A Compensation Method for Enhancing Aviation Drilling Robot Accuracy Based on Co-Kriging

  • Dongdong ChenEmail author
  • Peijiang Yuan
  • Tianmiao Wang
  • Ying Cai
  • Lei Xue
Regular Paper


The positional error of aviation drilling robot has a great influence on the strength and lives of aircrafts in the aircraft assembly. In order to improve the position accuracy of aviation drilling robot, an error compensation method based on co-kriging is proposed in this paper. The error similarity based on the kinematic of drilling robot is proposed firstly. Then, the positional errors of a set of points in the workspace are measured by using precision laser tracker. The measurement data are used to fit the cross-variogram of positional error. After the cross-variogram is obtained, the predicted positional errors of verification points can be estimated based on co-kriging. The positions after compensation are given to the drilling robot. The proposed method is carried out on an aviation drilling robot for practical compensation to verify the correctness and effectiveness of the error compensation method. The experimental results show that the average absolute positional error is reduced to 0.1150 mm from 0.7168 mm, and that the maximum absolute positional error is reduced to 0.2664 mm from 1.3073 mm. The experimental results also demonstrate that the proposed method can improve the absolute position accuracy of aviation robot and could meet the requirement of aircraft assembly.


Error similarity Spatial correlation Cross-variogram Co-kriging Error compensation Aviation drilling robot 





Modified Denavit-Hartenberg


Inverse Distance Weighted


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bi, S. and Liang, J., “Robotic Drilling System for Titanium Structures,” The International Journal of Advanced Manufacturing Technology, Vol. 54, Nos. 5–8, pp. 767–774, 2011.CrossRefGoogle Scholar
  2. 2.
    Atkinson, J., Hartmann, J., Jones, S., and Gleeson, P., “Robotic Drilling System for 737 Ailesron,” SAE Technical Paper, No. 2007-01-3821, 2007.Google Scholar
  3. 3.
    Zhao, J., Guo, H., Wang, L., Wang, Z., Chen, H., et al., “Study and Application Technology on Digital Flexible Accurate Assembly for Aircraft,” Aeronautical Manufacturing Technology, No. 21, pp. 32–35, 2014.Google Scholar
  4. 4.
    Guo, Y., Yin, S., Ren, Y., Zhu, J., Yang, S., and Ye, S., “A Multilevel Calibration Technique for an Industrial Robot with Parallelogram Mechanism,” Precision Engineering, Vol. 40, pp. 261–272, 2015.CrossRefGoogle Scholar
  5. 5.
    Messay, T., Ordóñez, R., and Marcil, E., “Computationally Efficient and Robust Kinematic Calibration Methodologies and their Application to Industrial Robots,” Robotics and Computer-Integrated Manufacturing, Vol. 37, pp. 33–48, 2016.CrossRefGoogle Scholar
  6. 6.
    Li, R. and Zhao, Y., “Dynamic Error Compensation for Industrial Robot Based on Thermal Effect Model,” Measurement, Vol. 88, pp. 113–120, 2016.CrossRefGoogle Scholar
  7. 7.
    Wu, Y., Klimchik, A., Caro, S., Furet, B., and Pashkevich, A., “Geometric Calibration of Industrial Robots Using Enhanced Partial Pose Measurements and Design of Experiments,” Robotics and Computer-Integrated Manufacturing, Vol. 35, pp. 151–168, 2015.CrossRefGoogle Scholar
  8. 8.
    Sun, T., Zhai, Y., Song, Y., and Zhang, J., “Kinematic Calibration of a 3-DOF Rotational Parallel Manipulator Using Laser Tracker,” Robotics and Computer-Integrated Manufacturing, Vol. 41, pp. 78–91, 2016.CrossRefGoogle Scholar
  9. 9.
    Gong, C., Yuan, J., and Ni, J., “Nongeometric Error Identification and Compensation for Robotic System by Inverse Calibration,” International Journal of Machine Tools and Manufacture, Vol. 40, No. 14, pp. 2119–2137, 2000.CrossRefGoogle Scholar
  10. 10.
    Joubair, A. and Bonev, I. A., “Non-Kinematic Calibration of a Six-Axis Serial Robot Using Planar Constraints,” Precision Engineering, Vol. 40, pp. 325–333, 2015.CrossRefGoogle Scholar
  11. 11.
    Stone, H. W. and Sanderson, A. C., “Statistical Performance Evaluation of the S-Model Arm Signature Identification Technique,” Proc. of IEEE International Conference on Robotics and Automation, pp. 939–946, 1988.Google Scholar
  12. 12.
    Stone, H., Sanderson, A., and Neuman, C., “Arm Signature Identification,” Proc. of IEEE International Conference on Robotics and Automation, pp. 41–48, 1986.Google Scholar
  13. 13.
    Bai, Y., Cong, M., Yang, X., and Liu, D., “Kinematic Parameter Identification for 6R Serial Robots Based on a 6-Parameter Model,” Robot, Vol. 37, No. 4, pp. 486–492, 2015.Google Scholar
  14. 14.
    Abderrahim, M. and Whittaker, A., “Kinematic Model Identification of Industrial Manipulators,” Robotics and Computer-Integrated Manufacturing, Vol. 16, No. 1, pp. 1–8, 2000.CrossRefGoogle Scholar
  15. 15.
    Denhavit, J., “A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices,” ASME Journal of Applied Mechanical, Vol. 22, No. 1, pp. 215–221, 1955.MathSciNetGoogle Scholar
  16. 16.
    Whitney, D., Lozinski, C., and Rourke, J. M., “Industrial Robot Forward Calibration Method and Results,” Journal of Dynamic Systems, Measurement, and Control, Vol. 108, No. 1, pp. 1–8, 1986.CrossRefzbMATHGoogle Scholar
  17. 17.
    Gatti, G. and Danieli, G., “A Practical Approach to Compensate for Geometric Errors in Measuring Arms: Application to a Six-Degreeof-Freedom Kinematic Structure,” Measurement Science and Technology, Vol. 19, No. 1, Paper No. 015107, 2007.Google Scholar
  18. 18.
    Nguyen, H.-N., Zhou, J., and Kang, H.-J., “A Calibration Method for Enhancing Robot Accuracy through Integration of an Extended Kalman Filter Algorithm and an Artificial Neural Network,” Neurocomputing, Vol. 151, pp. 996–1005, 2015.CrossRefGoogle Scholar
  19. 19.
    Nubiola, A. and Bonev, I. A., “Absolute Calibration of an ABB IRB 1600 Robot Using a Laser Tracker,” Robotics and Computer-Integrated Manufacturing, Vol. 29, No. 1, pp. 236–245, 2013.CrossRefGoogle Scholar
  20. 20.
    Chen, I.-M., Yang, G., Tan, C. T., and Yeo, S. H., “Local POE Model for Robot Kinematic Calibration,” Mechanism and Machine Theory, Vol. 36, Nos. 11–12, pp. 1215–1239, 2001.CrossRefzbMATHGoogle Scholar
  21. 21.
    Wang, H., Shen, S., and Lu, X., “A Screw Axis Identification Method for Serial Robot Calibration Based on the POE Model,” Industrial Robot: An International Journal, Vol. 39, No. 2, pp. 146–153, 2012.CrossRefGoogle Scholar
  22. 22.
    He, R., Zhao, Y., Yang, S., and Yang, S., “Kinematic-Parameter Identification for Serial-Robot Calibration Based on POE Formula,” IEEE Transactions on Robotics, Vol. 26, No. 3, pp. 411–423, 2010.CrossRefGoogle Scholar
  23. 23.
    Joubair, A., Zhao, L.F., Bigras, P., and Bonev, I., “Absolute Accuracy Analysis and Improvement of a Hybrid 6-DOF Medical Robot,” Industrial Robot: An International Journal, Vol. 42, No. 1, pp. 44–53, 2015.CrossRefGoogle Scholar
  24. 24.
    Nubiola, A. and Bonev, I. A., “Absolute Robot Calibration with a Single Telescoping Ballbar,” Precision Engineering, Vol. 38, No. 3, pp. 472–480, 2014.CrossRefGoogle Scholar
  25. 25.
    Nguyen, H.-N., Zhou, J., Kang, H.-J., and Ro, Y.-S., “Robot Geometric Parameter Identification with Extended Kalman Filtering Algorithm,” Proc. of International Conference on Intelligent Computing, pp. 165–170, 2013.Google Scholar
  26. 26.
    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 Transactions on Mechatronics, Vol. 17, No. 6, pp. 1059–1067, 2012.CrossRefGoogle Scholar
  27. 27.
    Omodei, A., Legnani, G., and Adamini, R., “Three Methodologies for the Calibration of Industrial Manipulators: Experimental Results on a SCARA Robot,” Journal of Robotic Systems, Vol. 17, No. 6, pp. 291–307, 2000.CrossRefzbMATHGoogle Scholar
  28. 28.
    Santolaria, J., Conte, J., and Ginés, M., “Laser Tracker-Based Kinematic Parameter Calibration of Industrial Robots by Improved CPA Method and Active Retroreflector,” The International Journal of Advanced Manufacturing Technology, Vol. 66, Nos. 9–12, pp. 2087–2106, 2013.CrossRefGoogle Scholar
  29. 29.
    Varziri, M. S. and Notash, L., “Kinematic Calibration of a Wire-Actuated Parallel Robot,” Mechanism and Machine Theory, Vol. 42, No. 8, pp. 960–976, 2007.CrossRefzbMATHGoogle Scholar
  30. 30.
    Zeng, Y., Tian, W., and Liao, W., “Positional Error Similarity Analysis for Error Compensation of Industrial Robots,” Robotics and Computer-Integrated Manufacturing, Vol. 42, pp. 113–120, 2016.CrossRefGoogle Scholar
  31. 31.
    Bai, Y., “On the Comparison of Model-Based and Modeless Robotic Calibration Based on A Fuzzy Interpolation Method,” The International Journal of Advanced Manufacturing Technology, Vol. 31, Nos. 11–12, pp. 1243–1250, 2007.CrossRefGoogle Scholar
  32. 32.
    Wang, D., Bai, Y., and Zhao, J., “Robot Manipulator Calibration Using Neural Network and a Camera-Based Measurement System,” Transactions of the Institute of Measurement and Control, Vol. 34, No. 1, pp. 105–121, 2012.CrossRefGoogle Scholar
  33. 33.
    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,” Proc. of 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5660–5665, 2010.CrossRefGoogle Scholar
  34. 34.
    Jang, J. H., Kim, S. H., and Kwak, Y. K., “Calibration of Geometric and Non-Geometric Errors of an Industrial Robot,” Robotica, Vol. 19, No. 3, pp. 311–321, 2001.CrossRefGoogle Scholar
  35. 35.
    Tian, W., Zeng, Y., Zhou, W., and Liao, W., “Calibration of Robotic Drilling Systems with a Moving Rail,” Chinese Journal of Aeronautics, Vol. 27, No. 6, pp. 1598–1604, 2014.CrossRefGoogle Scholar
  36. 36.
    Zhou, W., Liao, W., and Tian, W., “Theory and Experiment of Industrial Robot Accuracy Compensation Method Based on Spatial Interpolation,” Journal of Mechanical Engineering, Vol. 49, No. 3, pp. 42–48, 2013.CrossRefGoogle Scholar
  37. 37.
    Li, J. and Heap, A. D., “Spatial Interpolation Methods Applied in the Environmental Sciences: A Review,” Environmental Modelling & Software, Vol. 53, pp. 173–189, 2014.CrossRefGoogle Scholar
  38. 38.
    Aalto, J., Pirinen, P., Heikkinen, J., and Venäläinen, A., “Spatial Interpolation of Monthly Climate Data for Finland: Comparing the Performance of Kriging and Generalized Additive Models,” Theoretical and Applied Climatology, Vol. 112, Nos. 1–2, pp. 99–111, 2013.CrossRefGoogle Scholar
  39. 39.
    Myers, D. E., “Matrix Formulation of Co-Kriging,” Journal of the International Association for Mathematical Geology, Vol. 14, No. 3, pp. 249–257, 1982.MathSciNetCrossRefGoogle Scholar
  40. 40.
    Myers, D. E., “Estimation of Linear Combinations and Co-Kriging,” Journal of the International Association for Mathematical Geology, Vol. 15, No. 5, pp. 633–637, 1983.MathSciNetCrossRefGoogle Scholar
  41. 41.
    Olea, R. A., “A Six-Step Practical Approach to Semivariogram Modeling,” Stochastic Environmental Research and Risk Assessment, Vol. 20, No. 5, pp. 307–318, 2006.MathSciNetCrossRefGoogle Scholar

Copyright information

© Korean Society for Precision Engineering and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical and Automation EngineeringBeihang UniversityBeijingChina
  2. 2.Shanghai Aircraft Manufacturing Co., Ltd.ShanghaiChina

Personalised recommendations