Multi-Robot Trajectory Planning under Stochastic Uncertainty via Linearized Chance Constraints

This paper presents a probabilistic trajectory planning framework for multi-robot systems operating under stochastic uncertainty. To capture the uncertainty induced by state estimation errors and motion disturbances, we model the system noise as Gaussian distributions and impose chance constraints to ensure collision avoidance. To guarantee tractability and enable real-time performance, we adopt a fixed risk allocation strategy that decomposes joint chance constraint into individual constraints with predefined risk bounds. These probabilistic constraints are linearized into closed-form deterministic inequalities using Gaussian properties, allowing the original problem to be reformulated as a convex optimization problem. The resulting constraints are efficiently embedded into a distributed model predictive control (MPC) framework, enabling safe, scalable, and real-time trajectory planning.