Skip to main content
SpringerLink
Log in

Genetic Programming-Based Inverse Kinematics for Robotic Manipulators

  • Conference paper
  • First Online:
Genetic Programming (EuroGP 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13223))

Included in the following conference series:

Abstract

In this paper, we introduce an inverse kinematics model for a robotic manipulator using Genetic Programming (GP). The underlying problem requires learning of multiple joint parameters of the manipulator to reach a desired position in the Cartesian space. We present a new approach to identify a closed-form solution for the Inverse Kinematics (IK) problem, namely IK-CCGP. The novelty of IK-CCGP is the cooperative coevolutionary learning strategy. Unlike other GP approaches, IK-CCGP is not limited to a certain angle combination to reach a given pose and is designed to achieve more flexibility in the learning process. Moreover, it can operate both as single- and multi-objective variants. In this paper, we investigate whether the inclusion of further objectives, i.e. correlation and the consistency of a solution with physical laws, contributes to the search process. Our experiments show that the combination of the two objectives, error and correlation, performs very well for the given problem and IK-CCGP performs the best on a kinematic unit of two joints. While our approach cannot attain the same accuracy as Artificial Neural Networks, it overcomes the explainability gap of IK models developed using ANNs.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://github.com/hgrecco/pint.

References

  1. Almusawi, A.R., Dülger, L.C., Kapucu, S.: A new artificial neural network approach in solving inverse kinematics of robotic arm (Denso vp6242). Comput. Intell. Neurosci. 2016 (2016)

    Google Scholar 

  2. Aristidou, A., Lasenby, J., Chrysanthou, Y., Shamir, A.: Inverse kinematics techniques in computer graphics: a survey. Comput. Graph. Forum 37(6), 35–58 (2018)

    Article  Google Scholar 

  3. Chapelle, F., Bidaud, P.: A closed form for inverse kinematics approximation of general 6R manipulators using genetic programming. In: IEEE International Conference on Robotics and Automation, vol. 4, pp. 3364–3369 (2001)

    Google Scholar 

  4. Chapelle, F., Bidaud, P.: Closed form solutions for inverse kinematics approximation of general 6r manipulators. Mech. Mach. Theory 39(3), 323–338 (2004)

    Article  Google Scholar 

  5. Craig, J.J.: Introduction to Robotics: Mechanics and Control. Pearson Education Inc., 3rd edn. (1989)

    Google Scholar 

  6. Daunicht, W.J.: Approximation of the inverse kinematics of an industrial robot by defanet. In: IEEE International Joint Conference on Neural Networks, pp. 1995–2000 (1991)

    Google Scholar 

  7. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  8. Dolinsky, J.U., Jenkinson, I., Colquhoun, G.J.: Application of genetic programming to the calibration of industrial robots. Comput. Ind. 58(3), 255–264 (2007)

    Article  Google Scholar 

  9. Eckmiller, R., Beckmann, J., Werntges, H., Lades, M.: Neural kinematics net for a redundant robot arm. In: IEEE International Joint Conference on Neural Networks, vol. 2, pp. 333–339 (1989)

    Google Scholar 

  10. El-Sherbiny, A., Elhosseini, M.A., Haikal, A.Y.: A comparative study of soft computing methods to solve inverse kinematics problem. Ain Shams Eng. J. 9(4), 2535–2548 (2018)

    Article  Google Scholar 

  11. Fortin, F.A., De Rainville, F.M., Gardner, M.A., Parizeau, M., Gagné, C.: DEAP: evolutionary algorithms made easy. J. Mach. Learn. Res. 13, 2171–2175 (2012)

    MathSciNet  Google Scholar 

  12. Hakala, J., Fahner, G., Eckmiller, R.: Rapid learning of inverse robot kinematics based on connection assignment and topographical encoding (cate). In: IEEE International Joint Conference on Neural Networks, vol. 2, pp. 1536–1541 (1991)

    Google Scholar 

  13. Jazar, R.N.: Theory of Applied Robotics: Kinematics, Dynamics, and Control. Springer Science Business Media, Heidelberg (2010)

    Google Scholar 

  14. Kalra, P., Mahapatra, P., Aggarwal, D.: An evolutionary approach for solving the multimodal inverse kinematics problem of industrial robots. Mech. Mach. Theory 41(10), 1213–1229 (2006)

    Article  Google Scholar 

  15. Keijzer, M., Babovic, V.: Dimensionally aware genetic programming. In: Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation, vol. 2, pp. 1069–1076 (1999)

    Google Scholar 

  16. Kucuk, S., Bingul, Z.: Inverse kinematics solutions for industrial robot manipulators with offset wrists. Appl. Math. Model. 38(7–8), 1983–1999 (2014)

    Article  MathSciNet  Google Scholar 

  17. Li, D., Zhong, J.: Dimensionally aware multi-objective genetic programming for automatic crowd behavior modeling. ACM Trans. Model. Comput. Simulat. 30(3), 1–24 (2020)

    Article  MathSciNet  Google Scholar 

  18. Mckay, R.I., Hoai, N.X., Whigham, P.A., Shan, Y., O’neill, M.: Grammar-based genetic programming: a survey. Genetic Program. Evol. Mach. 11(3–4), 365–396 (2010)

    Google Scholar 

  19. Parker, J.K., Khoogar, A.R., Goldberg, D.E.: Inverse kinematics of redundant robots using genetic algorithms. In: IEEE International Conference on Robotics and Automation, vol. 1, pp. 271–276 (1989)

    Google Scholar 

  20. Rodriguez-Coayahuitl, L., Morales-Reyes, A., Escalante, H.J., Coello, C.A.C.: Cooperative co-evolutionary genetic programming for high dimensional problems. In: Parallel Problem Solving from Nature, pp. 48–62 (2020)

    Google Scholar 

  21. Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. John Wiley & Sons, Inc., New York (2005)

    Google Scholar 

  22. Srisuk, P., Sento, A., Kitjaidure, Y.: Forward kinematic-like neural network for solving the 3d reaching inverse kinematics problems. In: 14th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, pp. 214–217 (2017)

    Google Scholar 

  23. Wappler, S., Wegener, J.: Evolutionary unit testing of object-oriented software using strongly-typed genetic programming. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 1925–1932 (2006)

    Google Scholar 

  24. Wei, Y., Jian, S., He, S., Wang, Z.: General approach for inverse kinematics of NR robots. Mech. Mach. Theory 75, 97–106 (2014)

    Article  Google Scholar 

  25. Zhang, Y., Li, Y., Xiao, X.: A novel kinematics analysis for a 5-dof manipulator based on kuka youbot. In: IEEE International Conference on Robotics and Biomimetics, pp. 1477–1482 (2015)

    Google Scholar 

  26. Zille, H., Evrard, F., Reuter, J., Mostaghim, S., van Wachem, B.: Assessment of multi-objective and coevolutionary genetic programming for predicting the stokes flow around a sphere. In: Conference Proceedings EUROGEN 2021 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Intelligent Cooperating Systems, Faculty of Computer Science, Otto von Guericke University Magdeburg, Magdeburg, Germany

    Julia Reuter, Christoph Steup & Sanaz Mostaghim

Authors
  1. Julia Reuter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christoph Steup
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sanaz Mostaghim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julia Reuter .

Editor information

Editors and Affiliations

  1. University of Trieste, Trieste, Italy

    Eric Medvet

  2. Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil

    Gisele Pappa

  3. Victoria University of Wellington, Wellington, New Zealand

    Bing Xue

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Reuter, J., Steup, C., Mostaghim, S. (2022). Genetic Programming-Based Inverse Kinematics for Robotic Manipulators. In: Medvet, E., Pappa, G., Xue, B. (eds) Genetic Programming. EuroGP 2022. Lecture Notes in Computer Science, vol 13223. Springer, Cham. https://doi.org/10.1007/978-3-031-02056-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-02056-8_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-02055-1

  • Online ISBN: 978-3-031-02056-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation