Reduction of Necessary Conditions for the Variational Collision Avoidance Problem
Optimization and Control
2023-10-31 v1 Systems and Control
Systems and Control
Differential Geometry
Dynamical Systems
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.
Cite
@article{arxiv.2310.18389,
title = {Reduction of Necessary Conditions for the Variational Collision Avoidance Problem},
author = {Jacob R. Goodman and Leonardo J. Colombo},
journal= {arXiv preprint arXiv:2310.18389},
year = {2023}
}
Comments
7 pages, 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2024. arXiv admin note: text overlap with arXiv:2310.18057, arXiv:2207.13574