Multi-Robot Collision Avoidance with Probabilistic Mahalanobis Distance Constraints

Abstract

In multi-robot systems operating under uncertainty, maintaining safe inter-robot distances while avoiding collisions with obstacles is crucial. Although chance-constrained methods have been widely adopted to handle such uncertainties, existing approaches often exhibit conservatism due to their reliance on linearized integration regions. To address this limitation, this paper introduces a novel probabilistic Mahalanobis distance constraint that enables tighter reformulations of collision avoidance constraints both between robots and between robots and obstacles. These constraints are integrated into a Model Predictive Path Integral (MPPI) control framework for efficient trajectory optimization. The effectiveness of the proposed method is validated through comprehensive simulations comparing it against state-of-the-art approaches, as well as through real-world experiments conducted across various scenarios.