Impedance Control of a Two Degree-of-Freedom Flexible Link Manipulator Using Singular Perturbation and Sliding Mode Control Theory

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time. Impedance Control provides a universal approach to the control of flexible robots — in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use Hamilton’s principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed to the fast and the slow subsystems. The slow dynamic corresponds to the rigid manipulator and fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2^nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2 DOF robot in which only the 2^nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.