Nonlinear Impedance Control OF A One Link Flexible Manipulator Using Singular Perturbation Theory

In this article, impedance control of a one link flexible link manipulators is addressed. 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 2nd 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 are carried out for three values of environment stiffness (low,medium and high).As simulation results show, the impedance controller enables us to control of a position of robot in unconstrained environment and control the contact force in constrained environment. The task that usually must be performed by two different controllers (hybrid position/force controller) .

Keywords:

Manipulator-Flexible-Impedance-control-Singular perturbation