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A robust δ-persistently exciting controller for formation-agreement stabilization of multiple mobile robots

We propose a δ-persistently exciting controller [17] for leader-follower agreement control of a group of non-holonomic mobile robots, under the assumption that the virtual-leader velocities converge to zero. We assume that each of the vehicles in the formation communicates only with one leader and one, or several followers hence, that is, they form a spanning-tree communication topology rooted at the virtual leader. The control is decentralized and guarantees the convergence of the error coordinate of each agent, relatively to its neighbor. More significantly, our proofs are based on Lyapunov's direct method that is, we provide strict Lyapunov functions to guarantee strong integral input-to-state stability with respect to the reference velocities and, hence, uniform global asymptotic stability of the closed-loop system provided that the reference velocities are integrable.