Prediction of the Posture-Dependent Tool Tip Dynamics in Robotic Milling Based on Multi-Task Gaussian Process Regressions

Chatter vibration is one of the main factors that limit the productivity and quality of the robotic milling process. To predict the robotic milling stability, it is essential to obtain the tool tip frequency response function (FRF). The tool tip dynamics of a robot heavily depend on its postures and used tools. A state-of-art methodology of combining the regression model with the Receptance Coupling Substructure Analysis (RCSA) method is proved to be effective in predicting tool tip FRFs of machine tools for different positions and tools. However, for the milling robot, the cross coupling FRFs have an obvious influence on the dynamic property of the milling robot, thereby greatly affecting the milling stability boundary. It is of great challenge to directly integrate the effect of the cross coupling FRFs into the state-of-art approach to predict the tool tip dynamics. To tackle this challenge, in this paper, we propose an approach to predict the posture-dependent tool tip dynamics for different tools in robotic milling considering the cross coupling FRFs. First, a more comprehensive RCSA procedure is adopted to include the cross coupling FRFs. Then, the impact test is designed to measure the required FRF matrix. By fitting the measured FRF matrix with the multiple-degree-of-freedom (MDOF) model, the number of modal parameters is significantly reduced. Next, the Multi-Task Gaussian Process (MTGP) regression model is employed to mine the physical correlations between different modal parameters. Compared to the ordinary Gaussian Process regression model, the number of required regression models in MTGP is reduced and the prediction performance is improved in terms of accuracy and robustness. Furthermore, the effectiveness of the proposed approach is validated by the impact test and milling experiment on an industrial robot.