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Research Papers

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

[+] Author and Article Information
Mili Shah

Department of Mathematics and Statistics
at Loyola University Maryland,
4501 North Charles Street,
Baltimore, MD 21210;
Intelligent Systems Division at National Institute
of Standards and Technology (NIST),
100 Bureau Drive,
Gaithersburg, MD 20899
e-mail: mishah@loyola.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received September 1, 2012; final manuscript received April 29, 2013; published online June 20, 2013. Assoc. Editor: J. M. Selig.

J. Mechanisms Robotics 5(3), 031007 (Jun 24, 2013) (7 pages) Paper No: JMR-12-1131; doi: 10.1115/1.4024473 History: Received September 01, 2012; Revised April 29, 2013

This paper constructs a separable closed-form solution to the robot-world/hand-eye calibration problem AX = YB. 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.

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References

Shah, M., Eastman, R. D., and Hong, T., 2012, “An Overview of Robot-Sensor Calibration Methods for Evaluation of Perception Systems,” Proceedings of the Workshop on Performance Metrics for Intelligent Systems, PerMIS'12, ACM, pp. 15–20.
Strobl, K., and Hirzinger, G., 2006, “Optimal Hand-Eye Calibration,” IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4647–4653.
Remy, S., Dhome, M., Lavest, J., and Daucher, N., 1997, “Hand-Eye Calibration,” International Conference on Intelligent Robots and Systems, (IROS), Vol. 2, pp. 1057–1065.
Dornaika, F., and Horaud, R., 1998, “Simultaneous Robot-World and Hand-Eye Calibration,” IEEE Trans. Rob. Autom., 14(4), pp. 617–622. [CrossRef]
Hirsh, R. L., DeSouza, G. N., and Kak, A. C., 2001, “An Iterative Approach to the Hand-Eye and Base-World Calibration Problem,” International Conference on Robotics and Automation (ICRA), Vol. 3, pp. 2171–2176.
Kim, S.-J., Jeong, M.-H., Lee, J.-J., Lee, J.-Y., Kim, K.-G., You, B.-J., and Oh, S.-R., 2010, “Robot Head-Eye Calibration Using the Minimum Variance Method,” International Conference on Robotics and Biomimetics (ROBIO), IEEE, pp. 1446–1451.
Yang, G., Chen, I.-M., Yeo, S. H., Lim, W. K., 2002, “Simultaneous Base and Tool Calibration for Self-Calibrated Parallel Robots,” Robotica, 20(4), pp. 367–374. Available at: http://155.69.254.10/users/risc/Pub/Conf/00-c-icarcv-simcal.pdf [CrossRef]
Zhuang, H., Roth, Z. S., and Sudhakar, R., 1994, “Simultaneous Robot/World and Tool/Flange Calibration by Solving Homogeneous Transformation Equations of the Form AX = YB,” IEEE Trans. Rob. Autom., 10(4), pp. 549–554. [CrossRef]
Li, A., Wang, L., and Wu, D., 2010, “Simultaneous Robot-World and Hand-Eye Calibration Using Dual-Quaternions and Kronecker Product,” Inter. J. Phys. Sci., 5(10), pp. 1530–1536.
Ernst, F., Richter, L., Matthäus, L., Martens, V., Bruder, R., Schlaefer, A., and Schweikard, A., 2012, “Non-Orthogonal Tool/Flange and Robot/World Calibration,” Int. J. Med. Rob. Comput. Assist. Surg., 8(4), pp. 407–420. [CrossRef]
Shiu, Y. C., and Ahmad, S., 1989, “Calibration of Wrist-Mounted Robotic Sensors by Solving Homogeneous Transform Equations of the Form AX=XB,” IEEE Trans. Rob. Autom., 5(1), pp. 16–29. [CrossRef]
Tsai, R. Y., and Lenz, R. K., 1989, “A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration,” IEEE Trans. Rob. Autom., 5(3), pp. 345–358. [CrossRef]
Wang, C.-C., 1992, “Extrinsic Calibration of a Vision Sensor Mounted on a Robot,” IEEE Trans. Rob. Autom., 8, pp. 161–175. [CrossRef]
Park, F. C., and Martin, B. J., 1994, “Robot Sensor Calibration: Solving AX = XB on the Euclidean Group,” IEEE Trans. Rob. Autom., 10(5), pp. 717–721. [CrossRef]
Chou, J. C., and Kamel, M., 1991, “Finding the Position and Orientation of a Sensor on a Robot Manipulator Using Quaternions,” Int. J. Robot. Res., 10(3), pp. 240–254. [CrossRef]
Zhuang, H., Roth, Z., Shiu, Y., and Ahmad, S., 1991, “Comments on” Calibration of Wrist-Mounted Robotic Sensors by Solving Homogeneous Transform Equations of the Form AX = XB” [With Reply],” IEEE Trans. Rob. Autom., 7(6), pp. 877–878. [CrossRef]
Horaud, R., and Dornaika, F., 1995, “Hand-Eye Calibration,” Int. J. Robot. Res., 14(3), pp. 195–210. [CrossRef]
Lu, Y.-C., and Chou, J. C., 1995, “Eight-Space Quaternion Approach for Robotic Hand-Eye Calibration,” IEEE International Conference on Systems, Man and Cybernetics, 4, pp. 3316–3321.
Daniilidis, K., and Bayro-Corrochano, E., 1996, “The Dual Quaternion Approach to Hand-Eye Calibration,” Proceedings of the 13th International Conference on Pattern Recognition, Vol. 1, pp. 318–322.
Daniilidis, K., 1999, “Hand-Eye Calibration Using Dual Quaternions,” Int. J. Robot. Res., 18(3), pp. 286–298. [CrossRef]
Malti, A., and Barreto, J. P., 2010, “Robust Hand-Eye Calibration for Computer Aided Medical Endoscopy,” International Conference on Robotics and Automation (ICRA), pp. 5543–5549.
Chen, H. H., 1991, “A Screw Motion Approach to Uniqueness Analysis of Head-Eye Geometry,” IEEE Proceedings of Computer Vision and Pattern Recognition (CVPR), pp. 145–151.
Andreff, N., Horaud, R., and Espiau, B., 2001, “Robot Hand-Eye Calibration Using Structure From Motion,” Int. J. Robot. Res., 20(3), pp. 228–248. [CrossRef]
Laub, A. J., 2004, Matrix Analysis for Scientists and Engineers, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Shah, M., 2011, “Comparing Two Sets of Corresponding Six Degree of Freedom Data,” Comput. Vis. Image Underst., 115(10), pp. 1355–1362. [CrossRef]
Chang, T., Hong, T., Falco, J., Shneier, M., Shah, M., and Eastman, R., 2010, “Methodology for Evaluating Static Six-Degree-of-Freedom (6DOF) Perception Systems,” Proceedings of the 10th Performance Metrics for Intelligent Systems Workshop, PerMIS'10, ACM, pp. 290–297.

Figures

Grahic Jump Location
Fig. 1

Experimental setup consisting of two systems: a computer vision system and a precise sensor system considered ground truth

Grahic Jump Location
Fig. 2

Comparison of the Kronecker product method described in this paper (circles), the Li et al. Kronecker product method described in Ref. [9] (triangles), and the Dornaika and Horaud closed-form quaternion method described in Ref. [4] (solid line) on simulated data.

Grahic Jump Location
Fig. 3

Experimental setup of the commercial system with the laser tracker system

Grahic Jump Location
Fig. 4

Comparison of the Kronecker product method described in this paper (circles), the Li et al. Kronecker product method described in Ref. [9] (triangles), and hand-calibration results (squares) on real data.

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