In this paper, we study variational point-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 an static obstacle given by a point in the manifold, among a set of admissible curves. We derive the dynamical equations for stationary paths of the variational problem, in particular on compact connected Lie groups and Riemannian symmetric spaces. Numerical examples are presented to illustrate the proposed method.

中文翻译：

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黎曼流形上的变分点障碍规避

在本文中，我们研究了完整的黎曼流形上的变分点障碍避免问题。问题包括最小化取决于速度的能量函数，协变加速度和排斥势函数，这些函数用于避免在一组允许曲线中的歧管中的点给定的静态障碍。我们推导了变分问题平稳路径的动力学方程，特别是在紧连接的李群和黎曼对称空间上。数值例子说明了所提出的方法。