Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems

This paper deals with nonholonomic perturbed systems. Necessary and sufficient geometric conditions on the perturbation vector field are given in order to put the system into a perturbed one-chained form. Two different sliding mode control strategies are then designed to robustly stabilize, under some conditions, this chained system: one providing a practical stabilization, the other performing a finite time convergence. As a way of illustration, simulations on the example of the unicycle-type mobile robot are presented.