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Optimization of hand-eye calibration for blade repair robot based on anomalous sample detection
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摘要
为了降低叶片修复机器人视觉系统中随机误差对手眼标定的影响，提出了一种基于异常样本检测的手眼标定优化方法。首先，建立手眼矩阵的线性方程，通过奇异值分解(SVD)求解手眼矩阵的初始值；随后，利用初始值对样本进行反演操作，并基于
Z -分数检测和剔除异常样本，以获取更高准确性的手眼矩阵；最后，将得到的手眼矩阵作为优化的初始值，采用单位四元数表示旋转，并使用Levenberg-Marquardt算法对初始值进一步优化，最终得到手眼矩阵。在搭载双目深度相机的叶片修复机器人上进行了手眼标定实验，通过TCP标定工具获取目标点的真实坐标，利用所提方法得到的手眼矩阵预测坐标与真实坐标的平均欧式距离为0.858 mm，且方差稳定在0.1以内。相比其他对比方法，本文方法有效减少了随机误差的影响，具有良好的稳定性与准确性。-
关键词:
- 奇异值分解 /
- Z-分数 /
- Levenberg-Marquardt /
- 手眼标定 /
- TCP标定
Abstract
To reduce the impact of random errors on hand-eye calibration in the visual system of a blade repair robot, an optimization method based on outlier detection is proposed. Firstly, a linear equation for the hand-eye matrix is established. The initial hand-eye matrix is solved using singular value decomposition (SVD). Secondly, the initial value is used to perform an inversion operation on the samples. Outlier samples are detected and removed based on
Z -scores, leading to a more accurate hand-eye matrix. Finally, the obtained hand-eye matrix is used as the initial value for optimization. The rotation is represented by unit quaternions, and the Levenberg-Marquardt algorithm is applied to further optimize the initial value, yielding the final hand-eye matrix. Hand-eye calibration experiments were conducted on the blade repair robot equipped with a stereo depth camera. The real coordinates of the target points were obtained using a TCP calibration tool. The predicted coordinates from the hand-eye matrix, obtained by the proposed method, have an average Euclidean distance of 0.858 mm from the true coordinates, with a variance stabilizing below 0.1. Compared to other methods, the proposed approach effectively reduces the impact of random errors and demonstrates good stability and accuracy.-
Key words:
- singular value decomposition /
- Z-score /
- Levenberg-Marquardt /
- hand-eye calibration /
- TCP calibration
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Overview
Overview: The surface defect repair of high-altitude wind turbine blades using repair robots is important. The vision system on the repair robot plays a crucial role in guiding the localization of defects on the blade surface, making stable and accurate hand-eye calibration of the repair robot key to successful repair. During the calibration process, various random errors, such as image distortion and inaccurate parameters, may occur, leading to unstable and inaccurate calibration results. This paper proposes an optimized hand-eye calibration method based on anomaly sample detection. Firstly, a linear equation for the hand-eye matrix is established, and its initial value is obtained by solving the equation using singular value decomposition (SVD). Next, the initial value is used to invert the samples, and anomaly samples are detected and removed based on the Z-score method, ensuring a higher accuracy hand-eye matrix. Finally, the obtained hand-eye matrix is used as the initial value for further optimization using the Levenberg-Marquardt algorithm, where the rotation is represented by unit quaternions, and the hand-eye matrix is refined. To verify the effectiveness of the proposed method, hand-eye calibration experiments were conducted on a blade repair robot equipped with a binocular depth camera. The true coordinates of the target points were obtained through TCP calibration tools, and the hand-eye matrix's predicted coordinates yielded an average Euclidean distance of 0.858 mm from the true coordinates, with the variance remaining below 0.1. Compared with other calibration methods, the proposed method effectively reduces the influence of random errors, showing excellent stability and accuracy. Moreover, this method can be widely applied to hand-eye calibration tasks for other industrial robots.
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图 6 数据集Z-分数散点图。(a)第一次反演；(b)第二次反演；(c)第三次反演
Figure 6. Z-score scatter plot of dataset. (a) First inversion; (b) Second inversion; (c) Third inversion
图 7 实验步骤示例。(a) TCP标定；(b)触碰特征点；(c)拍摄图像；(d)获取特征点坐标
Figure 7. Example of experimental steps. (a) TCP calibration; (b) Touching characteristic points; (c) Taking images; (d) Obtain the coordinates of feature points
图 8 实验结果坐标波动对比图。(a) Method A；(b) Method B；(c)所提方法
Figure 8. Comparison diagram of coordinate fluctuation from experimental results. (a) Method A；(b) Method B；(c) Ours
图 10 机器人打磨修复作业。(a)机器人巡检；(b)安装打磨工具；(c)打磨动作；(d)深度相机提供信息
Figure 10. Robot grinding repair operation. (a) Robotic inspection; (b) Installation of sanding tools; (c) Grinding action; (d) Depth cameras provide information
表 1 实验设备参数
Table 1. Experimental equipment parameters
Key equipment parameter Specific parameter Robot arm Aelite EC66 Collaborative Robot Depth camera model Intel RealSense D405 Depth measurement method Stereo Vision Depth measurement accuracy ±2% at 50 cm RGB image resolution 1280×720 RGB image frame rate Up to 90 f/s Checkerboard array 12×9 Checkerboard square size 25 mm Checkerboard accuracy ±0.01 mm 
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表 2 欧式距离对比结果
Table 2. Results of Euclidean distance comparison
Number of images Method A Method B Ours 1 1.371 4.197 1.202 2 0.980 2.845 1.132 3 2.635 2.678 0.799 4 3.654 2.810 0.986 5 2.482 2.110 1.069 6 1.372 2.028 1.231 7 1.748 1.033 1.050 8 1.483 2.969 1.211 9 1.916 4.815 0.524 10 2.996 4.945 0.989 11 3.047 4.939 0.937 12 3.588 1.664 1.058 13 4.239 3.060 0.750 14 3.129 2.309 0.903 15 4.467 3.650 0.267 16 2.895 3.512 0.352 17 5.083 3.235 0.875 18 4.605 3.742 0.477 19 1.246 2.639 0.759 20 3.438 3.744 0.596 Average 2.818 3.146 0.858 Variance 1.442 1.092 0.078
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