Connected flocking of multi-agent system based on distributed eigenvalue estimation

As a global property, connectivity of group plays a critical role in cooperative flocking and its stability foundation of multi-agent system. In this paper, the algebraic value of group connectivity, i.e. the second smallest eigenvalue of group Laplacian, as well as the corresponding eigenvector is estimated in a completely distributed style. Based on the estimated parameters, a distributed cooperative algorithm is developed both to steer the agents to the desired flocking motion and to induce the second smallest eigenvalue of Laplacian to be positive, which implies the connectivity of controlled group is preserved during maneuvers. Different from the common potential/tension function method which keeps some certain edges all the time, the algorithm proposed in this paper guarantees the connectivity while permitting any existing edge to be broken, which thus forces more relaxed constraints to the motions of agents for the connectivity preservation compared with the former.