Leaderless affine formation maneuvers over directed graphs

This paper studies leaderless affine formation maneuver control over a directed sensing topology, in the presence of constant input disturbances. Directed sensing topology is important when limitations in the sensing capabilities of an agent are considered. Unlike traditional leader-follower approaches, in case of leaderless formation maneuvers, there are no leaders. First, control laws for leaderless affine formation maneuvering for single integrator agents are presented, considering a directed sensing graph. Global Asymptotic Stability (GAS) is proved for formation tracking error in presence of constant disturbances. Subsequently, for higher-order systems, control laws are designed using an adaptive back-stepping based approach and GAS is proved for such control laws. Simulations are provided to validate the results.