Decentralized Goal Assignment and Safe Trajectory Generation in Multi-Robot Networks via Multiple Lyapunov Functions

This paper considers the problem of decentralized goal assignment and trajectory generation for multi-robot networks when only local communication is available, and proposes an approach based on methods related to switched systems and set invariance. A family of Lyapunov-like functions is employed to encode the (local) decision making among candidate goal assignments, under which a group of connected agents chooses the assignment that results in the shortest total distance to the goals. An additional family of Lyapunov-like barrier functions is activated in the case when the optimal assignment may lead to colliding trajectories, maintaining thus system safety while preserving the convergence guarantees. The proposed switching strategies give rise to feedback control policies that are computationally efficient and scalable with the number of agents, and therefore suitable for applications including first-response deployment of robotic networks under limited information sharing. The efficacy of the proposed method is demonstrated via simulation results and experiments with six ground robots.