We propose an efficient framework using the Dehornoy order 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 under specific assumptions. Experimentally, we demonstrated that the runtime of our method grows approximately quintically with 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.

翻译：我们提出了一种基于Dehornoy序的高效框架，用于在平面中实现同伦感知的多智能体路径规划。通过将该框架与改进的优先级规划相结合，我们开发了一种在平面上生成拓扑不同解的多智能体路径规划方法，并在特定假设下证明了其完备性。实验表明，我们的方法运行时间随智能体数量呈约五次方增长。我们还通过实验验证了同伦感知的有效性：该方法生成的拓扑不同解有助于为智能体集群规划低成本轨迹。