Robust and Accurate Hand-Eye Calibration Method Based on Schur Matric Decomposition

Accuracy evaluation of hand-eye calibration techniques for vision-guided robots

Hand-eye calibration is an important step in controlling a vision-guided robot in applications like part assembly, bin picking and inspection operations etc. Many methods for estimating hand-eye transformations have been proposed in literature with varying degrees of complexity and accuracy. However, the success of a vision-guided application is highly impacted by the accuracy the hand-eye calibration of the vision system with the robot. The level of this accuracy depends on several factors such as rotation and translation noise, rotation and translation motion range that must be considered during calibration. Previous studies and benchmarking of the proposed algorithms have largely been focused on the combined effect of rotation and translation noise. This study provides insight on the impact of rotation and translation noise acting in isolation on the hand-eye calibration accuracy. This deviates from the most common method of assessing hand-eye calibration accuracy based on pose noise (combined rotation and translation noise). We also evaluated the impact of the robot motion range used during the hand-eye calibration operation which is rarely considered. We provide quantitative evaluation of our study using six commonly used algorithms from an implementation perspective. We comparatively analyse the performance of these algorithms through simulation case studies and experimental validation using the Universal Robot’s UR5e physical robots. Our results show that these different algorithms perform differently when the noise conditions vary rather than following a general trend. For example, the simultaneous methods are more resistant to rotation noise, whereas the separate methods are better at dealing with translation noise. Additionally, while increasing the robot rotation motion span during calibration enhances the accuracy of the separate methods, it has a negative effect on the simultaneous methods. Conversely, increasing the translation motion range improves the accuracy of simultaneous methods but degrades the accuracy of the separate methods. These findings suggest that those conditions should be considered when benchmarking algorithms or performing a calibration process for enhanced accuracy.

Research on the Hand–Eye Calibration Method of Variable Height and Analysis of Experimental Results Based on Rigid Transformation

In view of the phenomenon that camera imaging will appear large up close and small from afar in the eye-to-hand hand-calibration system, one hand–eye calibration is carried out. The manipulator is only suitable for grasping objects of the same height, and the calibration results cannot be applied to grasping products with variable height. Based on the study of the pinhole camera model and the rigid transformation model between coordinate systems, the introduction of the calibration height parameters, the relationship between parameters of the rigid transformation matrix between image the coordinate system and the robot coordinate system, and sampling height are established. In the experiment, firstly, through the calibration of camera parameters, the influence of camera distortion on imaging quality is eliminated, and the influence of calibration height is ignored. Then, the machine coordinate system and image coordinate system of the calibration plate at different heights are calibrated using the four-point calibration method. The parameters of the rigid transformation matrix at different heights (H) are calculated. Finally, through experimental analysis, the high linear relationship between the parameters of the rigid transformation matrix from the image coordinate system to the robot coordinate system and the calibration height is fitted. By analyzing the random error of the experiment, the linear relationship between calibration height and pixel density is further established, and the systematic error of the experimental process is deeply analyzed. The experimental results show that the hand–eye calibration system based on this linear relationship is precise and suitable for grabbing products of any height, and the positioning error is less than 0.08%.

A Novel Concentric Circular Coded Target, and Its Positioning and Identifying Method for Vision Measurement under Challenging Conditions

Coded targets have been demarcated as control points in various vision measurement tasks such as camera calibration, 3D reconstruction, pose estimation, etc. By employing coded targets, matching corresponding image points in multi images can be automatically realized which greatly improves the efficiency and accuracy of the measurement. Although the coded targets are well applied, particularly in the industrial vision system, the design of coded targets and its detection algorithms have encountered difficulties, especially under the conditions of poor illumination and flat viewing angle. This paper presents a novel concentric circular coded target (CCCT), and its positioning and identifying algorithms. The eccentricity error has been corrected based on a practical error-compensation model. Adaptive brightness adjustment has been employed to address the problems of poor illumination such as overexposure and underexposure. The robust recognition is realized by perspective correction based on four vertices of the background area in the CCCT local image. The simulation results indicate that the eccentricity errors of the larger and smaller circles at a large viewing angle of 70° are reduced by 95% and 77% after correction by the proposed method. The result of the wing deformation experiment demonstrates that the error of the vision method based on the corrected center is reduced by up to 18.54% compared with the vision method based on only the ellipse center when the wing is loaded with a weight of 6 kg. The proposed design is highly applicable, and its detection algorithms can achieve accurate positioning and robust identification even in challenging environments.