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 multiple 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 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.

翻译：我们提出了一种利用Dynnikov坐标的高效框架，用于平面上的同伦感知多智能体路径规划。我们开发了一种方法，通过将该框架与改进的优先级规划相结合，生成平面上多智能体路径规划问题的多个同伦类不同的解，并在特定假设下证明了该方法在网格世界中的完备性。实验表明，我们的方法在智能体数量方面具有良好的可扩展性。我们还通过实验证实，在连续环境中为智能体群体搜索低成本轨迹时，同伦感知规划有助于避免陷入局部最优解。