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A kinematic calibration method based on the product of exponentials formula for serial robot using position measurements

Published online by Cambridge University Press:  01 April 2014

Ruibo He ,
Xiwen Li ,
Tielin Shi ,
Bo Wu ,
Yingjun Zhao ,
Fenglin Han ,
Shunian Yang ,
Shuhong Huang  and
Shuzi Yang
Ruibo He
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China
Xiwen Li
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China
Tielin Shi*
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China
Bo Wu
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China
Yingjun Zhao
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China
Fenglin Han
Affiliation:
College of Mechanical and Electrical Engineering, Central South University, Changsha, Hunan, P.R. China
Shunian Yang
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China
Shuhong Huang
Affiliation:
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China
Shuzi Yang
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China
*
*Corresponding author. E-mail: tlshi@mail.hust.edu.cn
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Summary

Based on product of exponentials (POE) formula, three explicit error models are given in this paper for kinematic calibration of serial robot through measuring its end-effector positions. To obtain these error models, the tool frame should be chosen as reference frame at first, and then each position–error-related segment in the error models using pose measurement should be selected. And during kinematic parameter identification, all the errors in joint twists are identifiable, and the initial transformation errors and the joint zero-position errors can be identified conditionally. Namely, the initial transformation errors are identifiable if they do not contain orientation errors. And the joint zero-position errors are identifiable when a robot only consists of prismatic joints and the coordinates of its joint twists are linearly independent.

The effectiveness of this calibration method has been validated by simulations and experiments. The results show that: (1) the identification algorithms are robust and practical. (2) The method of position measurement is superior to that of pose measurement.

Keywords

Calibration and identificationProduct of exponentials formulaError modelKinematic calibration
Type
Articles
Information
Robotica , Volume 33 , Issue 6 , July 2015 , pp. 1295 - 1313
Copyright
Copyright © Cambridge University Press 2014 

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References

1. Zhuang, H. and Roth, Z. S., Camera-aided Robot Calibration (CRC Press, Boca Raton, Florida, 1996).Google Scholar
2. Zhuang, H. and Roth, Z. S., “Robot calibration using the CPC error model,” Robot. Cim.-Int. Manuf. 9 (3), 227–237 (1992).Google Scholar
3. Wu, C., “A kinematic CAD tool for the design and control of a robot manipulator,” Int. J. Robot. Res. 3 (1), 58–67 (1984).Google Scholar
4. Hayati, S. A., “Robot Arm Geometric Link Parameter Estimation,” Proceedings of the 22nd IEEE Conference on Decision and Control, San Antonio, TX, USA (Dec. 14–16, 1983) pp. 1477–1483.Google Scholar
5. Hayati, S. and Mirmirani, M., “Improving the absolute positioning accuracy of robot manipulators,” J. Robot. Syst. 2 (4), 397–413 (1985).Google Scholar
6. Hayati, S., Tso, K. and Roston, G., “Robot Geometry Calibration,” Proceedings of the IEEE International Conference on Robotics and Automation, Philadelphia, PA, USA (Apr. 24–29, 1988) pp. 947–951.Google Scholar
7. Veitschegger, W. and Wu, C. H., “Robot accuracy analysis based on kinematics,” IEEE Trans. Robot. Autom. RA-2 (3), 171–179 (1986).Google Scholar
8. He, R., Zhao, Y., Yang, S. and Yang, S., “Kinematic-parameter identification for serial-robot calibration based on POE formula,” IEEE Trans. Robot. 26 (3), 411–423 (2010).Google Scholar
9. Park, F. C. and Okamura, K., “Kinematic Calibration and the Product of Exponential Formula,” In: Advances in Robot Kinematics and Computational Geometry (Lenarčič, J. and Ravani, B., eds.) (MIT Press, Cambridge, 1994) pp. 119–128.Google Scholar
10. Okamura, K. and Park, F. C., “Kinematic calibration using the product of exponentials formula,” Robotica 14, 415–421 (1996).Google Scholar
11. Lou, Y., Chen, T., Wu, Y., Li, Z. and Jiang, S., “Improved and Modified Geometric Formulation of POE Based Kinematic Calibration of Serial Robots,” Proceedings of the 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, USA (Oct. 11–15, 2009) pp. 5261–5266.Google Scholar
12. Duelen, G. and Schröer, K., “Robot calibration–method and results,” Robot. Cim.-Int. Manuf. 8 (4), 223–231 (1991).Google Scholar
13. Mustafa, S. K., Yang, G., Yeo, S. H. and Lin, W., “Kinematic Calibration of a 7-DOF Self-calibrated Modular Cable-driven Robotic Arm,” Proceedings of the IEEE International Conference on Robotics and Automation, Pasadena, CA, USA (May 19–23, 2008) pp. 1288–1293.Google Scholar
14. Chen, I. M. and Yang, G., “Kinematic calibration of modular reconfigurable robots using product-of-exponentials formula,” J. Robot. Syst. 14 (11), 807–821 (1997).Google Scholar
15. Chen, I. M., Yang, G., Tan, C. T. and Yeo, S. H., “Local POE model for robot kinematic calibration,” Mech. Mach. Theory 36 (11/12), 1215–1239 (2001).Google Scholar
16. Sultan, I. A. and Wager, J. G., “A technique for independent-axis calibration of robot manipulators with experimental verification,” Int. J. Comput. Integ. M. 14 (5), 501–512 (2001).Google Scholar
17. Shih, S., Hung, Y. and Liu, W., “New closed-form solution for kinematic parameter identification of a binocular head using point measurements,” IEEE Trans. Syst. Man Cybern. Part B 28 (2), 258–267 (1998).Google Scholar
18. Barker, L. K., “Vector-algebra Approach to Extract Denavit–Hartenberg Parameters of Assembled Robot Arms,” NASA Technology Paper 2191, (Aug. 1983).Google Scholar
19. Meggiolaro, M. A. and Dubowsky, S., “An Analytical Method to Eliminate the Redundant Parameters in Robot Calibration,” Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA, USA (Apr. 24–28, 2000) pp. 3609–3615.Google Scholar
20. Schröer, K., Albright, S. L. and Grethlein, M., “Complete, minimal and model-continuous kinematic models for robot calibration,” Robot. Comput.-Integr. Manuf. 13 (1), 73–85 (1997).Google Scholar
21. Everett, L. J. and Ong, L. E., “Determining Essential Parameters for Calibration,” Proceedings of the 1993 ASME Winter Annual Meeting, New Orleans, LA, USA (Nov. 28–Dec. 3, 1993) pp. 295–302.Google Scholar
22. Khalil, W., Gautier, M. and Enguehard, C., “Identifiable parameters and optimum configurations for robots calibration,” Robotica 9, 63–70 (1991).Google Scholar
23. Bullo, F. and Murray, R. M., “Proportional Derivative (PD) Control on the Euclidean Group,” European Control Conference 1995, Rome, Italy (Sep. 5–8, 1995) pp. 1091–1097.Google Scholar
24. Murray, R. M., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation (CRC Press, Boca Raton, FL, USA 1994).Google Scholar
25. Selig, J. M., Geometric Fundamentals of Robotics (Springer, New York, 2005).Google Scholar