A New Formulation for Hand–Eye Calibrations as Point-Set Matching

Conventional methods formulate the calibration problem between a robot hand and a camera, also known as hand-eye-calibration problem, as AX = XB. However, in practice, these methods have limited accuracy, as will be shown in our experimental results. In this article, we formulated the hand-eye calibration problem as a point-set-matching problem and proposed a new approach to solve this problem. The proposed approach is particularly suitable for robotic applications and offers good accuracy. We obtain a solution for the said problem using the gradient-descent (GD) technique on the special Euclidean group SE(3). We call this approach GD-SE(3). To prove the validity of the proposed approach and to demonstrate its advantages, experimental results are provided, where we compare the performance of GD-SE(3) with both conventional solutions for the hand-eye calibration problem as well as those based on point-set matching. The results show that the accuracy of GD-SE(3) is comparable with those based on other point-set-matching algorithms. Yet, it outperforms conventional formulations based on AX = XB while offering a more suitable approach for the hand-eye calibration problem of robot manipulators.