A robust δ-persistently exciting controller for leader-follower tracking-agreement of multiple vehicles

We solve the leader-follower tracking-agreement control problem for Nonholonomic mobile robots with uncertainties; this consists in controlling a group of robots to take a pre-specified configuration (formation) and to move about following a vanishing reference trajectory. We assume that each robot has one unique leader and it is controlled by a local tracking controller that uses relative position and velocity measurements, but each robot may have one or several followers. We also assume that the reference trajectory is available to only one robot (the swarm leader). The control design is based on a δ-persistently exciting controller (for the kinematics model) that is robust to decaying perturbations and an outer control loop at the force-inputs level. Our proofs are constructive as they are based on Lyapunov's direct method; moreover, we establish strong integral input-to-state stability. To the best of our knowledge this is the first result of this nature in the literature of nonholonomic mobile robots.