2021/04/09 by Jacob R. Goodman, Goodman, Jacob R., Leonardo Colombo +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #FOS: Electrical engineering #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC) #Robotic Path Planning Algorithms #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2104.04285
openalex publication_date 2021/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies variational collision avoidance problems for multi-agents systems on complete Riemannian manifolds. That is, we minimize an energy functional, among a set of admissible curves, which depends on an artificial potential function used to avoid collision between the agents. We show the global existence of minimizers to the variational problem and we provide conditions under which it is possible to ensure that agents will avoid collision within some desired tolerance. We also study the problem where trajectories are constrained to have uniform bounds on the derivatives, and derive alternate safety conditions for collision avoidance in terms of these bounds - even in the case where the artificial potential is not sufficiently regular to ensure existence of global minimizers.