Industrial robots have become indispensable machining equipment alongside machine tools due to their large workspace and high flexibility. However, their inherent structural compliance and geometric imperfections introduce spatially distributed pose errors, particularly in high-precision applications. Current robot error compensation is mostly based on single-source adjustment of the body, which is affected by the spatial sensitivity relationship between joint space and pose errors. For this reason, a hybrid manufacturing system integrating a robot and an external linear cell was constructed. Based on this system, a physical-informed approach for distributed prediction and collaborative compensation of robot machining quality is proposed. Firstly, a novel spatial–temporal attention-based sensing model was built to predict the robot pose errors. Secondly, an unsupervised distributed prediction module with physics informatization is constructed based on the sensitivity analysis of joint pose errors. Finally, the collaborative compensation is realized by a hybrid manufacturing system containing the robot itself and the external linear axes. Experimental validation on large-curvature surface machining demonstrates the system’s ability to simultaneously predict and compensate machining quality deviations, achieving positioning accuracy with maximum/average errors of 0.14 mm/0.03 mm respectively. The physics-based approach significantly outperforms conventional methods by coordinating distributed prediction with collaborative compensation, reducing sensitive joint adjustments while suppressing regenerative errors. These advancements establish a new paradigm for precision robotic machining in industrial applications.

With the trend of lightweight in the field of intelligent electric vehicles and 3C, the demand for high precision machining of aluminum alloy parts is growing. And tool condition monitoring (TCM) is very important for quality control of parts, so intelligent high-accuracy wear prediction of aluminum alloy high precision machining tools has great industrial application value at present and in the future. This paper presents a novel TCM model (Conv-PhyFormer) of Transformer with physics informed. The model has excellent ability to capture short-term and long-term dependencies from nonlinear cutting time series data when there are few training samples. The embedded hard physical constraint and soft physical constraint in the model make the model partially interpretable. Soft physical constraint in the form of one-dimensional causal convolution can help the proposed model better learn the local context. Hard physical constraint in the form of the mathematical equation representing cutting physical knowledge are embedded, thus the model does not need to learn this knowledge from time series data from scratch. A large number of analysis results of aluminum alloy machining experimental data show that the proposed Conv-PhyFormer has significantly superior prediction accuracy and robustness compared with the current three popular deep learning models for TCM. Embedded soft and hard physical constraints can significantly reduce the training epochs of Transformer prediction model.