Distributed flocking of second-order multi-agent systems with global connectivity maintenance

This paper investigates the problem of connectivity-preserving flocking of multiple autonomous agents with second-order dynamics. First, the inverse power iteration algorithm is formulated in a completely distributed manner to estimate the algebraic connectivity, i.e., the second smallest eigenvalue of the group Laplacian, as well as the corresponding eigenvector. Furthermore, distributed gradient-based flocking algorithms that exploit decentralized eigenvalue/eigenvector estimation are developed both to steer the agent group to the desired flocking motion and to maintain the global connectivity of the underlying network during maneuvers. Different from the common potential/tension function method which keeps certain fixed edges all the time, the algorithm proposed in this paper guarantees the global connectivity which allows any existing edge to be broken, thus gives more freedom of motions for the agents. Finally, nontrivial simulations are performed to demonstrate the correctness and effectiveness of the theoretical results.