Set point stabilization of a 2DOF underactuated manipulator

Controlling an underactuated manipulator with less actuators than degrees of freedom is a challenging problem, specifically when it is to force the underactuated manipulator to track a given trajectory or to be configurated at a specific position in the work space. This paper presents two controllers for the set point regulation of 2-DOF underactuated manipulators. The first one is a cascade sliding mode tracking controller while the second one uses an inputoutput feedback linearization approach. The first algorithm builds on an observation that an underactuated manipulator can be treated as two subsystems. Consequently, a cascade sliding mode tracking controller has been designed. Firstly, a sliding mode surface is designed for both subsystems, these two sliding surfaces represent a first layer in the design architecture. A second layer sliding mode surface is then constructed based on the first layer sliding surface. The cascaded sliding mode controller is therefore deduced in terms of Lyapunov stability theorem. Robustness issues to bounded disturbances are then investigated. In a second stage of the paper, the input output feedback linearization (IOFL) control is presented. The latter, is then mixed to the sliding mode control scheme for robustness issues. Simulation results on 2-DOF whirling pendulum are presented to demonstrate the effectiveness of the proposed approach.