Hand-Eye Calibration: 4-D Procrustes Analysis Approach

We give a universal analytical solution to the hand-eye calibration problem {AX} = {XB} with known matrices {A} and {B} and unknown variable {X} , all in the set of special Euclidean group SE(3). The developed method relies on the 4-D Procrustes analysis. A unit-octonion representation is proposed for the first time to solve such a Procrustes problem through which an optimal closed-form eigendecomposition solution is derived. By virtue of such a solution, the uncertainty description of {X} , being a sophisticated problem previously, can be solved in a simpler manner. The proposed approach is then verified using simulations and real-world experimentations on an industrial robotic arm. The results indicate that it owns better accuracy and better description of uncertainty and consumes much less computation time.