In recent years, control and stabilization of mechanical systems with nonholonomic constraints has been an area of active research. Due to Brockett’s theorem [1], it is well known that nonholonomic systems with restricted mobility cannot be stabilized to a desired configuration (or posture) via differentiable, or even continuous, pure-state feedback, although it is controllable. A number of approaches including (i) discontinuous time-invariant stabilization [2,3], (ii) time-varying stabilization [4], and (iii) hybrid stabilization [5] have been proposed for the problem (see the Survey Paper 6 and the references therein for more details).