A sliding mode controller with generalized H<inf>2</inf> performance for dynamic of nonholonomic mobile robot

Abstract

In this paper, a sliding mode controller with a generalized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance is proposed for a unicycle-like mobile robot to implement the trajectory tracking mission. First, a kinematic controller is introduced for the mobile robot and generating the desired values of the linear and angular velocity for the dynamic controller. Secondly, a dynamic controller based on the sliding mode control with a generalized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance is proposed to make the real velocity of the mobile robot and reach the desired velocity command. The stability properties of the controllers are proved by the Lyapunov method. This control law providing smaller errors and better performance to deal with the slipping of the wheels and parameter uncertainty. Simulation is carried out for a mobile robot to verify the performance of the proposed control scheme.