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Application of Universal Kriging for Calibrating Offline-Programming Industrial Robots

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Abstract

The requirement for absolute positioning accuracy has also increased with the increasing use of industrial robots in offline programming. The present study proposed Universal Kriging (UK) for calibrating offline-programming industrial robots. This method was based on the similarities in positional errors. In addition, the method represented the positional errors as a deterministic drift and a residual part, which considered both geometric and non-geometric errors. The semivariogram was designed and the drift was determined to implement UK. Then, the method was applied for predicting positional errors and realizing error compensations. In addition, contrast experiments were performed to verify the practicality and superiority of UK compared with Ordinary Kriging (OK). Experimental results showed that after calibration by UK, the maximum of the original spatial positional errors reduced from 1.3073 mm to 0.2110 mm, that is, by 83.86%. Moreover, the maximum of the spatial positional errors reduced from 1.3073 mm to 0.3148 mm by only 75.92% after calibration using OK. An evident increase was reported in the maximum of the spatial positional errors from 0.3148 mm to 0.2110 mm, with an improvement rate of 32.97%. This is of great significance when accuracy is less than 0.5 mm. Overall, the experimental results proved the effectiveness of UK.

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References

  1. Wang, K., Luo, M.Z., Cao, Y., Li, K., Zhang, Q.J.: Kinematic parameter calibration of a serial manipulator based on genetic algorithm. J. Syst. Sci. Math. Sci. 35(1), 19–30 (2015)

    MATH  Google Scholar 

  2. Zhou, W., Liao, W.H., Tian, W., Wan, S.M., Liu, Y.: Method of industrial robot accuracy compensation based on particle swarm optimization neural network. Chin. Mech. Eng. 24(2), 174–179 (2013)

    Article  Google Scholar 

  3. Summers, M.: Robot capability test and development of industrial robot positioning system for the aerospace industry. SAE Tech. Pap. 114, 1108–1118 (2005)

    Google Scholar 

  4. Joubair, A., Bonev, I.A.: Kinematic calibration of a six-axis serial robot using distance and sphere constraints. Int. J. Adv. Manuf. Technol. 77(1–4), 515–523 (2015)

    Article  Google Scholar 

  5. Zeng, Y., Tian, W., Liao, W.: Positional error similarity analysis for error compensation of industrial robots. Robot. Comput. Integr. Manuf. 42, 113–120 (2016)

    Article  Google Scholar 

  6. Gatti, G., Danieli, G.: A practical approach to compensate for geometric errors in measuring arms: application to a six-degree-of-freedom kinematic structure. Meas. Sci. Technol. 19(1), 015107 (2007)

    Article  Google Scholar 

  7. Stone, H.W., Sanderson, A.C.: Statistical performance evaluation of the S-model arm signature identification technique. In: IEEE International Conference on Robotics and Automation, Piscataway, pp 939–946 (1988)

  8. Aoyagi, S., Kohama, A., Nakata, Y., Hayano, Y., 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. In: IEEE/RSJ Intelligent Robots and Systems, Leiden, pp 5660–5665 (2010)

  9. Wang, D., Bai, Y., Zhao, J.: Robot manipulator calibration using neural network and a camera-based measurement system. Trans. Inst. Meas. Control 34(1), 105–121 (2012)

    Article  Google Scholar 

  10. Beckers, F., Bogaert, P.: Nonstationarity of the mean and unbiased variogram estimation: extension of the weighted least-squares method. Math. Geol. 30(2), 223–240 (1998)

    Article  Google Scholar 

  11. Phan, A.V., Trochu, F.: Application of dual kriging to structural shape optimization based on the boundary contour method. Arch. Appl. Mech. 68(7), 539–551 (1998)

    Article  MATH  Google Scholar 

  12. Dai, K.Y., Liu, G.R., Lim, K.M., Gu, Y.T.: Comparison between the radial point interpolation and the Kriging interpolation used in meshfree methods. Comput. Mech. 32(1–2), 60–70 (2003)

    Article  MATH  Google Scholar 

  13. Zimmerman, D., Pavlik, C., Ruggles, A., Armstrong, M.P.: An experimental comparison of ordinary and universal kriging and inverse distance weighting. Math. Geol. 31(4), 375–390 (1999)

    Article  Google Scholar 

  14. Dayou, Y.S.L., Limin, S.: Universal Kriging: A method used in division of regional and local gravity (magnetic) anomalies. Comput. Tech. Geophys. Geochem. Explor. 21(1), 35–44 (1999)

    Google Scholar 

  15. Brus, D.J., Heuvelink, G.B.: Optimization of sample patterns for universal kriging of environmental variables. Geoderma 138(1), 86–95 (2007)

    Article  Google Scholar 

  16. Tian, W., Zeng, Y., Zhou, W., Liao, W.: Calibration of robotic drilling systems with a moving rail. Chin. J. Aeronaut. 27(6), 1598–1604 (2014)

    Article  Google Scholar 

  17. Cressie, N.: Statistics for Spatial Data. Wiley, Hoboken (2015)

    MATH  Google Scholar 

  18. Haining, R.P.: Spatial Data Analysis: Theory and Practice. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  19. Hong, P, Tian, W, Mei, D Q, Zeng, Y F: Robotic variable parameter accuracy compensation using space grid. Robot 37(3), 327–335 (2015)

    Google Scholar 

  20. Armstrong, M.: Problems with universal kriging. Math. Geol. 16(1), 101–108 (1984)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This research is supported by the National Nature Science Foundation of China(No.61375085).

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Correspondence to Peijiang Yuan.

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Cai, Y., Yuan, P., Shi, Z. et al. Application of Universal Kriging for Calibrating Offline-Programming Industrial Robots. J Intell Robot Syst 94, 339–348 (2019). https://doi.org/10.1007/s10846-018-0823-7

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  • DOI: https://doi.org/10.1007/s10846-018-0823-7

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