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.

References

References
1.
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
.
2.
Strobl
,
K.
, and
Hirzinger
,
G.
,
2006
, “
Optimal Hand-Eye Calibration
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
, pp.
4647
4653
.
3.
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
.
4.
Dornaika
,
F.
, and
Horaud
,
R.
,
1998
, “
Simultaneous Robot-World and Hand-Eye Calibration
,”
IEEE Trans. Rob. Autom.
,
14
(
4
), pp.
617
622
.10.1109/70.704233
5.
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
.
6.
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
.
7.
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
8.
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
.10.1109/70.313105
9.
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
.
10.
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
.10.1002/rcs.1427
11.
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
.10.1109/70.88014
12.
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
.10.1109/70.34770
13.
Wang
,
C.-C.
,
1992
, “
Extrinsic Calibration of a Vision Sensor Mounted on a Robot
,”
IEEE Trans. Rob. Autom.
,
8
, pp.
161
175
.10.1109/70.134271
14.
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
.10.1109/70.326576
15.
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
.10.1177/027836499101000305
16.
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
.10.1109/70.105398
17.
Horaud
,
R.
, and
Dornaika
,
F.
,
1995
, “
Hand-Eye Calibration
,”
Int. J. Robot. Res.
,
14
(
3
), pp.
195
210
.10.1177/027836499501400301
18.
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
.
19.
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
.
20.
Daniilidis
,
K.
,
1999
, “
Hand-Eye Calibration Using Dual Quaternions
,”
Int. J. Robot. Res.
,
18
(
3
), pp.
286
298
.10.1177/02783649922066213
21.
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
.
22.
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
.
23.
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
.10.1177/02783640122067372
24.
Laub
,
A. J.
,
2004
,
Matrix Analysis for Scientists and Engineers
,
Society for Industrial and Applied Mathematics
,
Philadelphia, PA
.
25.
Shah
,
M.
,
2011
, “
Comparing Two Sets of Corresponding Six Degree of Freedom Data
,”
Comput. Vis. Image Underst.
,
115
(
10
), pp.
1355
1362
.10.1016/j.cviu.2011.05.007
26.
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
.
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