Collision-Free Trajectory Planning for Multi-Robot Systems Under Stochastic Uncertainty

This paper presents a trajectory planning approach for multi-robot systems that focuses on collision avoidance in the presence of state estimation noises and motion disturbances. We utilize the MINVO basis to construct minimal-volume polyhedrons that enclose the predicted trajectories of surrounding robots and obstacles, thereby improving collision avoidance. To account for uncertainties, we introduce a method for converting probabilistic collision avoidance constraints into deterministic ones, using the mean and covariance of the robot states to enhance system robustness. Additionally, we propose a hierarchical strategy that integrates global path planning with decentralized local optimization, where a decentralized model predictive control (MPC) framework is employed to generate locally optimal trajectories. Simulation results demonstrate that our method ensures robust and safe navigation, significantly outperforming traditional approaches.