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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

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. 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.

Grahic Jump Location
Fig. 3

Experimental setup of the commercial system with the laser tracker system

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