IJAT Vol.15 No.5 pp. 599-610
doi: 10.20965/ijat.2021.p0599

Technical Paper:

Kinematic Modeling of Six-Axis Industrial Robot and its Parameter Identification: A Tutorial

Md. Moktadir Alam, Soichi Ibaraki, and Koki Fukuda

Graduate School of Advanced Science and Engineering, Hiroshima University
1-4-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8511, Japan

Corresponding author

February 26, 2021
June 21, 2021
September 5, 2021
kinematic modeling, robot, positioning accuracy, angular positioning deviation

In advanced industrial applications, like machining, the absolute positioning accuracy of a six-axis robot is indispensable. To improve the absolute positioning accuracy of an industrial robot, numerical compensation based on positioning error prediction by the Denavit and Hartenberg (D-H) model has been investigated extensively. The main objective of this study is to review the kinematic modeling theory for a six-axis industrial robot. In the form of a tutorial, this paper defines a local coordinate system based on the position and orientation of the rotary axis average lines, as well as the derivation of the kinematic model based on the coordinate transformation theory. Although the present model is equivalent to the classical D-H model, this study shows that a different kinematic model can be derived using a different definition of the local coordinate systems. Subsequently, an algorithm is presented to identify the error sources included in the kinematic model based on a set of measured end-effector positions. The identification of the classical D-H parameters indicates a practical engineering application of the kinematic model for improving a robot’s positioning accuracy. Furthermore, this paper presents an extension of the present model, including the angular positioning deviation of each rotary axis. The angular positioning deviation of each rotary axis is formed as a function of the axis’ command angles and the direction of its rotation to model the effect of the rotary axis backlash. The identification of the angular positioning deviation of each rotary axis and its numerical compensation are presented, along with their experimental demonstration. This paper provides an essential theoretical basis for the error source diagnosis and error compensation of a six-axis robot.

Cite this article as:
Md. Moktadir Alam, Soichi Ibaraki, and Koki Fukuda, “Kinematic Modeling of Six-Axis Industrial Robot and its Parameter Identification: A Tutorial,” Int. J. Automation Technol., Vol.15, No.5, pp. 599-610, 2021.
Data files:
  1. [1] A. Verl, A. Valente, S. Melkote, C. Brecher, E. Ozturk, and L. T. Tunc, “Robots in machining,” CIRP Ann., Vol.68, No.2, pp. 799-822, 2019.
  2. [2] W. Ji and L. Wang, “Industrial robotic machining: a review,” Int. J. Adv. Manuf. Technol., Vol.103, No.1-4, pp. 1239-1255, 2019.
  3. [3] I. Iglesias, M. A. Sebastián, and J. E. Ares, “Overview of the State of Robotic Machining: Current Situation and Future Potential,” Procedia Eng., Vol.132, pp. 911-917, 2015.
  4. [4] J. Denavit and R. S. Hartenberg, “A kinematic notation for lower-pair mechanisms based on matrices,” Trans. of ASME, J. Appl. Mech., pp. 215-221, 1955.
  5. [5] M. T. Nguyen, C. Yuan, and J. H. Huang, “Kinematic Analysis of A 6-DOF Robotic Arm,” Advances in Mechanism and Machine Science, Vol.73, pp. 2965-2974, 2019.
  6. [6] C. Faria, J. L. Vilaca, S. Monteiro, W. Erlhagen, and E. Bicho, “Automatic Denavit-Hartenberg Parameter Identification for Serial Manipulators,” Proc. of IECON 2019 – 45th Annual Conf. of the IEEE Industrial Electronics Society, pp. 610-617, 2019.
  7. [7] W. Guo, R. Li, C. Cao, and Y. Gao, “Kinematics Analysis of a Novel 5-DOF Hybrid Manipulator,” Int. J. Automation Technol., Vol.9, No.6, pp. 765-774, 2015.
  8. [8] Y. Wu, A. Klimchik, S. Caro, B. Furet, and A. Pashkevich, “Geometric calibration of industrial robots using enhanced partial pose measurements and design of experiments,” Robot. Comput. Integr. Manuf., Vol.35, pp. 151-168, 2015.
  9. [9] G. Gao, G. Sun, J. Na, Y. Guo, and X. Wu, “Structural parameter identification for 6 DOF industrial robots,” Mechanical Systems and Signal Processing, Vol.113, pp. 145-155, 2018.
  10. [10] A. Filion, A. Joubair, A. S. Tahan, and I. A. Bonev, “Robot calibration using a portable photogrammetry system,” Robotics and Computer-Integrated Manufacturing, Vol.49, pp. 77-87, 2018.
  11. [11] Y. Meng and H. Zhuang, “Autonomous robot calibration using vision technology,” Robotics and Computer-Integrated Manufacturing, Vol.23, No.4, pp. 436-446, 2007.
  12. [12] N. Zhao and S. Ibaraki, “Calibration and Compensation of Rotary Axis Angular Positioning Deviations on a SCARA-Type Industrial Robot Using a Laser Tracker,” Proc. of the JSME 2020 Conf. on Leading Edge Manufacturing/Materials and Processing, 2020.
  13. [13] M. M. Alam, S. Ibaraki, K. Fukuda, S. Morita and H. Usuki, “Identification of a kinematic model of a 6DOF industrial manipulator with angular positioning deviation “error map” of rotary axes,” Proc. of the ASME 2020 Int. Symp. on Flexible Automation (ISFA2020), 2020.
  14. [14] S. Ibaraki and W. Knapp, “Indirect Measurement of Volumetric Accuracy for Three-Axis and Five-Axis Machine tools: A review,” Int. J. Automation Technol., Vol.6, No.2, pp. 110-124, 2012.
  15. [15] “ISO/TR 16907:2015 Machine tools – Numerical compensation of geometric errors,” 2015.
  16. [16] “ISO 230-1:2012 Test code for machine tools – Part 1: Geometric accuracy of machines operating under no-load or quasi-static conditions,” 2012.
  17. [17] L. Ma, P. Bazzoli, P. M. Sammons, R. G. Landers, and D. A. Bristow, “Modeling and calibration of high-order joint-dependent kinematic errors for industrial robots,” Robotics and Computer-Integrated Manufacturing, Vol.50, pp. 153-167, 2018.
  18. [18] M. Ruderman, F. Hoffmann, and T. Bertram, “Modeling and Identification of Elastic Robot Joints with Hysteresis and Backlash,” IEEE Trans. on Industrial Electronics, Vol.56, No.10, pp. 3840-3847, 2009.
  19. [19] “Right-Handed 3D Coordinate Frame.” [Accessed December 23, 2020]
  20. [20] N. Zhao and S. Ibaraki, “Calibration of rotary axis angular positioning deviations on an industrial robot by using a laser tracker,” Proc. of the 8th Int. Conf. of Asian Society for Precision Engineering and Nanotechnology (ASPEN), 2019.
  21. [21] K. Fukuda, S. Ibaraki, M. M. Alam, S. Morita, H. Usuki, N. Ohtsuki, and H. Yoshioka, “Identification of a novel kinematic model of a 6-DOF robot with bidirectional angular positioning deviation of rotary axes,” Proc. of 18th Int. Conf. on Precision Engineering (ICPE20), C-3-6, 2020.
  22. [22] S. Ibaraki, C. Oyama, and H. Otsubo, “Construction of an error map of rotary axes on a five-axis machining center by static R-test,” Int. J. Mach. Tools Manuf., Vol.51, No.3, pp. 190-200, 2010.

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Last updated on Sep. 19, 2021