## 1 Introduction
Multilayer neural networks are utilized to simulate the distribution patterns of robot errors and dynamic status, thereby enhancing robot positioning accuracy without the need to establish dynamic equations. [PERSON] and [PERSON] et al. separately established RNN and MLP models to predict structural deformations and positioning errors caused by gravity, inertia forces, and other external forces, and applied robot compensation within the offline programming process [14; 15]. [PERSON] and [PERSON] et al., on the other hand, utilized real-time feedback information from the robot, including joint positions, velocities, and torques, to build robot compliance deformation prediction models based on CNN and RVM architectures, achieving the online prediction of robot errors [16; 17]. Another approach to enhance robot accuracy is to achieve robot error prediction utilizing a set of calibration points based on the robot error spatial similarity, without the complex error models. [PERSON] et al. analyzed the robot error evolution mechanism of the D-H error model, proposing that the geometric robot errors exhibit spatial similarity in Cartesian space, and achieved robot error prediction using calibration points distributed in uniform grids [18]. [PERSON] et al. experimentally validated the spatial similarity of the robot stiffness characteristics in Cartesian space and proposed a gridded variable stiffness model to predict the non-geometric errors of the robot [19]. Using the error data of the uniform gridded points in Cartesian space, [PERSON] and [PERSON] et al. separately implemented robot error prediction by employing the Inverse Distance Weighting (IDW) method and Kriging method [20; 21]. Neural network models constructed based on architectures such as the MLP, ELM, and RBF are also widely used in robot errors prediction [22; 23; 24; 25], although these methods often require a large number of data from grid-sampled points. [PERSON] and [PERSON] et al., respectively, proposed the SSA-Elman model and the OP-ELM model for processing the error data of grid points, improving the training efficiency and accuracy of the robot error prediction model through optimized training methods [26; 27]. According to the continuity of the robot motion process, [PERSON] and [PERSON] et al. proposed the similarity of robot positioning errors in continuous spatiotemporal domains and combined historical data from the robot motion process to establish neural network models, achieving real-time prediction of robot positioning errors [28; 29]. The aforementioned methods clearly analyze the distribution patterns and compensation principles of robot errors in Cartesian space. However, considering the serial rotary joint structure of industrial robots, utilizing joint angles to describe and control the robot status in configuration space is a more direct approach. [PERSON] et al. used surface reconstruction methods to fit the two-dimensional manifold of the robot error distribution in configuration space, revealing that the distribution of robot errors shows significant continuity in configuration space [30]. [PERSON] and [PERSON] et al. demonstrated through theoretical analysis and experimental results that both geometric and non-geometric robot errors show significant spatial similarity in configuration space, and prediction models of robot errors were achieved based on spatial-interpolation-based unbiased estimation methods [31; 32]. However, there is still a lack of analysis on the anisotropic distribution characteristics of the robot errors spatial similarity in configuration space. Additionally, existing error prediction methods that rely on the spatial similarity of robot errors still face challenges when the robot moves with changes in posture. This study analyzes the spatial similarity distribution patterns of robot errors under different loads and poses in both configuration space and Cartesian space, highlighting the advantages of using joint angles to predict robot errors in configuration space.