Local Minimizers for Variational Obstacle Avoidance on Riemannian manifolds

2022/01/12 by Jacob R. Goodman, Goodman, Jacob R.
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2201.04395

openalex publication_date 2022/01/12 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

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.

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