  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.
