Skip to main content
SpringerLink
Log in

Position-Based Robot Calibration and Compensation Using an Improved Adjoint Error Model

  • Short Paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

The original adjoint error model is a complete, continuous, and minimal calibration model. However, the original model is defective in its mathematical derivation, and the method of updating kinematic parameters is also complicated and indirect; meanwhile, the orientation measurement of the end-effector is very difficult to implement. To address these problems, we present a complete and unified model for robot calibration based on an improved adjoint error model, in which only the position measurements of the end-effector are required. In addition, a compensation algorithm is proposed to improve the robot position accuracy using the calibration results; the proposed algorithm does not require modification of the kinematic parameters of the robot controller and can be applied to robots with different degrees of freedom. Simulations on a PUMA560 robot and a SCARA robot were performed to validate our algorithms. Furthermore, the proposed algorithms were applied to our self-designed modular robots with four and six degrees of freedom. The experimental results show that the average accuracy of the robots is enhanced by approximately one order of magnitude after compensation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Availability of Data and Material

Not applicable.

References

  1. Sun, T., Liu, C., Lian, B., Wang, P., Song, Y.: Calibration for precision kinematic control of an articulated serial robot. IEEE Trans. Ind. Electron. 68(7), 6000–6009 (2021). https://doi.org/10.1109/TIE.2020.2994890

    Article  Google Scholar 

  2. Luo, G., Zou, L., Wang, Z., Lv, C., Ou, J., Huang, Y.: A novel kinematic parameters calibration method for industrial robot based on Levenberg-Marquardt and differential evolution hybrid algorithm. Robot. Comput. Integr. Manuf. 71(2021), 102165–102176 (2021). https://doi.org/10.1016/j.rcim.2021.102165

    Article  Google Scholar 

  3. Filion, A., Joubair, A., Tahan, A.S., Bonev, I.A.: Robot calibration using a portable photogrammetry system. Robot. Comput. Integr. Manuf. 49(2018), 77–87 (2018). https://doi.org/10.1016/j.rcim.2017.05.004

    Article  Google Scholar 

  4. Jiang, Y., Yu, L., Jia, H., Zhao, H., Xia, H.: Absolute positioning accuracy improvement in an industrial robot. Sensors 20(16), 4354–4368 (2020). https://doi.org/10.3390/s20164354

    Article  Google Scholar 

  5. Sun, T., Lian, B., Yang, S., Song, Y.: Kinematic calibration of serial and parallel robots based on finite and instantaneous screw theory. IEEE Trans. Robot. 36(3), 816–834 (2020). https://doi.org/10.1109/TRO.2020.2969028

    Article  Google Scholar 

  6. He, R., Zhao, Y., Yang, S., Yang, S.: Kinematic-parameter identification for serial-robot calibration based on POE formula. IEEE Trans. Robot. 26(3), 411–423 (2010). https://doi.org/10.1109/tro.2010.2047529

    Article  Google Scholar 

  7. Hayati, S., Mirmirani, M.: Improving the absolute positioning accuracy of robot manipulators. J. Robot. Syst. 2(4), 397–413 (1985). https://doi.org/10.1002/rob.4620020406

    Article  Google Scholar 

  8. Stone, H., Sanderson, A.: A prototype arm signature identification system. In: 1987 IEEE International Conference on Robotics and Automation, vol. 4, pp. 175–182. (1987). https://doi.org/10.1109/ROBOT.1987.1087835

  9. Zhuang, H., Roth, Z.S., Hamano, F.: A complete and parametrically continuous kinematic model for robot manipulators. IEEE Trans. Robot. Autom. 8(4), 451–463 (1992). https://doi.org/10.1109/70.149944

    Article  Google Scholar 

  10. Okamura, K., Park, F.C.: Kinematic calibration using the product of exponentials formula. Robotica 14(4), 415–421 (1996). https://doi.org/10.1017/s0263574700019810

    Article  Google Scholar 

  11. Lou, Y., Chen, T., Wu, Y., Li, Z., Jiang, S.: Improved and modified geometric formulation of POE based kinematic calibration of serial robots. In: 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5261–5266. (2009). https://doi.org/10.1109/iros.2009.5354219

  12. He, R., Li, X., Shi, T., Wu, B., Zhao, Y., Han, F., Yang, S., Huang, S., Yang, S.: A kinematic calibration method based on the product of exponentials formula for serial robot using position measurements. Robotica 33(6), 1295–1313 (2014). https://doi.org/10.1017/s026357471400071x

    Article  Google Scholar 

  13. Chen, G., Li, T., Chu, M., Xuan, J., Xu, S.: Review on kinematics calibration technology of serial robots. Int. J. Precis. Eng. Manuf. 15(8), 1759–1774 (2014). https://doi.org/10.1007/s12541-014-0528-1

    Article  Google Scholar 

  14. Li, C., Wu, Y., Lowe, H., Li, Z.: POE-based robot kinematic calibration using axis configuration space and the adjoint error model. IEEE Trans. Rob. 32(5), 1264–1279 (2016). https://doi.org/10.1109/tro.2016.2593042

    Article  Google Scholar 

  15. Yang, X., Wu, L., Li, J., Chen, K.: A minimal kinematic model for serial robot calibration using POE formula. Rob. Comput. Integr. Manuf. 30(2014), 326–334 (2014). https://doi.org/10.1016/j.rcim.2013.11.002

    Article  Google Scholar 

  16. Zou, Y., Lan, R.: An end-to-end calibration method for welding robot laser vision systems with deep reinforcement learning. IEEE Trans. Instrum. Meas. 69(7), 1–11 (2019). https://doi.org/10.1109/TIM.2019.2942533

    Article  Google Scholar 

  17. Chang, C., Liu, J., Ni, Z., Qi, R.: An improved kinematic calibration method for serial manipulators based on POE formula. Robotica 36(8), 1244–1262 (2018). https://doi.org/10.1017/s0263574718000280

    Article  Google Scholar 

  18. Schillreff, N., Ortmeier, F.: Learning-based kinematic calibration using adjoint error model. In: 15th International Conference on Informatics in Control, Automation and Robotics, vol. 2, pp. 372–379. (2018). https://doi.org/10.5220/0006870403720379

  19. Jiang, Z., Gao, W., Yu, X.: An improved robot calibration method using the modified adjoint error model based on POE. Adv. Robotics 34(19), 1229–1238 (2020). https://doi.org/10.1080/01691864.2020.1810772

    Article  Google Scholar 

  20. Wu, L., Yang, X., Chen, K., Ren, H.: A minimal POE-based model for robotic kinematic calibration with only position measurements. IEEE Trans. Autom. Sci. Eng. 12(2), 758–763 (2015). https://doi.org/10.1109/tase.2014.2328652

    Article  Google Scholar 

  21. Gao, W., Wang, H., Jiang, Y.: Research on the calibration for a modular robot. J. Mech. Eng. 50(3), 33–40 (2014). https://doi.org/10.3901/jme.2014.03.033

    Article  Google Scholar 

  22. Xu, P., Cheung, B.C.F., Li, B.: A complete, continuous, and minimal product of exponentials-based model for five-axis machine tools calibration with a single laser tracker, an r-test, or a double ball-bar. J. Manuf. Sci. Eng. 141(4), 041010–0410142 (2019). https://doi.org/10.1115/1.4042582

    Article  Google Scholar 

  23. Elatta, A.Y., Li, P., Fan, L., Yu, D., Fei, L.: An overview of robot calibration. Inf. Technol. J. 3(1), 74–78 (2004). https://doi.org/10.3923/itj.2004.74.78

    Article  Google Scholar 

  24. Mustafa, S.K., Tao, P.Y., Yang, G., Chen, I.M.: A geometrical approach for online error compensation of industrial manipulators. In: 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 738–743. (2010). https://doi.org/10.1109/AIM.2010.5695784

  25. Renders, J.M., Rossignol, E., Becquet, M., Hanus, R.: Kinematic calibration and geometrical parameter identification for robots. IEEE Trans. Robot. Autom. 7(6), 721–732 (1991). https://doi.org/10.1109/70.105381

    Article  Google Scholar 

  26. Kirchner, H.O.K., Gurumoorthy, B., Prinz, F.B.: A perturbation approach to robot calibration. Int. J. Robot. Res. 6(4), 47–59 (1987). https://doi.org/10.1177/027836498700600405

    Article  Google Scholar 

  27. Veitschegger, W.K., Wu, C.: Robot calibration and compensation. IEEE J. Robot. Autom. 4(6), 643–656 (1988). https://doi.org/10.1109/56.9302

    Article  Google Scholar 

  28. Mirman, C.R., Gupta, K.C.: Compensation of robot joint variables using special Jacobian matrices. J. Robot. Syst. 9(1), 113–137 (1992). https://doi.org/10.1002/rob.4620090107

    Article  MATH  Google Scholar 

  29. Murray, R.M., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC, Florida (1994)

  30. Wu, Y., Li, C., Li, J., Li, Z.: Comparative study of robot kinematic calibration algorithms using a unified geometric framework. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 1393–1398. (2014). https://doi.org/10.1109/icra.2014.6907034

  31. Kamali, K., Bonev, I.A.: Optimal experiment design for elasto-geometrical calibration of industrial robots. IEEE/ASME Trans. Mechatronics 24(6), 2733–2744 (2019). https://doi.org/10.1109/tmech.2019.2944428

    Article  Google Scholar 

  32. Boby, R.A., Saha, S.K.: Single image based camera calibration and pose estimation of the end-effector of a robot. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 2435–2440 (2016). https://doi.org/10.1109/icra.2016.7487395

  33. Nubiola, A., Slamani, M., Joubair, A., Bonev, I.A.: Comparison of two calibration methods for a small industrial robot based on an optical CMM and a laser tracker. Robotica 32(3), 447–466 (2013). https://doi.org/10.1017/s0263574713000714

    Article  Google Scholar 

  34. Chen, I.M., Yang, G., Tan, C.T., Yeo, S.H.: Local POE model for robot kinematic calibration. Mech. Mach. Theory 36(11–12), 1215–1239 (2001). https://doi.org/10.1016/s0094-114x(01)00048-9

    Article  MATH  Google Scholar 

  35. Li, C., Wu, Y., Li, Z.: Identifiability and improvement of adjoint error approach for serial robot calibration. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 1361–1366 (2014). https://doi.org/10.1109/icra.2014.6907029

Download references

Funding

This research was supported by the National Natural Science Foundation of China (No. 51605004).

Author information

Authors and Affiliations

  1. Anhui Province Key Laboratory of Special Heavy Load Robot, Ma’anshan, 243000, Anhui, China

    Zizhen Jiang, Wenbin Gao & Xiaoliu Yu

  2. School of Mechanical Engineering, Anhui University of Technology, Ma’anshan, 243000, Anhui, China

    Wenbin Gao & Xiaoliu Yu

Authors
  1. Zizhen Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenbin Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoliu Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Proving, coding, experiment preparation, data collection and analysis were performed by Zizhen Jiang. The first draft of the manuscript was written by Zizhen Jiang, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Wenbin Gao.

Ethics declarations

Ethics Approval

Not applicable.

Consent to Participate

Not applicable.

Consent to Publish

All authors have approved and consented to publish the manuscript.

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, Z., Gao, W. & Yu, X. Position-Based Robot Calibration and Compensation Using an Improved Adjoint Error Model. J Intell Robot Syst 108, 44 (2023). https://doi.org/10.1007/s10846-023-01891-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-023-01891-6

Keywords

Search

Navigation