Formation control of a leader–follower structure in three dimensional space using bearing measurements

This paper addresses the problem of leader–follower formation control in three dimensional space by exploring persistence of excitation (PE) of the desired formation. Using only bearing and relative velocity measurements, distributed control laws are derived for a group of agents with double-integrator dynamics. The key contribution is that the exponential stabilization of the actual formation to the desired one in terms of shape and scale is guaranteed as long as the PE conditions on the desired formation are satisfied. The approach generalizes stability results provided in prior work for leader–first follower (LFF) structures which are based on bearing rigidity and constraint consistence under a specific graph topology to ensure the exponential stabilization of the actual formation to a desired static geometric pattern up to a scale factor. Simulations results are provided to illustrate the performance of the proposed control method.