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

Submillimeter-Accurate Markerless Hand-Eye Calibration Based on a Robot's Flange Features

An accurate and reliable estimation of the transformation matrix between an optical sensor and a robot is a key aspect of the hand-eye system calibration process in vision-guided robotic applications. This paper presents a novel approach to markerless hand-eye calibration that achieves streamlined, flexible, and highly accurate results, even without error compensation. The calibration procedure is mainly based on using the robot's tool center point (TCP) as the reference point. The TCP coordinate estimation is based on the robot's flange point cloud, considering its geometrical features. A mathematical model streamlining the conventional marker-based hand-eye calibration is derived. Furthermore, a novel algorithm for the automatic estimation of the flange's geometric features from its point cloud, based on a 3D circle fitting, the least square method, and a nearest neighbor (NN) approach, is proposed. The accuracy of the proposed algorithm is validated using a calibration setting ring as the ground truth. Furthermore, to establish the minimal required number and configuration of calibration points, the impact of the number and the selection of the unique robot's flange positions on the calibration accuracy is investigated and validated by real-world experiments. Our experimental findings strongly indicate that our hand-eye system, employing the proposed algorithm, enables the estimation of the transformation between the robot and the 3D scanner with submillimeter accuracy, even when using the minimum of four non-coplanar points for calibration. Our approach improves the calibration accuracy by approximately four times compared to the state of the art, while eliminating the need for error compensation. Moreover, our calibration approach reduces the required number of the robot's flange positions by approximately 40%, and even more if the calibration procedure utilizes just four properly selected flange positions. The presented findings introduce a more efficient hand-eye calibration procedure, offering a superior simplicity of implementation and increased precision in various robotic applications.