Leader-Follower Formation Control with Prescribed Convergence Rates under Bearing Persistence of Excitation

Abstract

This paper addresses leader-follower formation control using only relative bearing and velocity measurements. Bearing-based leader-follower control strategies commonly use fixed control gains, for which the guaranteed convergence rates explicitly depend on the persistence of excitation (PE) properties of the desired formations. We propose a time-varying matrix gain that evolves according to the bearing information available to each follower and decouples the convergence rate from the PE bound. We establish the well-posedness and uniform boundedness of the proposed gain for bearing-persistently exciting formations, and characterize the exponential convergence rate through a tunable design parameter. The proposed control design is further extended to leader-follower formations with double-integrator dynamics. Simulations illustrate the resulting convergence properties compared with fixed gain designs.