Solving the Robot-World/Hand-Eye Calibration Problem Using the Kronecker Product

This paper constructs a separable closed-form solution to the robot-world/hand-eye calibration problem AX1⁄4YB. Qualifications and properties that determine the uniqueness of X and Y as well as error metrics that measure the accuracy of a given X and Y are given. The formulation of the solution involves the Kronecker product and the singular value decomposition. The method is compared with existing solutions on simulated data and real data. It is shown that the Kronecker method that is presented in this paper is a reliable and accurate method for solving the robot-world/hand-eye calibration problem. [DOI: 10.1115/1.4024473]

[1]  Mili Shah.  Comparing two sets of corresponding six degree of freedom data , 2011, Comput. Vis. Image Underst..

[2]  Abed Malti,et al.  Robust hand-eye calibration for computer aided medical endoscopy , 2010, 2010 IEEE International Conference on Robotics and Automation.

[3]  Frank Chongwoo Park,et al.  Robot sensor calibration: solving AX=XB on the Euclidean group , 1994, IEEE Trans. Robotics Autom..

[4]  Kostas Daniilidis,et al.  Hand-Eye Calibration Using Dual Quaternions , 1999, Int. J. Robotics Res..

[5]  Mili Shah,et al.  An overview of robot-sensor calibration methods for evaluation of perception systems , 2012, PerMIS.

[6]  Ji-Yong Lee,et al.  Robot Head-Eye calibration using the Minimum Variance method , 2010, 2010 IEEE International Conference on Robotics and Biomimetics.

[7]  Alexander Schlaefer,et al.  Non‐orthogonal tool/flange and robot/world calibration , 2012, The international journal of medical robotics + computer assisted surgery : MRCAS.

[8]  Ching-Cheng Wang,et al.  Extrinsic calibration of a vision sensor mounted on a robot , 1992, IEEE Trans. Robotics Autom..

[9]  Defeng Wu,et al.  Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product , 2010 .

[10]  Fadi Dornaika,et al.  Hand-Eye Calibration , 1995, Int. J. Robotics Res..

[11]  Jack C. K. Chou,et al.  Eight-space quaternion approach for robotic hand-eye calibration , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[12]  H.H. Chen,et al.  A screw motion approach to uniqueness analysis of head-eye geometry , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  Yiu Cheung Shiu,et al.  Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB , 1989, IEEE Trans. Robotics Autom..

[14]  Jack C. K. Chou,et al.  Finding the Position and Orientation of a Sensor on a Robot Manipulator Using Quaternions , 1991, Int. J. Robotics Res..

[15]  Mili Shah,et al.  Methodology for evaluating static six-degree-of-freedom (6DoF) perception systems , 2010, PerMIS.

[16]  Alan J. Laub,et al.  Matrix analysis - for scientists and engineers , 2004 .

[17]  Gerd Hirzinger,et al.  Optimal Hand-Eye Calibration , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[18]  Avinash C. Kak,et al.  An iterative approach to the hand-eye and base-world calibration problem , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[19]  Roger Y. Tsai,et al.  A new technique for fully autonomous and efficient 3D robotics hand/eye calibration , 1988, IEEE Trans. Robotics Autom..

[20]  Fadi Dornaika,et al.  Simultaneous robot-world and hand-eye calibration , 1998, IEEE Trans. Robotics Autom..

[21]  Eduardo Bayro-Corrochano,et al.  The dual quaternion approach to hand-eye calibration , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[22]  Radu Horaud,et al.  Robot Hand-Eye Calibration Using Structure-from-Motion , 2001, Int. J. Robotics Res..

[23]  Hanqi Zhuang,et al.  Simultaneous robot/world and tool/flange calibration by solving homogeneous transformation equations of the form AX=YB , 1994, IEEE Trans. Robotics Autom..

[24]  Yiu Cheung Shiu,et al.  Comments on 'Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB' [with reply] , 1991, IEEE Trans. Robotics Autom..

[25]  Guilin Yang,et al.  Simultaneous base and tool calibration for self-calibrated parallel robots , 2002, Robotica.