A unique robust controller for tracking and stabilisation of non-holonomic vehicles
Résumé
After (Lizárraga, 2004) it is known that for nonholonomic systems it is impossible to design a universal controller able to asymptotically stabilize any feasible reference trajectory. In this paper we present a smooth time-varying controller able to stabilize a wide class of reference trajectories that include converging (parking problem) and persistently exciting (tracking problem) ones, as well as set-points. To the best of our knowledge, for the first time in the literature, we establish uniform global asymptotic stability for the origin of the closed-loop system in the kinematics state space. We also show that the kinematics controller renders the system robust to perturbations in the sense of integral-input-to-state stability. Then, we show that for the case in which the velocity dynamics equations are also considered (full model), any velocity-tracking controller with the property that the error velocities are square integrable may be used to ensure global tracking or stabilization. This modularity and robustness of our controller, added to the strength of our stability statements, renders possible the extension of our main results to the difficult scenario of control under parametric uncertainty.
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