Trajectory Tracking Control of Flexible Manipulators Considering Modeling Discrepancy

A new method is proposed for the end-effector motion control of flexible manipulators. The dynamic equations of flexible robot manipulators are partitioned as pseudostatic equilibrium equations and deviations from them. The pseudostatic equilibrium considered here is defined as a hypothetical state where the end-effector motion variables have their desired values while the elastic deformations are instantaneously constant. Then, the control torques for the pseudostatic equilibrium are computed and the feedback stabilization of the deviation equations is achieved using strain gage and joint variable or tip point variable measurements. A planar two link robot with flexible forearm is taken into consideration for demonstration of the method. The elasticity of the forearm is approximately described by the first two modes and a controller is designed using this two-mode model. Furthermore, in order to investigate the effects of modeling discrepancies, a “submodel controller” is considered using a model that has only the first mode. The performances of these two controllers are compared by means of simulations. It is observed that the proposed control method does not seem to be sensitive to the number of modes included in the model of the manipulator.