Multi-Robot Collision Avoidance with Probabilistic Mahalanobis Distance Constraints
Zhaodong Chen, Dingfu Liu, Chuqing Feng, Yunxiao Shan
AI summary
Problem
Existing chance-constrained collision avoidance methods rely on linearized integration regions, causing unnecessary conservatism and computational inefficiency in multi-robot systems operating under measurement uncertainty.
Approach
The authors derive a tighter deterministic reformulation of probabilistic collision constraints using Gaussian covariance properties and embed them as soft penalties within a Model Predictive Path Integral (MPPI) framework for efficient trajectory optimization.
Key results
- Novel probabilistic Mahalanobis distance constraint formulation
- Tighter collision boundary approximation outperforming linear chance constraints
- Seamless integration of probabilistic constraints as soft penalties in MPPI
- Validated via simulations and real-world experiments across static, dynamic, and symmetrical scenarios
Why it matters
Enables safer and more efficient multi-robot navigation in uncertain, real-world environments by reducing overly cautious planning while maintaining rigorous probabilistic safety guarantees.
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 dis- tance 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. The code and video of our experiment could be available at the https://github.com/CreedonChan/MRCA-PMDC.