## 1 Introduction  
Industrial robots with serial multi-joints are widely applied in aerospace manufacturing, undertaking tasks such as robotic welding, grinding, and hole-making. However, the lack of positioning accuracy limits their uses in high-precision machining and assembly processes. With a positional accuracy requirement of \(\pm\)0.5 mm for assembly holes in aerospace components, which is significantly higher than the original accuracy of robots, error prediction and accuracy compensation methods for robots are essential. Robot position accuracy, which refers to the consistency between the theoretical and actual position within any position and posture, is influenced by various factors, including manufacturing errors of the robot, drive errors caused by actuators and encoders, deformations in robot joints and links due to external loads and gravity, backlash in gearboxes, and temperature fluctuations. Robot errors can be categorized into geometric errors and non-geometric errors, each with different distributions and modeling methods. Kinematic models, which describe the mathematical relationship between the joint angles of a robot and its geometric state theoretically, are the primary means for analyzing geometric errors. The D-H model simplifies the parameterization of the geometric relationship between robot joints and links [1], making it commonly used, despite its incomplete parameters and singularities. To address the incompleteness in the D-H model, [PERSON] proposed the M-DH model, which includes additional joint geometric parameters [2]. Additionally, to overcome the singularity problems inherent in various D-H models, the Product of Exponentials (POE) formula is frequently used in the construction of robot kinematic models [3]. Distortions in the kinematic model parameters causing robot geometric errors are a major factor affecting robot positioning accuracy, and accurate identification of kinematic parameters can significantly improve robot accuracy [4; 5]. The prediction and compensation of non-geometric errors, caused by factors such as structural deformations, joint backlash, or temperature changes, are also key methods to further enhance robot accuracy. [PERSON] and [PERSON] et al. considered the influence of elastic deformation in robot joints and links and bidirectional backlash of joints, introducing various non-geometric parameters to extend the kinematic model, and achieved precise prediction of robot positioning errors through accurate parameter identification [6; 7]. [PERSON] et al. considered the influence of both geometric and non-geometric factors on positioning errors simultaneously, establishing a rigid-flexible coupled robot error prediction model, which was further applied to trajectory accuracy compensation in robots [8]. In the prediction of robot errors, [PERSON] et al. separated geometric and non-geometric factors, establishing both an M-DH error model and a non-geometric error model based on LSSVR, and conducted parameter identification for each model separately [9]. For scenarios where robots carry heavy loads or experience significant load changes such as robotic casting or continuous milling, [PERSON] et al. developed joint stiffness models for the robots and predicted real-time deformation states during robot motion by utilizing joint torques either from robot joints feedback or predicted by kinematic equations, thereby achieving real-time position compensation during the robot's movement [10; 11; 12; 13]. The aforementioned modeling approaches aim to analyze the true mapping process between configuration space and Cartesian space theoretically. However, this process is influenced by various geometric and non-geometric factors which pose challenges to modeling, and the error evolution mechanisms of some non-geometric factors are difficult to describe. Therefore, neural-network-based methods for predicting non-geometric errors have gradually been adopted.