Analysis of Computed Torque Control Applied with Command Shaping to Minimize Residual Vibration in a Flexible-Joint Robot

During fast point-to-point motion, the inherent joint flexibility could be detrimental in terms of residual vibration. Aiming to minimize the vibration, the command shaping method has been developed so as to remove critical energy from the input profile at resonant frequencies. Since this method requires information of a physical model in order to find the target frequencies, the quality of the shaped command profile relies on the accuracy of the model parameter estimation. Therefore, in this work, a system identification method using Instrumental Variables is applied from the literature. Compared with the classic Ordinary Least Square method, the IV approach has successfully improved the estimation of parameters, based on simulation results. The accuracy of parameter estimation influences the command profile, as does the feedback controller. In this work, starting from a mathematical derivation with a mismatch model due to a feedback controller called Computed Torque Control, insight for the closed-loop system is given with regard to the interaction between control gains and the actual resonant frequencies. It is found that the control gain is able to modify the actual resonant frequency curve, and push it into or out of the shaping bounds which are generated from the command shaping method. Further analysis based on the simulation results shows that the overlap area between the shaping bounds and the actual frequencies affects the level of residual vibration. In light of this fact, an optimal control gain exists and is found when the estimation error is in a certain range. At the end, recommendations for choosing the control gains are provided.