A Self-Correctional Hand-Eye Calibration Regime Using Extensive Pose-Image Pairs with Quantifiable Gaussian Errors from Homogeneous Matrices Decomposition

Normally, the eye-to-hand calibration algorithm usually requires 10-20 pairs of coupled robot and object poses in the camera frame to solve the overdetermined linear system of AX=XB. One significant contribution of this research is in quantifying the uncertainties in the results of calibration. The fixed poses represented as homogeneous matrices can be separated into the rotation vectors and the translation vectors, and the rotation vectors are further decoupled into the magnitudes of rotation and the normal vectors representing the direction of rotation. The Gaussian distributions of the magnitudes of rotation, the direction cosines from the average normal direction, and L2 norms of the translation are computed. The spreads of the distributions will not only serve as the close-loop convergence parameters for self-correcting the calibration result, but also as the indicator for the overall quality of the calibration. In addition, given the same set of 100 pose pairs, under the self-correctional approach, we study and compare the rate of convergence, the accuracy of the final calibration results, and the speed of calibration among the algorithms for overdetermined AX=XB developed by Tsai, Park, Horaud, Andreff, and Danillidis.