Small-time stabilization of nonholonomic or underactuated mechanical\n systems: the unicycle and the slider examples

Abstract

This paper concerns the small-time stabilization of some classes of\nmechanical systems which are not stabilizable by means of at least continuous\nstate feedback laws. This is the case of nonholonomic mechanical systems, an\nexample being the unicycle robot, or for underactuated mechanical systems, an\nexample being the slider. Explicit time-varying feedback laws leading to\nsmall-time stabilization are constructed for these two control systems. The\nmain tools are homogeneity, backstepping, and desingularization technics.\n