Adaptive sliding mode control for a second order nonholonomic planar four-link UMS

Abstract

This article presents a novel solution to the stabilization problem of a second order nonholonomic planar four-link Active-Passive-Active-Active (APAA) underactuated mechanical system (UMS). Four rigid links are used to represent the mechanical system and a multi-mass-spring model is used to include the liquid slosh dynamics. Furthermore, it is assumed that the control inputs are available in form of two forces and a torque. The forces are applied to the prismatic joints and the torque is applied to the revolute joint. The overall control objective is to move the robot end-effector towards equilibrium point. The control methodology presented in this article is based on adaptive sliding mode. Firstly, the 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> order chained form system is converted into a special structure containing nominal part and some unknown term. Then the system is stabilized using adaptive sliding mode control and the unknown term is computed adaptively. The controller and the adapted law are derived in a way that derivative of a suitable Lyapunov function becomes strictly negative. The effectiveness of the proposed control laws is illustrated by simulations.