Homotopy-aware Multi-agent Navigation via Distributed Model Predictive Control

Multi-agent trajectory planning requires ensuring both safety and efficiency, yet deadlocks remain a significant challenge, especially in obstacle-dense environments. Such deadlocks frequently occur when multiple agents attempt to traverse the same long and narrow corridor simultaneously. To address this, we propose a novel distributed trajectory planning framework that bridges the gap between global path and local trajectory cooperation. At the global level, a homotopy-aware optimal path planning algorithm is proposed, which fully leverages the topological structure of the environment. A reference path is chosen from distinct homotopy classes by considering both its spatial and temporal properties, leading to improved coordination among agents globally. At the local level, a model predictive control-based trajectory optimization method is used to generate dynamically feasible and collision-free trajectories. Additionally, an online replanning strategy ensures its adaptability to dynamic environments. Simulations and experiments validate the effectiveness of our approach in mitigating deadlocks. Ablation studies demonstrate that by incorporating time-aware homotopic properties into the underlying global paths, our method can significantly reduce deadlocks and improve the average success rate from 4%-13% to over 90% in randomly generated dense scenarios.