Formation-Tracking Control of Autonomous Vehicles Under Relaxed Persistency of Excitation Conditions

We present a smooth nonlinear time-varying formation-tracking controller for autonomous vehicles modeled as a nonholonomic unicycle. Our first result consists of a leader-follower tracking controller that guarantees uniform global asymptotic stability under the standing assumption that either the rotational or the translational reference velocity is persistently exciting. Then, we extend this result to the case of formation control of a swarm of vehicles. We show that this problem may be solved via decentralized tracking control, under the assumption that each robot communicates with one leader and one follower.