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This paper studies a variational obstacle avoidance problem on completeRiemannian manifolds. That is, we minimize an action functional, among a set ofadmissible curves, which depends on an artificial potential function used toavoid obstacles. In particular, we generalize the theory of bi-Jacobi fieldsand biconjugate points and present necessary and sufficient conditions foroptimality. Local minimizers of the action functional are divided into twocategories and subsequently classified, with local uniqueness results obtainedin both cases.

Local Minimizers for Variational Obstacle Avoidance on Riemannian manifolds