Calibration method for hand-eye system with rotation and translation couplings

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.

Improved Calibration of Eye-in-Hand Robotic Vision System Based on Binocular Sensor

Eye-in-hand robotic binocular sensor systems are indispensable equipment in the modern manufacturing industry. However, because of the intrinsic deficiencies of the binocular sensor, such as the circle of confusion and observed error, the accuracy of the calibration matrix between the binocular sensor and the robot end is likely to decline. These deficiencies cause low accuracy of the matrix calibrated by the traditional method. In order to address this, an improved calibration method for the eye-in-hand robotic vision system based on the binocular sensor is proposed. First, to improve the accuracy of data used for solving the calibration matrix, a circle of confusion rectification method is proposed, which rectifies the position of the pixel in images in order to make the detected geometric feature close to the real situation. Subsequently, a transformation error correction method with the strong geometric constraint of a standard multi-target reference calibrator is developed, which introduces the observed error to the calibration matrix updating model. Finally, the effectiveness of the proposed method is validated by a series of experiments. The results show that the distance error is reduced to 0.080 mm from 0.192 mm compared with the traditional calibration method. Moreover, the measurement accuracy of local reference points with updated calibration results from the field is superior to 0.056 mm.

Hand-eye calibration for an unfocused light-field camera

A calibration framework is established for an unfocused light-field camera and a robotic arm. With Gaussian optics and light-field imaging principles, the mapping relationship between a point light source and its corresponding plenoptic disc feature is established, and the intrinsic and extrinsic parameters of the unfocused light-field camera are calculated through nonlinear optimization. Transformation matrices for eye-to-hand and eye-in-hand configurations are subsequently solved and are validated by applying them to an industrial light-field camera-robotic arm system. With the proposed calibration method, 3D reconstruction for calibration board in different poses is demonstrated and calibration uncertainty is discussed in detail.

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%.