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Pose error real-time prediction and compensation of a 5-DOF hybrid robot based on laser tracker and externally mounted encoders
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  • Published: 01 April 2026

Pose error real-time prediction and compensation of a 5-DOF hybrid robot based on laser tracker and externally mounted encoders

  • Hao Guo1,
  • Guangxi Li2 &
  • Songtao Liu3 

Scientific Reports , Article number:  (2026) Cite this article

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Engineering
  • Mechanical engineering

Abstract

Error compensation is an effective approach for robots to improve accuracy. This paper presents a novel method to predict and compensate for pose error of a 5-DOF hybrid robot on-line with the usage of externally mounted encoders, concentrating particularly on compensating dynamic errors on the account of changes in external forces or disturbances. A novel method to estimate pose error is proposed employing the offline sampling data from a laser tracker as well as the online measurement data from the external encoders. A real-time procedure for pose error prediction and compensation is applied into the NC system, which involves two successive steps: (1) calculation of pose error based on the online measurement from externally mounted encoders and the offline data measured by the laser tracker employing the moving least squares algorithm, and (2) compensation for the command pose in every interpolation cycle. Experimental verification shows that the residual inaccuracy of pose error prediction is reduced by 61% with respect to that only estimated from offline data under the condition of changing loads and the deviations of predicted errors respect to actual errors are within 5% under a constant load.

Data availability

Due to [reasons for data non disclosure], the datasets generated and/or analyzed during the current research period are not publicly available, but can be obtained from the corresponding author.

References

  1. Zhou J, Yu Y. Simulation and control of reconfigurable modular robot arm based on close-loop real-time feedback[C]//2010 2nd International Conference on Computer Engineering and Technology. IEEE, 2010, 3: V3–35-V3–40.

  2. Sciavicco L, Siciliano B. Modelling and control of robot manipulators[M]. Springer Science & Business Media, 2012.

  3. Ramesh, R., Mannan, M. A. & Poo, A. N. Error compensation in machine tools—A review: Part I: Geometric, cutting-force induced and fixture-dependent errors. Int. J. Mach. Tools Manuf. 40(9), 1235–1256 (2000).

    Google Scholar 

  4. Tian, W. et al. Kinematic calibration of a 3-DOF spindle head using a double ball bar. Mech. Mach. Theory 102, 167–178 (2016).

    Google Scholar 

  5. Mekid, S. & Ogedengbe, T. A review of machine tool accuracy enhancement through error compensation in serial and parallel kinematic machines. Int. J. Precis. Technol. 1(3), 251–286 (2010) ((36)).

    Google Scholar 

  6. Koliskor A S. Compensation for automatic cycle machining error. Machines and Tooling. 1971. 41(5).

  7. Zhang, G., Wang, C. & Hu, X. Error compensation of coordinate measuring machines. Ann. CIRP 34(1), 445–448 (1985).

    Google Scholar 

  8. Mahbubur, R. M. D. et al. Positioning accuracy improvement in five-axis milling by post processing. Int. J. Mach. Tools Manuf. 37(2), 223–236 (1997).

    Google Scholar 

  9. Kvrgic, V. et al. A control algorithm for improving the accuracy of five-axis machine tools. Int. J. Prod. Res. 52(10), 2983–2998 (2014).

    Google Scholar 

  10. Hsu, Y. Y. & Wang, S. S. A new compensation method for geometry errors of five-axis machine tools. Int. J. Mach. Tools Manuf. 47(2), 352–360 (2007).

    Google Scholar 

  11. Liu H, Huang T, Chetwynd D G. A general approach for geometric error modeling of lower mobility parallel manipulators. 2011.

  12. Luo, X. et al. Kinematic calibration of a 5-axis parallel machining robot based on dimensionless error mapping matrix. Robot. Comput. Integr. Manuf. 70, 102115 (2021).

    Google Scholar 

  13. Wu, J., Wang, J. & You, Z. An overview of dynamic parameter identification of robots. Robot. Comput. Integr. Manuf. 26(5), 414–419 (2010).

    Google Scholar 

  14. Wu, J. et al. An iterative learning method for realizing accurate dynamic feedforward control of an industrial hybrid robot. Sci. China Technol. Sci. 64(6), 1177–1188 (2021).

    Google Scholar 

  15. Huang, T. et al. Kinematic calibration of a 6-DOF hybrid robot by considering multicollinearity in the identification Jacobian. Mech. Mach. Theory 131, 371–384 (2019).

    Google Scholar 

  16. Nguyen, H. N., Zhou, J. & Kang, H. J. A calibration method for enhancing robot accuracy through integration of an extended Kalman filter algorithm and an artificial neural network. Neurocomputing 151, 996–1005 (2015).

    Google Scholar 

  17. Ma, L. et al. Modeling and calibration of high-order joint-dependent kinematic errors for industrial robots. Robotics and Computer-Integrated Manufacturing 50, 153–167 (2018).

    Google Scholar 

  18. Chen, D. et al. A compensation method based on error similarity and error correlation to enhance the position accuracy of an aviation drilling robot. Meas. Sci. Technol. 29(8), 085011 (2018).

    Google Scholar 

  19. Alici, G. & Shirinzadeh, B. A systematic technique to estimate positioning errors for robot accuracy improvement using laser interferometry based sensing. Mech. Mach. Theory 40(8), 879–906 (2005).

    Google Scholar 

  20. Alıcı, G. et al. Prediction of geometric errors of robot manipulators with Particle Swarm Optimisation method. Robot. Auton. Syst. 54(12), 956–966 (2006).

    Google Scholar 

  21. Bai, Y. & Wang, D. On the comparison of trilinear, cubic spline, and fuzzy interpolation methods in the high-accuracy measurements. IEEE Trans. Fuzzy Syst. 18(5), 1016–1022 (2010).

    Google Scholar 

  22. Bai, Y. & Wang, D. Calibrate parallel machine tools by using interval type-2 fuzzy interpolation method. The International Journal of Advanced Manufacturing Technology 93, 3777–3787 (2017).

    Google Scholar 

  23. Chen, D. et al. A compensation method for enhancing aviation drilling robot accuracy based on co-kriging. Int. J. Precis. Eng. Manuf. 19, 1133–1142 (2018).

    Google Scholar 

  24. Cai, Y. et al. Application of universal kriging for calibrating offline-programming industrial robots. J. Intell. Rob. Syst. 94, 339–348 (2019).

    Google Scholar 

  25. Tian, W. et al. Calibration of robotic drilling systems with a moving rail. Chin. J. Aeronaut. 27(6), 1598–1604 (2014).

    Google Scholar 

  26. Tian, W. et al. Determination of optimal samples for robot calibration based on error similarity. Chin. J. Aeronaut. 28(3), 946–953 (2015).

    Google Scholar 

  27. Zhao, G. et al. System identification of the nonlinear residual errors of an industrial robot using massive measurements. Robotics and Computer-Integrated Manufacturing 59, 104–114 (2019).

    Google Scholar 

  28. Liu, H., Yan, Z. & Xiao, J. Pose error prediction and real-time compensation of a 5-DOF hybrid robot. Mech. Mach. Theory. 170, 104737 (2022).

    Google Scholar 

  29. Belchior, J. et al. Off-line compensation of the tool path deviations on robotic machining: Application to incremental sheet forming. Robot. Comput. Integr. Manuf. 29(4), 58–69 (2013).

    Google Scholar 

  30. Donmez, M. A. et al. A general methodology for machine tool accuracy enhancement by error compensation. Precis. Eng. 8(4), 187–196 (1986).

    Google Scholar 

  31. Lei, W. T. & Hsu, Y. Y. Accuracy enhancement of five-axis CNC machines through real-time error compensation. Int. J. Mach. Tools Manuf. 43(9), 871–877 (2003).

    Google Scholar 

  32. Barman, S. & Sen, R. Enhancement of accuracy of multi-axis machine tools through error measurement and compensation of errors using laser interferometry technique. MAPAN-J. Metrol. Soc. India. 25(2), 79–87 (2010).

    Google Scholar 

  33. Ni, J. CNC machine accuracy enhancement through real-time error compensation. J. Manuf. Sci. Eng. 119(4), 717–725 (1997).

    Google Scholar 

  34. Chen, J. S. Computer-aided accuracy enhancement for multi-axis CNC machine tool. Int. J. Mach. Tools Manuf. 35(4), 593–605 (1995).

    Google Scholar 

  35. Chen, J. S. & Hsu, W. Y. Real time compensation for time variant volumetric errors on a machining center. J. Manuf. Sci. Eng. 115(4), 472–479 (2013).

    Google Scholar 

  36. Wang, Z. & Maropolous, P. G. Real-time error compensation of a three-axis machine tool using a laser tracker. Int. J. Adv. Manuf. Technol. 69(1–4), 935 (2013).

    Google Scholar 

  37. Wang Z, Maropoulos P G. Real-time laser tracker compensation of a 3-axis positioning system-dynamic accuracy characterization. International Journal of Advanced Manufacturing Technology, 2015:1–8.

  38. Yang, S., Yuan, J. & Ni, J. Accuracy enhancement of a horizontal machining center by real-time error compensation. J. Manuf. Syst. 15(2), 113–124 (1996).

    Google Scholar 

  39. Ruiz, A. R. J. et al. A real-time tool positioning sensor for machine-tools. Sensors 9(10), 7622–7647 (2009).

    Google Scholar 

  40. Gan, S. W. et al. A fine tool servo system for global position error compensation for a miniature ultra-precision lathe. Int. J. Mach. Tools Manuf. 47(7–8), 1302–1310 (2007).

    Google Scholar 

  41. Liu, Q. et al. Real-time error compensation of a 5-axis machining robot using externally mounted encoder systems. Int. J. Adv. Manuf. Technol. 120(3), 2793–2802 (2022).

    Google Scholar 

  42. Liu, Q. & Huang, T. Inverse kinematics of a 5-axis hybrid robot with non-singular tool path generation. Robot. Comput. Integr. Manuf. 56, 140–148 (2019).

    Google Scholar 

  43. Saund, B. & DeVlieg, R. High accuracy articulated robots with CNC control systems. SAE Int. J. Aerosp. 6(2), 780–784 (2013).

    Google Scholar 

  44. Dong, C. et al. Stiffness modeling and analysis of a novel 5-DOF hybrid robot. Mech. Mach. Theory 125, 80–93 (2018).

    Google Scholar 

  45. Levin, D. The approximation power of Moving Least-Squares. Math. Comput. 67(224), 1517–1531 (1998).

    Google Scholar 

  46. Oudjene, M. et al. Shape optimization of clinching tools using the response surface methodology with Moving Least-Square approximation. J. Mater. Process. Technol. 209(1), 289–296 (2009).

    Google Scholar 

  47. Huang, X. et al. Adaptive moving least squares for scattering points fitting. WSEAS Trans. Comput. 9(6), 664–673 (2010).

    Google Scholar 

  48. Lancaster, P. & Salkauskas, K. Surfaces generated by moving least squares methods. Math. Comput. 37(155), 141–158 (1981).

    Google Scholar 

  49. Liu, Y. & Wang, X. Adaptive support domain size selection in moving least squares for high-precision scattered data approximation. Comput. Aided Des. 136, 103028 (2021).

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant 52505006), the National Natural Science Foundation of China (grant 52175025) and the Guangdong Basic and Applied Basic Research Foundation (grant 2024A1515110021). The authors sincerely thank Professor Huang and Professor Xiao at Tianjin University for providing the experimental devices. The authors also thank the editors and reviewers for their patient work and constructive suggestions.

Author information

Authors and Affiliations

  1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300072, China

    Hao Guo

  2. School of Mechanical Engineering, Dongguan University of Technology, Dongguan, 523808, China

    Guangxi Li

  3. Chenxing (Tianjin) Automation Equipment Co., Ltd, Tianjin, 300450, China

    Songtao Liu

Authors
  1. Hao Guo
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  2. Guangxi Li
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  3. Songtao Liu
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Contributions

H.G.: Conceptualization, Methodology, Simulation, Writing- Original draft preparation. G. L., Supervision, Writing—Review & Editing. S. L.: Validation, Writing—Review & Editing.

Corresponding author

Correspondence to Guangxi Li.

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The authors declare no competing interests.

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Guo, H., Li, G. & Liu, S. Pose error real-time prediction and compensation of a 5-DOF hybrid robot based on laser tracker and externally mounted encoders. Sci Rep (2026). https://doi.org/10.1038/s41598-026-42162-2

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  • Received: 13 April 2025

  • Accepted: 24 February 2026

  • Published: 01 April 2026

  • DOI: https://doi.org/10.1038/s41598-026-42162-2

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Keywords

  • Real-time error compensation
  • Hybrid machining robot
  • Laser tracker
  • External metrology systems
  • Moving least square
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