[go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Solving the forward kinematics problem in parallel manipulators using an iterative artificial neural network strategy

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In this paper we address the forward kinematics problem of a parallel manipulator and propose an iterative neural network strategy for its real-time solution to a desired level of accuracy. Parallel manipulators are closed kinematic structures that possess requisite rigidity to yield a high payload to self-weight ratio. Because of this unique feature, they have been employed in manufacturing, flight simulation systems, and medical robotics. However, it is this closed kinematic structure that has led to difficulty in their kinematic control, especially the forward kinematics control. The iterative neural network strategy we propose employs a trained neural network and an error compensation algorithm in the feedback loop. The proposed strategy was tested with data from a real-world flight simulation system. Results show that solutions with a maximum error in the position and orientation parameters of 0.25 mm and 0.01°, respectively, can be achieved in less than five iterations (or about 1 second). Because of the nature of this strategy, it is possible to implement it in a hardware form, which can result in a multi-fold reduction in the solution time for the same accuracy level.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Parikh PJ, Lam SSY (2005) A hybrid strategy to solve the forward kinematics problem in parallel manipulators. IEEE Trans Robot 21(1):18–25

    Article  Google Scholar 

  2. Merlet JP (2004) Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis. Int J Robot Res 23(3):221–235

    Article  Google Scholar 

  3. Nanua P, Waldron KJ, Murthy V (1990) Direct kinematic solution of a Stewart platform. IEEE Trans Robot Automat 6(4):438–444

    Article  Google Scholar 

  4. Waldron KJ, Raghavan M, Roth B (1989) Kinematics of a hybrid series-parallel manipulation system. J Dyn Syst Meas Control 111(2):211–221

    Article  Google Scholar 

  5. Innocenti C, Parenti-Castelli V (1992) Direct kinematics of the 6–4 fully parallel manipulator with position and orientation decoupled. In: Tzafestas SG (ed) Robotic systems. Kluwer Academic, Amsterdam, pp 3–10

  6. Ji P, Wu H (2001) A closed-form forward kinematics solution for the 6–6p Stewart platform. IEEE Trans Robot Automat 17(4):522–526

    Article  Google Scholar 

  7. Wampler CW (1996) Forward displacement analysis of general six-in-parallel SPS (Stewart) platform manipulators using soma coordinates. Mech Mach Theory 31(3):331–337

    Article  Google Scholar 

  8. Innocenti C (2001) Forward kinematics in polynomial form of the general Stewart platform. ASME J Mech Des 123:254–260

    Article  Google Scholar 

  9. Lee T-Y, Shim J-K (2001) Forward kinematics of the general 6–6 Stewart platform using algebraic elimination. Mech Mach Theory 36:1073–1085

    Article  MATH  Google Scholar 

  10. Merlet JP (2004) Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis. Int J Robot Res 23(3):221–235

    Article  Google Scholar 

  11. Zhao J-S, Yun Y, Wang L-P, Wan J-S, Dong J-X (2006) Investigation of the forward kinematics manipulator with natural coordinates. Int J Adv Manuf Technol 30:700–716

    Article  Google Scholar 

  12. Zanganeh KE, Angeles J (1995) Real-time direct kinematics of general six-degree-of-freedom parallel manipulators with minimum-sensor data. J Robot Syst 12(12):833–844

    Article  MATH  Google Scholar 

  13. Dieudonne JE, Parrish RV, Bardusch RE (1972) An actuator extension transformation for a motion simulator and an inverse transformation applying Newton-Raphson’s method. NASA Langley Research Center, Hampton, VA, Tech. Rep. NASA TND-7067

  14. Merlet JP (1993) Direct kinematics of parallel manipulator. IEEE Trans Robot Automat 9(6):842–846

    Article  Google Scholar 

  15. Ascher M (1974) Cycling in the Newton–Raphson algorithm. Int J Math Educ Sci Technol 5(2):229–235

    Article  MATH  MathSciNet  Google Scholar 

  16. Wang Y (2007) A direct numerical solution to forward kinematics of general Stewart-Gough platforms. Robotica 25(1):121–128

    Article  Google Scholar 

  17. Parikh PJ, Lam SSY (2005) A hybrid strategy to solve the forward kinematics problem in parallel manipulators. IEEE Trans Robot 21(1):18–25

    Article  Google Scholar 

  18. Geng Z, Haynes LS (1992) Neural network solution for the forward kinematics problem of a Stewart platform. Robot Comput Integr Manuf 9(6):485–495

    Google Scholar 

  19. Yee CS, Lim KB (1997) Forward kinematics solution of Stewart platform using neural networks. Neurocomputing 16(4):333–349

    Article  Google Scholar 

  20. Haykin S (1999) Neural networks: a comprehensive foundation, 2nd edn. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

  21. Hornik KM, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366

    Article  Google Scholar 

  22. Parrish RV, Dieudonne JE, Martin DJ Jr. (1973) Motion software for a synergistic six-degree-of-freedom motion base. NASA Langley Research Center, Hampton, VA, Tech. Rep. NASA TND-7350

Download references

Author information

Authors and Affiliations

  1. Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    Pratik J. Parikh

  2. Systems Science and Industrial Engineering Department, State University of New York at Binghamton, Binghamton, NY, 13902, USA

    Sarah S. Lam

Authors
  1. Pratik J. Parikh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sarah S. Lam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pratik J. Parikh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Parikh, P.J., Lam, S.S. Solving the forward kinematics problem in parallel manipulators using an iterative artificial neural network strategy. Int J Adv Manuf Technol 40, 595–606 (2009). https://doi.org/10.1007/s00170-007-1360-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-007-1360-x

Keywords

Search

Navigation