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Registration of a hybrid robot using the Degradation-Kronecker method and a purely nonlinear method

Published online by Cambridge University Press:  28 May 2015

S. J. Yan ,
S. K. Ong  and
A. Y. C. Nee
S. J. Yan
Affiliation:
Mechanical Engineering Department, National University of Singapore, 9 Engineering Drive 1, Singapore117576
S. K. Ong*
Affiliation:
Mechanical Engineering Department, National University of Singapore, 9 Engineering Drive 1, Singapore117576
A. Y. C. Nee
Affiliation:
Mechanical Engineering Department, National University of Singapore, 9 Engineering Drive 1, Singapore117576
*
*Corresponding author. E-mail: [email protected]
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Summary

Although the registration of a robot is crucial in order to identify its pose with respect to a tracking system, there is no reported solution to address this issue for a hybrid robot. Different from classical registration, the registration of a hybrid robot requires the need to solve an equation with three unknowns where two of these unknowns are coupled together. This property makes it difficult to obtain a closed-form solution. This paper is a first attempt to solve the registration of a hybrid robot. The Degradation-Kronecker (D-K) method is proposed as an optimal closed-form solution for the registration of a hybrid robot in this paper. Since closed-form methods generally suffer from limited accuracy, a purely nonlinear (PN) method is proposed to complement the D-K method. With simulation and experiment results, it has been found that both methods are robust. The PN method is more accurate but slower as compared to the D-K method. The fast computation property of the D-K method makes it appropriate to be applied in real-time circumstances, while the PN method is suitable to be applied where good accuracy is preferred.

Keywords

Hybrid robotRegistrationRobot-world calibrationHand-eye calibrationDegradation-Kronecker (D-K) methodNonlinear error function
Type
Articles
Information
Robotica , Volume 34 , Issue 12 , December 2016 , pp. 2729 - 2740
Copyright
Copyright © Cambridge University Press 2015 

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References

1. Shiu, Y. and Ahmad, S., “Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX = XB,” IEEE Trans. Robot. Autom. 5 (1), 16–29 (1989).CrossRefGoogle Scholar
2. Tsai, R. Y. and Lenz, R. K., “A new technique for fully autonomous and efficient 3D robotics hand/eye calibration,” IEEE Trans. Robot. Autom. 5 (3), 345–358 (1989).CrossRefGoogle Scholar
3. Richter, L., Ernst, F., Schlaefer, A. and Schweikard, A., “Robust real-time robot–world calibration for robotized transcranial magnetic stimulation,” Int. J. Med. Robot. Comput. Assist. Surg. 7 (4), 414–422 (2011).CrossRefGoogle ScholarPubMed
4. Andreff, N., Horaud, R. and Espiau, B., “On-line Hand-eye Calibration,” Proceedings of the 2nd International Conference on 3-D Digital Imaging and Modeling, Ottawa, Ontario, Canada (1999) pp. 430–436.Google Scholar
5. Chou, J. C. K. and Kamel, M., “Finding the position and orientation of a sensor on a robot manipulator using quaternions,” Int. J. Robot. Res. 10 (3), 240–254 (1991).CrossRefGoogle Scholar
6. Horaud, R. and Dornaika, F., “Hand-eye calibration,” Int. J. Robot. Res. 14 (3), 195–210 (1995).CrossRefGoogle Scholar
7. Daniilidis, K., “Hand-eye calibration using dual quaternions,” Int. J. Robot. Res. 18 (3), 286–298 (1999).CrossRefGoogle Scholar
8. Chen, H., “A Screw Motion Approach to Uniqueness Analysis of Head-Eye Geometry,” Proceedings CVPR '91., IEEE Computer Society Conference on, Computer Vision and Pattern Recognition, Maui, Hawaii, U.S. (1991) pp. 145–151.Google Scholar
9. Zhao, Z. and Liu, Y., “A hand–eye calibration algorithm based on screw motions,” Robotica, 27 (02), 217–223 (2008).CrossRefGoogle Scholar
10. Malti, A., “Hand–eye calibration with epipolar constraints: Application to endoscopy,” Robot. Auton. Syst. 61 (2), 161–169 (2013).CrossRefGoogle Scholar
11. Zhao, Z. and Weng, Y., “A flexible method combining camera calibration and hand–eye calibration,” Robotica, 31 (05), 747–756 (2013).CrossRefGoogle Scholar
12. Motai, Y. and Kosaka, A., “Hand–eye calibration applied to viewpoint selection for robotic vision,” IEEE Trans. Ind. Electron. 55 (10), 3731–3741 (2008).CrossRefGoogle Scholar
13. Ackerman, M. K. and Chirikjian, G. S., “A Probabilistic Solution to the AX = XB Problem: Sensor Calibration without Correspondence,” In: Geometric Science of Information (Nielsen, F. and Barbaresco, F., eds.) (Berlin, Heidelberg, Germany Springer Berlin Heidelberg, 2013) pp. 693–701.CrossRefGoogle Scholar
14. Ackerman, M. K., Cheng, A. and Chirikjian, G. S., “An Information-Theoretic Approach to the Correspondence-Free AX = XB Sensor Calibration Problem,” IEEE International Conference on, Robotics and Automation (ICRA), Hong Kong, China (2014) pp. 4893–4899.Google Scholar
15. Dornaika, F. and Horaud, R., “Simultaneous robot-world and hand-eye calibration,” IEEE Trans. Robot. Autom. 14 (4), 617–622 (1998).CrossRefGoogle Scholar
16. Li, A., Wang, L. and Wu, D., “Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product,” Int. J. Phys. Sci. 5 (10), 1530–1536 (2010).Google Scholar
17. Shah, M., “Solving the robot-world/hand-eye calibration problem using the kronecker product,” J. Mech. Robot. 5 (3), 031007 (2013).CrossRefGoogle Scholar
18. Zhuang, H. Q., Roth, Z. S. and Sudhakar, R., “Simultaneous robot/world and tool/flange calibration by solving homogeneous transformation equations of the form AX = YB,” IEEE Trans. Robot. Autom. 10 (4), 549–554 (1994).CrossRefGoogle Scholar
19. Ernst, F., Richter, L., Matthäus, L., Martens, V., Bruder, R., Schlaefer, A. and Schweikard, A., “Non-orthogonal tool/flange and robot/world calibration,” Int. J. Med. Robot. Comput. Assist. Surg. 8 (4), 407–420 (2012).CrossRefGoogle ScholarPubMed
20. Hirsh, R. L., DeSouza, G. N. and Kak, A. C., “An Iterative Approach to the Hand-Eye and Base-World Calibration Problem,” IEEE International Conference on, Robotics and Automation, 2001. Proceedings 2001 ICRA. Seoul, Korea (2001), vol. 3, pp. 2171–2176.Google Scholar
21. Strobl, K. and Hirzinger, G., “Optimal Hand-Eye Calibration,” IEEE/RSJ International Conference on, Intelligent Robots and Systems, Beijing, China (2006), vol. 3, pp. 4647–4653.Google Scholar
22. Wang, J., Wu, L., Meng, M. Q. H. and Ren, H., “Towards simultaneous coordinate calibrations for cooperative multiple robots,” IEEE/RSJ International Conference on, Intelligent Robots and Systems (IROS 2014), Chicago, Illinois, U.S. (2014) pp. 410–415.Google Scholar
23. Pisla, D., Gherman, B., Vaida, C., Suciu, M. and Plitea, N., “An active hybrid parallel robot for minimally invasive surgery,” Robot. Comput.-Integr. Manuf. 29 (4), 203–221 (2013).CrossRefGoogle Scholar
24. Nakano, T., Sugita, N., Ueta, T., Tamaki, Y. and Mitsuishi, M., “A parallel robot to assist vitreoretinal surgery,” Int. J. Comput. Assist. Radiol. Surg. 4 (6), 517–526 (2009).CrossRefGoogle ScholarPubMed
25. Carbone, G. and Ceccarelli, M., “A serial-parallel robotic architecture for surgical tasks,” Robotica, 23 (03), 345–354 (2005).CrossRefGoogle Scholar