Sampled-data output feedback control of uncertain nonholonomic systems in chained forms with applications to mobile robots

Abstract

It is imperative to find a sampled-data controller for nonholonomic systems due to their implementation within digital computers. Nonholonomic systems in chained form are sufficiently important to research via the numerous real world applications, mobile robots being one of the biggest. Moreover, due to the presence of uncertain nonlinearities, most of the existing design methods are inapplicable to these systems. It has been proven that under a lower-triangular growth condition, a class of uncertain nonlinear systems can be globally stabilized by a sampled-data output feedback controller whose observer and control laws are discrete-time and linear. In this paper, using a change of coordinates and combining the recently developed sampled-data output feedback control method, we first design a sampled-data output feedback controller to stabilize the nonholonomic system with a single z-state. For nonholonomic systems with two-dimensional z-states, the output feedback control problem becomes much more challenging since the boundedness of the change of coordinates is not proved; we shall consider this in future works. Examples and computer simulations were conducted to show the effectiveness of the proposed controllers for a single z-state.