  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 safe motion 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 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.
