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

TL;DR

This paper develops explicit time-varying feedback laws to achieve small-time stabilization of nonholonomic and underactuated mechanical systems, such as unicycles and sliders, using homogeneity, backstepping, and desingularization techniques.

Contribution

It introduces novel explicit feedback control strategies for small-time stabilization of systems previously considered not stabilizable by continuous feedback.

Findings

Successful design of explicit time-varying feedback laws

Achieved small-time stabilization for unicycle and slider systems

Utilized homogeneity, backstepping, and desingularization methods

Abstract

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