Simultaneous Robot - World and Hand - Eye

1 Simultaneous Robot-World and Hand-Eye Calibration Fadi Dornaika and Radu Horaud, Member, IEEE Abstract|Recently, Zhuang, Roth, & Sudhakar [1] proposed a method that allows simultaneous computation of the rigid transformations from world frame to robot base frame and from hand frame to camera frame. Their method attempts to solve a homogeneous matrix equation of the form AX = ZB. They use quaternions to derive explicit linear solutions for X and Z. In this short paper, we present two new solutions that attempt to solve the homogeneous matrix equation mentioned above: (i) a closed-form method which uses quaternion algebra and a positive quadratic error function associated with this representation and (ii) a method based on non-linear constrained minimization and which simultaneously solves for rotations and translations. These results may be useful to other problems that can be formulated in the same mathematical form. We perform a sensitivity analysis for both our two methods and the linear method developed by Zhuang et al. [1]. This analysis allows the comparison of the three methods. In the light of this comparison the non-linear optimization method, which solves for rotations and translations simultaneously, seems to be the most stable one with respect to noise and to measurement errors. Keywords| hand/eye calibration, robot/world calibration, quaternion algebra.