardo Colombo. 2019-09-26. Variational point-obstacle avoidance on Riemannian manifolds. https://arxiv.org/abs/1909.12321

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