Local minimizers for variational obstacle avoidance on Riemannian manifolds

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 biJacobi fields and biconjugate points and present necessary and sufficient conditions for optimality. Local minimizers of the action functional are divided into two categories—called &-local minimizers and Ω-local minimizers—and subsequently classified, with local uniqueness results obtained in both cases.

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