Global Connectivity Maintenance in Distributed Coordination: An Eigen-Estimator-Based Control Barrier Function Method

Maintaining connectivity is a crucial yet challenging aspect in achieving collaborative goals within multi-robot systems. While local connectivity maintenance methods such as workplace confinement or fixed spanning trees are commonly used, global connectivity maintenance offers a less conservative approach. However, ensuring global connectivity while also guaranteeing collision avoidance, formation convergence and observer perturbation in safety-critical systems still remains a significant challenge. In this study, a novel approach utilizing control barrier functions based on a decentralized eigenvalue estimator is introduced to approximate the second smallest eigenvalue of the Laplacian matrix. By integrating multiple collaborative control objectives, including collision avoidance, formation convergence and Prescribed Performance Control (PPC), an all-in-one eigen-estimator-based control barrier function framework is developed. Furthermore, the robustness of the proposed controller is investigated in perturbed systems. Through two numerical cases, we demonstrate the effectiveness of the proposed control barrier functions and the distributed controller, highlighting their ability to maintain connectivity while achieving various control objectives in multi-robot systems.