🤖 AI Summary
In multi-agent path planning within obstacle-populated planar environments, simultaneously achieving homotopy-class awareness and global optimality remains challenging.
Method: This paper introduces Dynnikov coordinates—previously unexplored in this domain—to explicitly model homotopy classes and generate multiple topologically distinct solutions, ensuring completeness. Our framework integrates Dynnikov coordinate representation, a modified priority-based planning strategy, and continuous trajectory optimization subject to homotopy-class constraints.
Contribution/Results: Compared with baseline methods, our approach significantly improves computational efficiency while effectively escaping local optima. Experiments demonstrate its capability to produce cooperative trajectories with high topological diversity and reduced path cost. The method establishes a novel paradigm for homotopy-aware multi-agent motion planning, advancing both theoretical expressiveness and practical solution quality in constrained planar environments.
📝 Abstract
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.