论文标题
在里曼尼亚语中，避免障碍问题的对称性减少
Reduction by Symmetry in Obstacle Avoidance Problems on Riemannian Manifolds
论文作者
论文摘要
本文研究了通过对称性避免障碍物问题的对称性的减少。在具有剩余的不变度量的谎言组的情况下，我们得出了减少的必要条件，并通过考虑以谎言组水平束上的连接而编写的替代变异问题，以实现其相应的riemannian同质空间。许多特殊情况可以详细研究可以显式计算障碍潜力的特殊情况，并且这些想法适用于以$（3）$和单位球体$ s^2 $进化的刚体避免障碍的任务。
This paper studies the reduction by symmetry of a variational obstacle avoidance problem. We derive the reduced necessary conditions in the case of Lie groups endowed with a left-invariant metric, and for its corresponding Riemannian homogeneous spaces by considering an alternative variational problem written in terms of a connection on the horizontal bundle of the Lie group. A number of special cases where the obstacle avoidance potential can be computed explicitly are studied in detail, and these ideas are applied to the obstacle avoidance task for a rigid body evolving on SO$(3)$ and for the unit sphere $S^2$.
