Advertisement

Journal of Mechanical Science and Technology

, Volume 32, Issue 11, pp 5401–5409 | Cite as

A svd-least-square algorithm for manipulator kinematic calibration based on the product of exponentials formula

  • Nguyen Van Toan
  • Phan Bui Khoi
Article
  • 3 Downloads

Abstract

In recent years, a great deal of research is conducted to improve the accuracy of manipulator kinematic calibration of which the product of exponential formula (PoE) is used to represent the manipulator kinematics, whose purpose is to solve the singularity problem of the Denavit-Hartenberg (D-H) parameters. However, the noise sensibility is still an open problem since a matrix inverse calculation of Jacobian matrix is inevitable during the process of solving the kinematic-linearized-equations to obtain the calibrated parameters. This problem may causes non-convergence, or low-accurate solution of calibration algorithm if the environmental noises and the error of endeffector’s actual frame measurement techniques are considerable. This paper presents a kinematic calibration method using singular value decomposition least square algorithm based on the product of exponentials formula (SVD-PoE-least-squares algorithm) to improve the accuracy of calibrated parameters. The proposed algorithm is evaluated in simulation level using a 6-DOF puma 560-type manipulator. The obtained results have shown that SVD-PoE-least-square algorithm is insignificantly affected by environmental noises, and, the proposed method can complete the robot calibration with respect to the work frame directly.

Keywords

Kinematic calibration Product of exponentials formula SVD-least-square Sensibility reduce 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    K. M. Lynch and F. C. Park, Modern robotics: Mechanics, planning, and control, Cambridge University Press, England (2017).Google Scholar
  2. [2]
    R. W. Brockett, Robotic manipulators and the product of exponentials formula, Proc. Int. Symp. Math. Theory of Networks and Systems, Beer Sheba, Isarel (1983) 120–129.Google Scholar
  3. [3]
    F. C. Park, Computational aspects of the product of exponentials formula for robot kinematics, IEEE Transactions on Automatic Control, 39 (3) (1994) 643–647.CrossRefzbMATHGoogle Scholar
  4. [4]
    K. Okamura and F. C. Park, Kinematic calibration using the product of exponentials formula, Robotica, 14 (4) (1996) 415–421.CrossRefGoogle Scholar
  5. [5]
    S. Sastry and M. Bodson, Adaptive control: Stability, convergence, and robustness, Prentice–Hall, Englewood Cliffs, New Jersey (1989).zbMATHGoogle Scholar
  6. [6]
    J. Moreno–Valenzuela and C. Aguilar–Avelar, Motion control of underactuated mechanical systems, Chapter 3, Spinger International Publishing AG, Cham (2018).CrossRefGoogle Scholar
  7. [7]
    A. Filion, A. Joubair, A. S. Tahan and I. A. Bonev, Robot calibration using a portable photogrammetry system, Robotics and Computer–Integrated Manufacturing, 49 (2018) 77–87.CrossRefGoogle Scholar
  8. [8]
    E. Shammas and S. Najjiar, Kinematic calibration of serial manipulators using Bayesian inference, Robotica, 36 (5) (2018) 738–766.CrossRefGoogle Scholar
  9. [9]
    Keli et al., Optimal measurement for kinematic calibration of a six–DOF spatial robotic manipulator, 2017 IEEE International Conference on Real–time Computing and Robotics (RCAR), Japan (2017) 252–257.Google Scholar
  10. [10]
    P. T. Katsiaris, G. Adams, S. Pollard and S. J. Simske, A kinematic calibration technique for robotic manipulators with multiple degrees of freedom, 2017 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Germany (2017) 358–363.CrossRefGoogle Scholar
  11. [11]
    H. Zhuang, Self–calibration of parallel mechanisms with a case study on Stewart platforms, IEEE Transactions on Robotics and Automation, 13 (3) (1997) 387–397.MathSciNetCrossRefGoogle Scholar
  12. [12]
    W. Khalil and S. Bernard, Self–calibration of Stewart–Gough parallel robots without extra sensors, IEEE Transactions on Robotics and Automation, 15 (6) (1999) 1116–1121.CrossRefGoogle Scholar
  13. [13]
    I.–W. Park, B.–J. Lee, S.–H. Cho, Y.–D. Hong and J.–H. Kim, Laser based kinematic calibration of robot manipulator using differential kinematics, IEEE/ASME Transactions on Mechatronics, 17 (6) (2012) 1059–1067.CrossRefGoogle Scholar
  14. [14]
    D. J. Bennett and J. M. Hollerbach, Autonomous calibration of single–loop closed kinematic chains formed by manipulators with passive endpoint constraints, IEEE Transactions on Robotics and Automation, 7 (5) (1991) 597–606.CrossRefGoogle Scholar
  15. [15]
    D. J. Bennett, D. Geiger and J. M. Hollerbach, Autonomous robot calibration for hand–eye coordination, International Journal of Robotics Research, 10 (5) (1991) 550–559.CrossRefGoogle Scholar
  16. [16]
    W. S. Newman, C. E. Birkhimer, R. J. Horning and A. T. Wilkey, Calibration of a Motorman P8 robot based on laser tracking, Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), USA (2000) 3597–3602.Google Scholar
  17. [17]
    A. Omodei, G. Legnani and R. Adamini, Three methodologies for the calibration of industrial manipulators: Experimental results on SCARA robot, Journal of Robotic Systems, 17 (6) (2000) 291–307.CrossRefzbMATHGoogle Scholar
  18. [18]
    A. Omodei, G. Legnani and R. Adamini, Calibration of a measuring robot: experimental results on a 5 DOF structure, Journal of Robotic Systems, 18 (5) (2001) 237–250.CrossRefzbMATHGoogle Scholar
  19. [19]
    G. Alici and B. Shirinzadeh, A systematic technique to estimate positioning errors for robot accuracy improvement using laser interferometry based sensing, Mechanism and Machine Theory, 40 (8) (2005) 879–906.CrossRefzbMATHGoogle Scholar
  20. [20]
    G. Alici, R. Jagielski, Y. Sekercioglu and B. Shirinzadeh, Prediction of geometric errors of robot manipulators with particle swarm optimisation method, Robotics and Autonomous Systems, 54 (12) (2006) 956–966.CrossRefGoogle Scholar
  21. [21]
    J. O’Brian, R. Bodenheimer, G. Brostow and J. Hodgins, Automatic joint parameter estimation from magnetic motion capture data, Proceedings of Graphics Interface, USA (2000) 53–60.Google Scholar
  22. [22]
    P. Renaud, N. Andreff, J.–M. Lavest and M. Dhome, Simplifying the kinematic calibaration of parallel mechanisms using vision–based metrology, IEEE Transactions on Robotics, 22 (1) (2006) 12–22.CrossRefGoogle Scholar
  23. [23]
    A. Rauf, A. Pervez and J. Ryu, Experimental results on kinematic calibration of parallel manipulators using a partial pose measurement device, IEEE Transactions on Robotics, 22 (2) (2006) 379–384.CrossRefGoogle Scholar
  24. [24]
    S. K Mustafa, G. Yang, S. H. Yeo, W. Lin and I.–M. Chen, Self–calibration of a biologically inspired 7 DOF cabledriven robotic arm, IEEE/ASME Transactions on Mechatronics, 13 (1) (2008) 66–75.CrossRefGoogle Scholar
  25. [25]
    H. Zhuang, Z. S. Roth and K. Wang, Robot calibration by mobile camera systems, Journal of Robotic Systems, 11 (3) (1994) 155–167.CrossRefGoogle Scholar
  26. [26]
    P. Renaud, N. Andreff, F. Marquet and P. Martinet, Vision–based kinematic calibration of a H4 parallel mechanism, IEEE International Conference on Robotics and Automation (ICRA), Taiwan (2003) 1191–1196.Google Scholar
  27. [27]
    D. Daney, N. Andreff and Y. Papegay, Interval method for calibration of parallel robots: A vision–based experimentaion, International Workshop on Computational Kinematics, Italy (2005).zbMATHGoogle Scholar
  28. [28]
    S. Hu, M. Zhang, C. Zhou and F. Tian, A novel selfcalibration method with POE–based model and distance error measurement for serial manipulators, Journal of Mechanical Science and Technology, 31 (10) (2017) 4911–4923.CrossRefGoogle Scholar
  29. [29]
    P. Renaud, N. Andreff, M. Philippe and G. Gogu, Kinematic calibration of parallel mechanisms: a novel approach using legs observation, IEEE Transactions on Robotics, 21 (4) (2005) 529–538.CrossRefGoogle Scholar
  30. [30]
    N. Andreff and P. Martinet, Unifying kinematic modelling, identification, and control of Gough–Stewart parallel robot into a vision–based framework, IEEE Transactions on Robotics, 22 (6) (2006) 1077–1086.CrossRefGoogle Scholar
  31. [31]
    N. Andreff, P. Renaud, P. Martinet and F. Pierrot, Visionbased kinematic calibration of an H4 parallel mechanism: practical accuracies, Industrial Robot: An International Journal, 31 (3) (2004) 273–283.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringHanoi University of Science and TechnologyHanoiVietnam

Personalised recommendations