Bearing Leader-Follower Formation Control under Persistence of Excitation

Abstract

This paper addresses the problem of formation control with a leader-follower structure in three dimensional space by exploring persistence of excitation (PE) of the desired bearing reference, which is provided by a possibly moving or time-varying desired formation. Using only bearing measurements, control laws are proposed for a group of agents with single-integrator dynamics. By defining a desired formation such that the corresponding inter-vehicle bearing measurements are persistently exciting, relaxed conditions on the interaction topology (which do not require bearing rigidity nor constraint consistence) can be used to derive distributed control laws that guarantee exponential stabilization of the desired formation in terms of relative position. A key outcome of this approach is that even if there is only one connection originated from each follower, exponential stability of the formation can be achieved as long as the excitation conditions are met on the desired formation. The approach generalizes stability results provided in prior work for leader-first follower (LFF) structure, based on bearing rigidity and constraint consistence that required at least two connections for each follower except for the first one. Simulations results are provided to illustrate the performance of the proposed control method.