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.

颤振是限制机器人铣削过程生产率和质量的主要因素之一。要预测机器人铣削稳定性，必须获得刀尖频率响应函数 (FRF)。机器人的工具尖端动力学在很大程度上取决于其姿势和使用的工具。事实证明，将回归模型与接收耦合子结构分析 (RCSA) 方法相结合的最先进方法可有效预测不同位置和工具的机床的刀尖 FRF。然而，对于铣削机器人，交叉耦合频响函数对铣削机器人的动力学特性有明显的影响，从而极大地影响铣削稳定边界。将交叉耦合 FRF 的影响直接集成到最先进的方法中以预测刀尖动力学是一项巨大的挑战。为了应对这一挑战，在本文中，我们提出了一种方法来预测机器人铣削中不同工具的姿态相关工具尖端动力学，考虑交叉耦合 FRF。首先，采用更全面的 RCSA 程序来包括交叉耦合 FRF。然后，设计冲击试验以测量所需的FRF矩阵。通过用多自由度 (MDOF) 模型拟合测得的 FRF 矩阵，模态参数的数量显着减少。接下来，采用多任务高斯过程 (MTGP) 回归模型来挖掘不同模态参数之间的物理相关性。相较于普通的高斯过程回归模型，减少了 MTGP 中所需的回归模型的数量，并在准确性和鲁棒性方面提高了预测性能。此外，通过工业机器人的冲击试验和铣削实验验证了所提方法的有效性。