Invariant manifold approach for the stabilization of nonholonomic systems in chained form: application to a car-like mobile robot

It is shown that the class of n-dimensional nonholonomic chained systems can be exponentially stabilized using the invariant manifold techniques. To this end, an invariant manifold, on which all the closed-loop trajectories tend to the origin, is derived for this class of systems under a linear smooth time-invariant state feedback. Thereafter, this manifold is made attractive by means of a discontinuous, time-invariant, state feedback. The proposed control scheme ensures exponential stability of the closed-loop system in a large domain excluding, at the initial time, the null value of the first state variable. Finally, our controller is applied for the stabilization of a car-like mobile robot and simulation results are given to highlight its effectiveness.