Singularity Analysis for the Existing Closed-Form Solutions of the Hand-Eye Calibration

• Main Authors: Huajian Song, Zhijiang Du, Weidong Wang, Lining Sun
• Format: Article
• Language: English
• Published: IEEE 2018-01-01
• Series: IEEE Access
• Subjects: Hand-eye calibration; singularity analysis; observability index; additional rotation theory; surgical robot; closed-form solution
• Online Access: https://ieeexplore.ieee.org/document/8540357/

In this paper, a class of singular phenomenon is first found for the existing closed-form solutions of the hand-eye calibration problem with the form AiX = XBi when the angles corresponding to rotational parts of Ai and Bi are near or equal to π radian. A universal observability index is put forward to detect when this singularity would undoubtedly occur. For avoiding this singularity, a novel analytical solution based on a new cost function is proposed to estimate the hand-eye matrix in the presence of measurement errors. Simulation and experimental results can illustrate the feasibility and benefits of the proposed observability index and the singular-free closed-form solution. In addition, the other kind of singular phenomenon is also discovered for the existing closed-form solution, where the orientation of the unknown hand-eye matrix is parameterized by modified Rodrigues parameters. Therefore, in order to obtain the non-singular analytical solution based on modified Rodrigues parameters, a novel additional rotation theory is introduced and verified by the hand-eye calibration of a novel surgical robot.