Reduction of Necessary Conditions for the Variational Collision Avoidance Problem

Jacob R. Goodman; Leonardo J. Colombo

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arXiv · 2310.18389

Reduction of Necessary Conditions for the Variational Collision Avoidance Problem

Jacob R. Goodman·Leonardo J. Colombo

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Abstract

In this work, we study the reduction by a Lie group of symmetries of variational collision avoidance probelms of multiple agents evolving on a Riemannian manifold and derive necessary conditions for the reduced extremals. The problem consists of finding non-intersecting trajectories of a given number of agents, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the velocity, covariant acceleration and an artificial potential function used to prevent collision among the agents.

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Jacob R. Goodman, Leonardo J. Colombo. 2023-10-27. Reduction of Necessary Conditions for the Variational Collision Avoidance Problem. https://arxiv.org/abs/2310.18389

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