Distributed Constrained Connectivity-Keeping Supervision Scheme in the Presence of Static Obstacles

Connectivity maintenance and safe navigation around obstacles are fundamental challenges for vehicle formations. This paper introduces a novel multi-level supervision distributed architecture aimed at supervising a set of dynamically decoupled agents operating in a 2D space and subject to obstacle avoidance and connectivity-keeping constraints. An existing supervision scheme based on Distributed Command Governor ideas is here extended in order to adequately tackle non-convex obstacle avoidance constraints while maintaining the communication connectivity of the formation, here modeled as a dynamic graph. To this end, the proposed method enforces the existence of a specific minimum spanning tree at each time instant while fulfilling obstacle avoidance constraints by using a separation hyperplane. Conditions that formally prove the feasibility of the proposed strategy are included along with simulations that show the effectiveness of the proposed method.