Dynamics and control of light weight flexible manipulators.

Abstract

Current robot manipulators are controlled using methods that do not take into account the links and joints flexibility. Consequently, tasks are usually carried in a slow fashion. The objective of this research is to improve the performance of light weight flexible manipulators by developing dynamic models and control strategies that include the effects of the links flexibility. Toward achieving this objective, the dynamic model of a single link flexible manipulator has been developed. Two hermit cubic functions are used in conjunction with the deflection and the slope at the tip of the link in order to express the deflection at any point along the link. The model is used to simulate the response of the single link manipulator and its ability to follow various trajectories under collocated control. Even though collocated control such as the computed torque method leads to asymptotic stability in the case of rigid link manipulators, the end point of the single link flexible manipulator has shown sustained oscillations under this type of control. In order to improve the performance of the single link and reduce the tip deflection, dynamic stiffening has been added to the link by using the angular position of a point along the link as the controlled variable. This control method is referred to as the non collocated control. Simulations of the robot motion under non collocated control has shown a significant reduction in the position error of the end point. In order to increase the damping of the flexible link, a new approach referred to as the Computed Torque/Delayed Deflection (CTDD) has been used. The CTDD approach combines the non collocated control with a delayed deflection at the point being used for non collocation feedback. The fastest decay in the end point vibrations was obtained when the delay time is selected to be half the period of the lowest frequency in the system. The CTDD has been extended to the case of a two link flexible manipulator. Simulations results for the tracking performance of the two link flexible manipulator have been carried out using two paths: A straight line path and a four points path. The advantages of using the CTDD approach are outlined by comparing its performance to those of a collocated control (computed torque method) and the non collocated control.