Reduction of Necessary Conditions for the Variational Collision Avoidance Problem

2023/10/27 by Goodman, Jacob R., Colombo, Leonardo J.
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2310.18389

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.

Related

• Variational collision avoidance problems on Riemannian manifolds
• Variational Collision Avoidance on Riemannian Manifolds
• Variational collision and obstacle avoidance of multi-agent systems on\n Riemannian manifolds
• Variational obstacle avoidance problem on Riemannian manifolds
• Variational point-obstacle avoidance on Riemannian manifolds