A Distributed System for Connectivity Tracking with UAVs

Algebraic connectivity is the second-smallest eigenvalue of the Laplacian matrix and can be used as a metric for the communication robustness of a network of agents. This connectivity concept applies to teams of multiple unmanned aerial vehicles (UAVs) performing cooperative tasks, such as arriving at a consensus while sharing sensor information through communication. The algebraic connectivity can be controlled by altering edge weights through movement of individual UAVs in a team, or by adding and deleting edges. The addition and deletion of edges to achieve a desired algebraic connectivity, however, is an NP-hard problem, leading to the development of multiple heuristic methods. A primary method, the greedy perturbation heuristic, relies on global knowledge of the system to determine the eigenvector associated with the algebraic connectivity. Using an existing method for determining algebraic connectivity distributively, the primary contributions of this paper are 1) the introduction of a decentralized estimation of the Fiedler vector and 2) a decentralized Fiedler vector-based connectivity tracking algorithm.