A rapid prediction method for pose-dependent tool point dynamics of milling robots based on multiple output Gaussian process regression and proper orthogonal decomposition

Chatter is a critical limitation to productivity and machining quality in robotic milling. Accurate prediction of the pose-dependent tool point frequency response functions (FRFs) of milling robots is essential for effectively predicting and suppressing chatter. This paper presents a rapid prediction method for predicting the pose-dependent tool point dynamics of milling robots, incorporating cross receptances, which significantly influence both the dynamic behavior of milling robots and the stability of robotic milling processes. First, a comprehensive and generalized receptance coupling substructure analysis (RCSA) procedure is presented to couple the dynamics of the robot-spindle-holder-tool-shank (RSHTS) subsystem and cutting tools. Next, a surrogate model that combines proper orthogonal decomposition (POD) with multiple output Gaussian process regression (MOGPR) is developed to predict the pose-dependent receptances of the RSHTS subsystem. To facilitate accurate and efficient data collection, a measurement strategy using modal impact tests is introduced to acquire the full receptance matrix, including cross receptances. By preprocessing the measured receptance matrix with the POD method, the time-consuming step of extracting individual modal parameters is eliminated. Then the MOGPR model is used to exploit the inherent correlativity between different FRFs, significantly reducing the number of regression models compared to the Single Output Gaussian Process Regression (SOGPR) model while improving predictive performance and generalization capability. Finally, the presented method is validated through modal impact tests and milling tests conducted on an industrial robot. Experimental results confirm the accuracy, efficiency, and robustness of the presented method in predicting pose-dependent tool point dynamics. The effectiveness of the presented method is also demonstrated in enhancing stability predictions in robotic milling processes.