GBEC: Geometry-Based Hand-Eye Calibration

Hand-eye calibration is the problem of solving the transformation from the end-effector of a robot to the sensor attached to it. Commonly employed techniques, such as AXXB or AXZB formulations, rely on regression methods that require collecting pose data from different robot configurations, which can produce low accuracy and repeatability. However, the derived transformation should solely depend on the geometry of the end-effector and the sensor attachment. We propose Geometry-Based End-Effector Calibration (GBEC) that enhances the repeatability and accuracy of the derived transformation compared to traditional hand-eye calibrations. To demonstrate improvements, we apply the approach to two different robot-assisted procedures: Transcranial Magnetic Stimulation (TMS) and femoroplasty. We also discuss the generalizability of GBEC for camera-in-hand and marker-in-hand sensor mounting methods. In the experiments, we perform GBEC between the robot end-effector and an optical tracker’s rigid body marker attached to the TMS coil or femoroplasty drill guide. Previous research documents low repeatability and accuracy of the conventional methods for robot-assisted TMS hand-eye calibration. Applying GBEC to repeated calibrations, we obtain transformations with standard deviations of 0.37mm, 0.65mm, and 0.40mm (translation) along x, y, and z axes of the end-effector, respectively. The tool alignment experiments after using GBEC achieve a mean accuracy around 0.2mm in Euclidean distance. When compared to some existing methods, the proposed method relies solely on the geometry of the flange and the pose of the rigid-body marker, making it independent of workspace constraints or robot accuracy, without sacrificing the orthogonality of the rotation matrix. Our results validate the accuracy and applicability of the approach, providing a new and generalizable methodology for obtaining the transformation from the end-effector to a sensor.