Higher order sliding mode control of uncertain robot manipulators

Abstract

This chapter dealswith the tracking problem of robot manipulators. These systems are described by highly nonlinear and coupled equations. Higher order slidingmode controllers are then proposed to ensure stability and robustness of uncertain robot manipulators. The motivation for using high order sliding mode mainly relies on its appreciable features, such as high precision and elimination of chattering in addition that ensures the same performance of conventional slidingmode like robustness. In this chapter we propose two high order sliding mode controllers. The first guarantees a continuous control eliminating the chattering phenomenon. Instead of a regular control input, the derivative of the control input is used in the proposed control law. The discontinuity in the controller is made to act on the time derivative of the control input. The actual control signal obtained by integrating the derivative control signal is smooth and chattering free. The second controller is an adaptive version of high order sliding mode controller. The goal is to obtain a robust high order sliding mode adaptive gain control law to respect to uncertainties and perturbations without the knowledge of uncertainties/perturbations bound. The proposed controller ensures robustness, precision and smoothness of the control signal. The stability and the robustness of the proposed controllers can be easily verified by using the classical Lyapunov criterion. The proposed controllers are tested to a three-degree-of-freedom robot to prove their effectiveness.