Distributed Control Barrier Functions for Global Connectivity Maintenance

In this work, we propose a framework for the distributed implementation of Quadratic Programs-based controllers, building upon and rectifying a significant limitation in a previously presented approach. The proposed framework is primarily motivated by the distributed implementation of Control Barrier Functions (CBFs), whose primary objective is to make minimal adjustments to a nominal controller while ensuring constraint satisfaction. By improving over some limitations in the current state-of-the-art, we are able to apply distributed CBFs to the problem of global connectivity maintenance in presence of communication and sensing constraints. Specifically, we consider the problem of preserving connectivity for a group of quadrotors with onboard sensors under distance and field of view constraints. Leveraging distributed control barrier functions, our approach maintains global graph connectivity while optimizing the performance of the desired task. Numerical simulations validate its effectiveness.