Distributed formation control of mobile autonomous agents using relative position measurements

In this study, we consider an acyclic rigid formation with a group of mobile autonomous agents moving in a two-dimensional space. The formation is generated via a Henneberg sequence construction in which there is one global leader that does not follow any other agents, one first-follower that only follows the global leader, and each of other agents has two leaders, which is added by a vertex addition or an edge splitting operation. The entire formation moves with the leadership of the global leader. Every follower agent tries to maintain distances towards its leaders. Under the constraint of the acceleration for the global leader, the distributed formation control laws are proposed for the followers that only use the locally relative distance measurement. The control law of the first-follower is proposed, which needs to know the velocity of the global leader and the relative distance between the global leader and itself. The global asymptotic stability of the expected formation is proved via a Lyapunov-based technique for the considered multi-agent system. Moreover, the stable rigidity problem of a formation is investigated for the proposed distributed relative position-only formation control law. Necessary and sufficient conditions are provided that must be satisfied by the architecture of the underlying graph. Simulation results illustrate the effectiveness of the proposed formation control approach.