Variational collision and obstacle avoidance of multi-agent systems on Riemannian manifolds

TL;DR

This paper develops a variational framework for planning collision-free trajectories for multi-agent systems on Riemannian manifolds, incorporating obstacle avoidance and inter-agent collision prevention.

Contribution

It introduces a novel variational approach to multi-agent path planning on Riemannian manifolds, accounting for collision avoidance through energy minimization.

Findings

Successfully applied to planar rigid body examples.

Extended to agents on a spherical manifold.

Demonstrated effective collision and obstacle avoidance.

Abstract

In this paper we study a path planning problem from a variational approach to collision and obstacle avoidance for multi-agent systems evolving on a Riemannian manifold. The problem consists of finding non-intersecting trajectories between the agent and prescribed obstacles on the workspace, 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 with the obstacles and among the agents. We apply the results to examples of a planar rigid body, and collision and obstacle avoidance for agents evolving on a sphere.