Distributed Safe Learning and Planning for Multirobot 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 <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</b>istributed <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</b>afe <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</b>earning <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b>nd <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</b>lanning 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 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. Monte Carlo simulations are conducted for evaluation.