Distributed Safe Learning and Planning for Multi-robot Systems

This paper considers the problem of online multi-robot motion planning with general nonlinear dynamics subject to unknown external disturbances. We propose dSLAP, a distributed safe learning and planning framework that allows the robots to safely navigate through the environments by coupling online learning and motion planning. Gaussian process regression is used to online learn the disturbances with uncertainty quantification. The planning algorithm ensures collision avoidance against the learning uncertainty and utilizes set-valued analysis to achieve fast adaptation in response to the newly learned models. A set-valued model predictive control problem is then formulated and solved to return a control policy that balances between actively exploring the unknown disturbances and reaching goal regions. Sufficient conditions are established to guarantee the safety of the robots in the absence of backup policy. Monte Carlo simulations are conducted for evaluation.