论文标题
当地的最小化器，以避免利马尼亚歧管的差异障碍
Local Minimizers for Variational Obstacle Avoidance on Riemannian manifolds
论文作者
论文摘要
本文研究了完整的Riemannian歧管上的各种障碍物避免问题。也就是说，我们在一组可接受的曲线中最小化了动作功能，该曲线取决于用于避免障碍的人造潜在功能。特别是，我们概括了双雅各布田和双缀合物的理论，并提出了最佳性的必要条件和足够的条件。动作功能的局部最小化器分为两类，然后分类，在两种情况下都获得了局部唯一性结果。
This paper studies a variational obstacle avoidance problem on complete Riemannian manifolds. That is, we minimize an action functional, among a set of admissible curves, which depends on an artificial potential function used to avoid obstacles. In particular, we generalize the theory of bi-Jacobi fields and biconjugate points and present necessary and sufficient conditions for optimality. Local minimizers of the action functional are divided into two categories and subsequently classified, with local uniqueness results obtained in both cases.
