Homotopy-Aware Multi-Agent Path Planning in Plane

We propose an efficient framework using the Dynnikov coordinates for homotopy-aware multi-agent path planning in the plane. We developed a method to generate homotopically distinct solutions of multi-agent path planning problem in the plane by combining our framework with revised prioritized planning and proved its completeness in the grid world under specific assumptions. Experimentally, we demonstrated the scalability of our method for the number of agents. We also confirmed the usefulness of homotopy-awareness by showing experimentally that generation of homotopically distinct solutions by our method contributes to planning low-cost trajectories for a swarm of agents.