## 1 Introduction
To further enhance the accuracy of industrial robots, non-kinematic compensation methods emerged. It can be further divided into compensation methods targeting specific non-kinematic error characteristics and compensation methods based on the principle of error similarity. The former mainly includes robot compliance error [18; 19; 20] and thermal drift error [21; 22]. The basic principle of error similarity is that there is a correlation between the robot positioning errors in Cartesian space and joint space. Based on this principle, one can estimate the error of desired points by the error of sampled points. Commonly used estimation methods include spatial interpolation, a neural network and the Kriging method. [PERSON] [23] proposed an inverse distance weighted interpolation method for the robotic drilling system on the moving rail. [PERSON] [24] compared estimation functions, including Fourier polynomials and ordinary polynomials, with robot joint angles as the variables. To further improve the accuracy of non-kinematic compensation methods, a lot of methods using neural networks have been proposed. [PERSON] [25] used a neural network optimized by genetic particle swarm optimization and reduced the positioning error of the robot to 0.227 mm via a robotic drilling test. [PERSON] [26] developed two hidden layers of deep neural networks to estimate the error and reached an accuracy of 0.22 mm. [PERSON] [27] combined the inverse distance weighted method and deep belief network, which led to an accuracy of 0.24 mm. Our previous research [28; 29] developed error-similarity-based estimation methods in joint space to estimate the error in the entire Cartesian workspace, achieving an accuracy of 0.3 mm. However, the existing robotic drilling system is often used in wing skin assembly scenarios, as shown in Figure 1, where the robot's orientation variation is usually less than \(\pm\)10\({}^{\circ}\). In these cases, the method in Ref. [28] combined with other offline compensation methods ignores the uncertainties of TCP calibration and is limited to applications with small variations in TCP orientation [30]. As a result, when the tool has a large orientation variation, the positioning accuracy of the robot varies,and the robot accuracy after error compensation still cannot meet the requirements of aerospace manufacturing. To deal with the problem mentioned above, a regionalized robot compensation approach based on error similarity is proposed in this study. A novel TCP calibration method is proposed to reduce the initial positioning error of the robot in each region. Then, the offline compensation method based on error similarity is used to further compensate for the positioning error of the robot in each region so that the robot maintains high positioning accuracy under the large orientation variation of TCP in the whole workspace. The main contributions of this paper are listed below. 1. The influence of TCP calibration uncertainties on the Cartesian positioning error similarity is analyzed compared with Ref. [29], which only considered joint errors;
2. Considering the uncertainties of TCP calibration, a robot compensation method based on regionalized error similarity is proposed, which broadens the application limits of robot compensation technology;
3. The proposed method is applied successfully to the robotic drilling, which effectively reduces the positioning error under the large variation of the TCP, and the accuracy is improved from 0.96 mm with the method in Ref. [28] to 0.23 mm. The structure of the rest of this paper is outlined as follows. In Section 2, the uncertainties in TCP calibration and their impact on the robot's error similarity are analyzed and modeled. Then, a TCP calibration method to reduce initial positioning error and a regionalized error similarity offline compensation method are presented. The experimental setup is introduced in Section 3. The experiments and their results, as well as the effectiveness of the proposed method, are discussed in Section 4.