Collective control objective and connectivity preservation for multi-robot systems with bounded input

In this work, we address the connectivity maintenance problem for a team of mobile robots which move according to a given collective control objective. In our framework, the interaction among the robots is limited by a given visibility radius both in terms of sensing and communication. For this scenario, we propose a bounded control law which can provably preserve the connectivity of the multi-robot system over time even in the presence of any desired bounded control objective. Furthermore, we characterize the effects of the connectivity control term on the collective control objective, in terms of robustness of the desired control objective to the disturbance of the connectivity, by resorting to the set Input-to-State Stability framework (set-ISS). For the validation of the proposed bounded connectivity control law we consider the encirclement problem as an example of collective control objective. Simulations are provided to corroborate the theoretical results.