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.

翻译：我们提出了一种利用Dynnikov坐标在平面中进行同伦感知多智能体路径规划的高效框架。通过将该框架与改进的优先级规划相结合，我们开发了一种生成平面多智能体路径规划问题中同伦不同解的方法，并在特定假设下证明了该方法在栅格世界中的完备性。实验表明，我们的方法在智能体数量方面具有可扩展性。我们还通过实验证实了同伦感知的实用性——我们的方法生成同伦不同解的能力有助于为智能体群规划低成本轨迹。