Precise hand–eye calibration method based on spatial distance and epipolar constraints

Abstract

In this paper, a new hand–eye calibration method based on spatial distance and epipolar constraints is proposed to obtain the transformation X between the end effector (hand) of the robotic arm and the camera (eye) fixed on the end effector. Most of the current effective hand–eye calibration methods utilize the classical identity, AX=XB, to obtain the analytical solution of X, and then apply various constraints to iteratively optimize the initial X, but these constraints are often at the 2D level. However, the result of hand–eye​ calibration needs to ensure the accuracy of the vision-guided robot arm system operating in 3D space, which leads to inconsistency between optimization goals and the actual requirements. Therefore, the proposed method introduces 3D constraints into the iterative optimization of X and takes 3D error as an evaluation indicator of the calibration quality. There are two main steps in the proposed method. Firstly, the initial value of hand–eye transformation matrix is calculated by utilizing Kronecker product, which avoids the error propagation from rotation parameters to translation parameters. Then, the inherent epipolar constraints and the spatial distance constraints between feature points are combined to optimize hand–eye calibration parameters iteratively. To evaluate the precision and robustness of the proposed method, both simulation experiment and real experiment are carried out. The experimental results show that compared with conventional methods, the proposed method has higher accuracy and stronger robustness.