A unique robust controller for tracking and stabilisation of non-holonomic vehicles

It is known that for non-holonomic systems it is impossible to design a universal controller able to asymptotically stabilise any feasible reference trajectory. We present a smooth time-varying controller able to stabilise a wide class of reference trajectories that include converging (parking problem) and persistently exciting (tracking problem) ones, as well as set-points. 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 stabilisation even under parametric uncertainty.