dSLAP: Distributed Safe Learning and Planning for Multi-robot Systems

This paper considers the problem where a group of mobile robots subject to unknown external disturbances aim to safely reach goal regions. We develop a distributed safe learning and planning algorithm that allows the robots to learn about the external unknown disturbances and safely navigate through the environment via their single trajectories. We use Gaussian process regression for online learning where variance is adopted to quantify the learning uncertainty. By leveraging set-valued analysis, the developed algorithm enables fast adaptation to newly learned models while avoiding collision against the learning uncertainty. Active learning is then applied to return a control policy such that the robots are able to actively explore the unknown disturbances and reach their goal regions in time. Sufficient conditions are established to guarantee the safety of the robots. A set of simulations are conducted for evaluation.