Reprojection Error Analysis and Algorithm Optimization of Hand-Eye Calibration for Manipulator System

The Euclidean distance error of calibration results cannot be calculated during the hand-eye calibration process of a manipulator because the true values of the hand-eye conversion matrix cannot be obtained. In this study, a new method for error analysis and algorithm optimization is presented. An error analysis of the method is carried out using a priori knowledge that the location of the augmented reality markers is fixed during the calibration process. The coordinates of the AR marker center point are reprojected onto the pixel coordinate system and then compared with the true pixel coordinates of the AR marker center point obtained by corner detection or manual labeling to obtain the Euclidean distance between the two coordinates as the basis for the error analysis. We then fine-tune the results of the hand-eye calibration algorithm to obtain the smallest reprojection error, thereby obtaining higher-precision calibration results. The experimental results show that, compared with the Tsai-Lenz algorithm, the optimized algorithm in this study reduces the average reprojection error by 44.43% and the average visual positioning error by 50.63%. Therefore, the proposed optimization method can significantly improve the accuracy of hand-eye calibration results.