Homotopy-Aware Multi-Agent Path Planning on Plane

We propose an efficient framework using Dynnikov coordinates for homotopy-aware multi-agent path planning in planar domains that may contain obstacles. We developed a method for generating multiple homotopically distinct solutions for the multi-agent path planning problem in planar domains by combining our framework with revised prioritized planning and proved its completeness under specific assumptions. Experimentally, we demonstrated that our method is significantly faster than a method without Dynnikov coordinates. We also confirmed experimentally that homotopy-aware planning contributes to avoiding locally optimal solutions when searching for low-cost trajectories for a swarm of agents in a continuous environment.