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Kinematic calibration of serial manipulators using Bayesian inference

Published online by Cambridge University Press:  25 January 2018

Elie Shammas  and
Shadi Najjar
Elie Shammas*
Affiliation:
Department of Mechanical Engineering and Department of Civil and Environmental Engineering American University of Beirut, Beirut, Lebanon. E-mail: sn06@aub.edu.lb
Shadi Najjar
Affiliation:
Department of Mechanical Engineering and Department of Civil and Environmental Engineering American University of Beirut, Beirut, Lebanon. E-mail: sn06@aub.edu.lb
*
*Corresponding author. E-mail: es34@aub.edu.lb
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Summary

In this paper, a new calibration method for open-chain robotic arms is developed. By incorporating both prior parameter information and artifact measurement data, and by taking recourse to Bayesian inference methods, not only are the robot kinematic parameters updated but also confidence bounds are computed for all measurement data. In other words, for future measurement data not only the most likely end-effector configuration is estimated but also the uncertainty represented as 95% confidence bounds of that pose is computed. To validate the proposed calibration method, a three degree-of-freedom robotic arm was designed, constructed, and calibrated using both typical regression methods and the proposed calibration method. The results of an extensive set of experiments are presented to gauge the accuracy and utility of the proposed calibration method.

Keywords

Kinematic calibrationBayesian updatingLikelihood functionSecond-moment Bayesian method
Type
Articles
Information
Robotica , Volume 36 , Issue 5 , May 2018 , pp. 738 - 766
Copyright
Copyright © Cambridge University Press 2018 

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References

1. Aoyagi, S., Kohama, A., Nakata, Y., Hayano, Y. and Suzuki, M., “Improvement of Robot Accuracy by Calibrating Kinematic Model Using a Laser Tracking System-Compensation of Non-Geometric Errors Using Neural Networks and Selection of Optimal Measuring Points Using Genetic Algorithm,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (2010) pp. 5660–5665.Google Scholar
2. ASME B89, “ASME B89.4.22-2004, methods for performance evaluation of articulated arm coordinate measuring machines,” Technical report, ASME (2004).Google Scholar
3. Bennett, D. J., Geiger, D. and Hollerbach, J. M., “Autonomous robot calibration for hand-eye coordination,” Int. J. Robot. Res. 10 (5), 550–559 (1991).CrossRefGoogle Scholar
4. Borm, J. H. and Meng, C. H., “Determination of optimal measurement configurations for robot calibration based on observability measure,” Int. J. Robot. Res. 10 (1), 51–63 (1991).Google Scholar
5. Brooks, S., Gelman, A., Jones, G. and Meng, X. L., Handbook of Markov Chain Monte Carlo. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. (Boca Raton, FL, U.S.A., CRC Press/Taylor & Francis, 2011).CrossRefGoogle Scholar
6. Chen, J. and Chao, L. M., “Positioning error analysis for robot manipulators with all rotary joints,” IEEE J. Robot. Autom. 3 (6), 539–545 (1987).Google Scholar
7. Christian, J. T. and Baecher, G. B., “Point-estimate method as numerical quadrature,” J. Geotech. Geoenvironmental Eng. 125 (9), 779–786 (1999).Google Scholar
8. Daney, D., Papegay, Y. and Madeline, B., “Choosing measurement poses for robot calibration with the local convergence method and tabu search,” Int. J. Robot. Res. 24 (6), 501–518 (2005).CrossRefGoogle Scholar
9. Denavit, J. and Hartenberg, R. S., “A kinematic notation for lower-pair mechanisms based on matrices,” Trans. ASME J. Appl. Mech. 22, 215–221 (1955).Google Scholar
10. Driels, M. R. and Pathre, U. S., “Vision-based automatic theodolite for robot calibration,” IEEE Trans. Robot. Autom. 7 (3), 351–360 (1991).Google Scholar
11. Driels, M. R., Swayze, L. W. and Potter, L. S., “Full-pose calibration of a robot manipulator using a coordinate-measuring machine,” Int. J. Adv. Manuf. Technol. 8 (1), 34–41 (1993).Google Scholar
12. Dumas, C., Caro, S., Cherif, M., Garnier, S. and Furet, B., “A Methodology for Joint Stiffness Identification of Serial Robots,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (2010) pp. 464–469.Google Scholar
13. Edwards, C. A. and Galloway, R. L., “A single-point calibration technique for a six degree-of-freedom articulated arm,” Int. J. Robot. Res. 13 (3), 189–198 (1994).CrossRefGoogle Scholar
14. Everett, L. J., “Forward calibration of closed-loop jointed manipulators,” 8 (4), 85–91 (1989).Google Scholar
15. Gatla, C. S., Lumia, R., Wood, J. and Starr, G., “An automated method to calibrate industrial robots using a virtual closed kinematic chain,” IEEE Trans. Robot. 23 (6), 1105–1116 (2007).CrossRefGoogle Scholar
16. Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B., “Bayesian Data Analysis, volume 2 (Chapman & Hall/CRC Boca Raton, FL, USA, 2014).Google Scholar
17. Gilbert, R., “First-order, second-moment Bayesian method for data analysis in decision making,” Technical report, Department of Civil Engineering, The University of Texas at Austin (1999).Google Scholar
18. Zhuang, H., “A note on the use of identification Jacobians for robot calibration,” Int. J. Robot. Res. 14 (1), 87–89 (1995).CrossRefGoogle Scholar
19. Hartenberg, R. S. and Denavit, J., Kinematic Synthesis of Linkages. McGraw-Hill series in mechanical engineering. (New York, NY, U.S.A., McGraw-Hill, 1964).Google Scholar
20. Hayati, S., Tso, K. and Roston, G., “Robot Geometry Calibration,” Proceedings of the IEEE International Conference on Robotics and Automation (1988) pp. 947–951.Google Scholar
21. Hayati, S. A., “Robot Arm Geometric Link Parameter Estimation,” Proceedings of the 22nd IEEE Conference on Decision and Control, Vol. 22 (1983) pp. 1477–1483.Google Scholar
22. He, R., Li, X., Shi, T., Wu, B., Zhao, Y., Han, F., Yang, S., Huang, S. and Yang, S., “A kinematic calibration method based on the product of exponentials formula for serial robot using position measurements,” Robotica 33, 1295–1313 (2015).Google Scholar
23. 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
24. Hexagon, A. B., “Hexagon Metrology: Romer protable coordinate measuring machines,” hexagonmi.com/products/portable-measuring-arms (2015).Google Scholar
25. Hollerbach, J. M. and Wampler, C. W., “The calibration index and taxonomy for robot kinematic calibration methods,” Int. J. Robot. Res. 15 (6), 573–591 (1996).CrossRefGoogle Scholar
26. Hoppe, W., “Method and system to provide improved accuracies in multi-jointed robots through kinematic robot model parameters determination,” US Patent 7,904,202 (2011).Google Scholar
27. Huang, C., Xie, C. and Zhang, T., “Determination of Optimal Measurement Configurations for Robot Calibration Based on a Hybrid Optimal Method,” Proceedings of the International Conference on Information and Automation, ICIA (2008) pp. 789–793.Google Scholar
28. Ikits, M. and Hollerbach, J. M., “Kinematic Calibration Using a Plane Constraint,” Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 4, (1997) pp. 3191–3196.Google Scholar
29. ISO/DIS 10360, “ISO/DIS 10360-12 - geometrical product specifications (gps) acceptance and reverification tests for coordinate measuring systems (cms) part 12: Articulated arm coordinate measurement machines (cmm),” Technical report, ISO (2014).Google Scholar
30. Jang, J. H., Kim, S. H. and Kwak, Y. K., “Calibration of geometric and non-geometric errors of an industrial robot,” Robotica 19, 311–321 (2001).CrossRefGoogle Scholar
31. Jing, W., Tao, P. Y., Yang, G. and Shimada, K., “Calibration of Industry Robots with Consideration of Loading Effects Using Product-of-Exponential (poe) and Gaussian Process (gp),” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (2016) pp. 4380–4385.Google Scholar
32. Joubair, A., Slamani, M. and Bonev, I. A., “Kinematic Calibration of a Five-Bar Planar Parallel Robot Using All Working Modes,” Robot. Comput.-Integr. Manuf. 29 (4), 15–25 (2013).Google Scholar
33. Judd, R. P. and Knasinski, A. B., “A technique to calibrate industrial robots with experimental verification,” IEEE Trans. Robot. Autom. 6 (1), 20–30 (1990).CrossRefGoogle Scholar
34. Karlsson, B. and Brogårdh, T., “A new calibration method for industrial robots,” Robotica 19, 691–693 (2001).CrossRefGoogle Scholar
35. Khalil, W., Gautier, M. and Enguehard, C., “Identifiable parameters and optimum configurations for robots calibration,” Robotica 9, 63–70 (1991).Google Scholar
36. Kirchner, H. O. K., Gurumoorthy, B. and Prinz, F. B., “A perturbation approach to robot calibration,” Int. J. Robot. Res. 6 (4), 47–59 (1987).Google Scholar
37. Knoll, A. and Kovacs, P., “Method and device for the improvement of the pose accuracy of effectors on mechanisms and for the measurement of objects in a workspace,” US Patent 6,529,852 (2003).Google Scholar
38. Larson, H., Introduction to Probability Theory and Statistical Inference. Probability and Mathematical Statistics Series. (New York, NY, U.S.A., Wiley, 1982). ISBN 9780471099192.Google Scholar
39. McGrath, T. C. and Gilbert, R. B., “Analytical method for designing and analyzing 1d search programs,” J. Geotech. Geoenvironmental Eng. 125 (12), 1043–1056 (1999).CrossRefGoogle Scholar
40. Meggiolaro, M. A., “Manipulator Calibration Using a Single Endpoint Contact Constraint,” Proceedings of ASME Design Engineering Technical Conference (2000).Google Scholar
41. Najjar, S. S., Shammas, E. and Saad, M., “Updated normalized load-settlement model for full-scale footings on granular soils,” Georisk: Assess. Manage. Risk Engineered Syst. Geohazards 8 (1), 63–80 (2014).Google Scholar
42. Newman, W. S. and Osborn, D. W., “A New Method for Kinematic Parameter Calibration Via Laser Line Tracking,” Proceedings of the IEEE International Conference on Robotics and Automation (1993) pp. 160–165.Google Scholar
43. Nubiola, A., Slamani, M., Joubair, A. and Bonev, I. A., “Comparison of two calibration methods for a small industrial robot based on an optical cmm and a laser tracker,” Robotica 32, 447–466 (2014).Google Scholar
44. Okamura, K. and Park, F., “Kinematic calibration using the product of exponentials formula,” Robotica 14, 415–421 (1996).CrossRefGoogle Scholar
45. Park, I. W., Lee, B. J., Cho, S. H., Hong, Y. D. and Kim, J. H., “Laser-based kinematic calibration of robot manipulator using differential kinematics,” IEEE/ASME Trans. Mechatron. 17 (6), 1059–1067 (2012).Google Scholar
46. Renders, J. M., Rossignol, E., Becquet, M. and Hanus, R., “Kinematic calibration and geometrical parameter identification for robots,” IEEE Trans. Robot. Autom. 7 (6), 721–732 (1991).Google Scholar
47. Robert, C. and Casella, G., Monte Carlo Statistical Methods. (New York, NY, U.S.A., Springer Science & Business Media, 2013).Google Scholar
48. Roth, Z. S., Mooring, B. and Ravani, B., “An overview of robot calibration,” IEEE J. Robot. Autom. 3 (5), 377–385 (1987).CrossRefGoogle Scholar
49. Scholz, F., “Tolerance stack analysis methods,” Technical report, The Department of Statistics at the University of Washington (1995).Google Scholar
50. Spiess, S., Vincze, M. and Ayromiou, M., “On the calibration of a 6-d laser tracking system for dynamic robot measurements,” IEEE Trans. Instrum. Meas. 47 (1), 270–274 (1998).Google Scholar
51. Tarantola, A., Inverse Problem Theory and Methods for Model Parameter Estimation. Other Titles in Applied Mathematics. (Philadelphia, PA, U.S.A., Society for Industrial and Applied Mathematics, 2005).Google Scholar
52. Welker, A. L. and Gilbert, R. B., “Calibration of flow and transport model with a bench-scale prefabricated vertical drain remediation system,” J. Geotech. Geoenvironmental Eng. 129 (1), 81–90 (2003).CrossRefGoogle Scholar
53. Welker, A. L. and Gilbert, R. B., “Design of a measurement program for a bench-scale pvd remediation system using Bayesian updating,” Geotech. Testing J. 27 (3), 239–249 (2004).Google Scholar
54. Whitney, D., Lozinski, C. and Rourke, J. M., “Industrial robot forward calibration method and results,” J. Dyn. Syst. Meas. Control 108 (1), 1–8 (1986).Google Scholar
55. Zhang, D. and Wei, B., “Design, analysis and modelling of a hybrid controller for serial robotic manipulators,” Robotica 35 (9), 1888–1905 (2017).Google Scholar
56. Zhuang, H., Roth, Z. S. and Hamano, F., “A complete and parametrically continuous kinematic model for robot manipulators,” IEEE Trans. Robot. Autom. 8 (4), 451–463 (1992).Google Scholar