Eight-space quaternion approach for robotic hand-eye calibration

In this paper, normalized quaternions (Euler parameters) are used to transform the kinematic equation into two simple and well-structured linear systems; where the kinematic equation, H_lH_x=H_xH_c, is formulated for the problem of finding the relative position and orientation between the reference frames of a link-mounted sensor and the link. Two distinct robot movements are required to obtain a unique solution. This leaps to an overdetermined system of equations, and the least-squares solution are obtained. Further, least-squares closed-form solutions to these systems are derived using the Gaussian elimination and Schur decomposition analysis. The selection criterion and the solution formulae can be easily incorporated in application programs which require the calculation of the relative position and orientation of the sensor