Flocking of Multi-Agent Systems with a Virtual Leader

This paper considers the flocking problem of a group of autonomous agents moving in the space with a virtual leader. We investigate the dynamic properties of the group for the case where the state of the virtual leader may be time-varying and the topology of the neighboring relations between agents is dynamic. To track such a leader, we introduce a set of switching control laws that enable the entire group to generate the desired stable flocking motion. The control law acting on each agent relies on the state information of its neighboring agents and the external reference signal (or "virtual leader"). Then we prove that, if the acceleration input of the virtual leader is known, then each agent can follow the virtual leader, and moreover, the convergence rate of the center of mass (CoM) can be estimated; if the acceleration input is unknown, then the velocities of all agents asymptotically approach the velocity of the CoM, and thus the flocking motion can be obtained, however in this case, the final velocity of the group may not be equal to the desired velocity. Numerical simulations are worked out to further illustrate our theoretical results