Lyapunov-based formation-tracking control of nonholonomic systems under persistency of excitation

We present a smooth nonlinear time-varying controller for leader-follower tracking of non-holonomic mobile robots. Our design relies upon the standing assumption that either the rotational or the translational reference velocity is persistently exciting. Then, we extend our results to cover the problem of formation tracking for a swarm of vehicles interconnected under a spanning tree communication topology rooted at the virtual leader. In this case, we propose a simple distributed control law that establishes the convergence of the error coordinate of each agent, relatively to its neighbourhood, under the same condition of persistency of excitation. In addition, our proofs are based on Lyapunov's second method, that is, we provide a strict Lyapunov function.