Safe decentralized and reconfigurable multi-agent control with guaranteed convergence

In this paper, we consider a networked multi-robot system operating in an obstacle populated planar workspace under a single leader-multiple followers architecture. We propose a decentralized reconfiguration strategy of the set of connectivity and formation specifications that assures convergence to the desired point, while guaranteeing global connectivity. In particular, we construct a low-level Decentralized Navigation Functions based controller that encodes the goals and safety requirements of the system. However, owing to topological obstructions, stable critical points other than the desired one may appear. In such case, we employ a high-level distributed discrete procedure which attempts to solve a Distributed Constraint Satisfaction Problem on a local Voronoi partition, providing the necessary reconfiguration for the system to progress towards its goal. Eventually, we show that the system either converges to the desired point or attains a tree configuration with respect to the formation topology, in which case the system switches to a novel controller based on the Prescribed Performance technique, that eventually guarantees convergence. Finally, a simulation study clarifies and verifies the approach.