Coordination of a group of agents with a leader - part I: general case

This paper studies coordinated control of a group of agents with a leader based on a coupled phase oscillator model. The leader is unaffected by the other agent members while each member is influenced by the leader and the other members with the same coupling strengths. By using coupled oscillators theory, it is shown that the group dynamics depends on the motion of the leader and the coupling strengths among all agents. Two types of collective motions occur generally, depending on different ranges of the coupling strengths. One is that all the member agents would move in the same direction while the other is that all the member agents move in a way such that the centroid of the group approaches a fixed position. In each case, all the member agents eventually move in the same manner if the directions of the motion are neglected. We also present the analytical results for two special cases of weak and strong couplings. Numerical simulations are worked out to demonstrate the theoretical analysis. The results suggest potential approaches to control a group motion by steering the motion of the leader and adjusting appropriate coupling patterns. This is of practical interest in applications of multiagent systems.