Determining normalized friction torque of an industrial robotic manipulator using the symbolic regression method

  • 1 Faculty of Engineering, University of Rijeka, Croatia


The goal of the paper is estimating the normalized friction torque of a joint in an industrial robotic manipulator. For this purpose a source data, given as a figure, is digitized using a tool WebPlotDigitizer in order to obtain numeric data. The numeric data is the used within the machine learning algorithm genetic programming (GP), which performs the symbolic regression in order to obtain the equation that regresses the dataset in question. The obtained model shows a coefficient of determination equal to 0.87, which indicates that the model in question may be used for the wide approximation of the normalized friction torque using the torque load, operating temperature and joint velocity as inputs.



  1. Murphy, R. R. (2019). Introduction to AI robotics. MIT press. (doi:
  2. Lorencin, I., Baressi Šegota, S., AnĎelić, N., Blagojević, A., Šušteršić, T., Protić, A., ... & Car, Z. (2021). Automatic evaluation of the lung condition of covid-19 patients using x-ray images and convolutional neural networks. Journal of Personalized Medicine, 11(1), 28. (doi:
  3. Car, Z., Baressi Šegota, S., AnĎelić, N., Lorencin, I., & Mrzljak, V. (2020). Modeling the spread of COVID-19 infection using a multilayer perceptron. Computational and mathematical methods in medicine, 2020. (doi:
  4. Baressi Šegota, S., Lorencin, I., AnĎelić, N., Mrzljak, V., & Car, Z. (2020). Improvement of marine steam turbine conventional exergy analysis by neural network application. Journal of Marine Science and Engineering, 8(11), 884. (doi:
  5. Baressi Šegota, S., AnĎelić, N., Lorencin, I., Saga, M., & Car, Z. (2020). Path planning optimization of six-degree-of-freedom robotic manipulators using evolutionary algorithms. International Journal of Advanced Robotic Systems, 17(2), 1729881420908076. (doi:
  6. Šegota, S. B., AnĎelić, N., Mrzljak, V., Lorencin, I., Kuric, I., & Car, Z. (2021). Utilization of multilayer perceptron for determining the inverse kinematics of an industrial robotic manipulator. International Journal of Advanced Robotic Systems, 18(4), 1729881420925283. (doi:
  7. Baressi Šegota, S., AnĎelić, N., Šercer, M., & Meštrić, H. (2022). Dynamics Modeling of Industrial Robotic Manipulators: A Machine Learning Approach Based on Synthetic Data. Mathematics, 10(7), 1174. (doi:
  8. AnĎelić, N., Car, Z., & Šercer, M. (2022). Prediction of Robot Grasp Robustness using Artificial Intelligence Algorithms. Tehnički vjesnik, 29(1), 101-107. (doi: 20210204092154)
  9. AnĎelić, N., Car, Z., & Šercer, M. (2021). Neural Network- Based Model for Classification of Faults During Operation of a Robotic Manipulator. Tehnički vjesnik, 28(4), 1380-1387. (doi:
  10. Koza, J. R., & Poli, R. (2005). Genetic programming. In Search methodologies (pp. 127-164). Springer, Boston, MA. (doi:
  11. Park, J. Y., & Salmeron, M. (2014). Fundamental aspects of energy dissipation in friction. Chemical reviews, 114(1), 677-711. (doi:
  12. Khan, Z. A., Chacko, V., & Nazir, H. (2017). A review of friction models in interacting joints for durability design. Friction, 5(1), 1-22. (doi:
  13. Amanov, A., & Pyun, Y. S. (2018). Lowering friction of ball screws made of different steel grades through ultrasonic impact treatment. Tribology International, 123, 105-119. (doi:
  14. Rudin, C., & Radin, J. (2019). Why are we using black box models in AI when we don’t need to? A lesson from an explainable AI competition. (doi:
  15. Garcia, R. R., Bittencourt, A. C., & Villani, E. (2018). Relevant factors for the energy consumption of industrial robots. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(9), 1-15. (doi: 1376-1)
  16. Drevon, D., Fursa, S. R., & Malcolm, A. L. (2017). Intercoder reliability and validity of WebPlotDigitizer in extracting graphed data. Behavior modification, 41(2), 323-339. (doi:
  17. AnĎelić, N., Baressi Šegota, S., Lorencin, I., Poljak, I., Mrzljak, V., & Car, Z. (2021). Use of Genetic Programming for the Estimation of CODLAG Propulsion System Parameters. Journal of Marine Science and Engineering, 9(6), 612. (doi:
  18. AnĎelić, N., Baressi Šegota, S., Lorencin, I., Mrzljak, V., & Car, Z. (2021). Estimation of COVID-19 epidemic curves using genetic programming algorithm. Health informatics journal, 27(1), 1460458220976728. (doi:
  19. Koza, J. R. (2010). Human-competitive results produced by genetic programming. Genetic programming and evolvable machines, 11(3), 251-284. (doi: 010-9112-3)
  20. Hancock, P. J. (1994, April). An empirical comparison of selection methods in evolutionary algorithms. In AISB workshop on evolutionary computing (pp. 80-94). Springer, Berlin, Heidelberg. (doi:
  21. Nazif, H., & Lee, L. S. (2012). Optimised crossover genetic algorithm for capacitated vehicle routing problem. Applied Mathematical Modelling, 36(5), 2110-2117. (doi:
  22. Hong, T. P., & Wang, H. S. (1996, October). A dynamic mutation genetic algorithm. In 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No. 96CH35929) (Vol. 3, pp. 2000-2005). IEEE. (doi:
  23. Bridges, C. L., & Goldberg, D. E. (1987). An analysis of reproduction and crossover in a binary-coded genetic algorithm. Grefenstette, 878, 9-13.
  24. Meurer, A., Smith, C. P., Paprocki, M., Čertík, O., Kirpichev, S. B., Rocklin, M., ... & Scopatz, A. (2017). SymPy: symbolic computing in Python. PeerJ Computer Science, 3, e103. (doi:
  25. Ferreira, J., Pedemonte, M., & Torres, A. I. (2019). A genetic programming approach for construction of surrogate models. In Computer Aided Chemical Engineering (Vol. 47, pp. 451-456). Elsevier. (doi: 2)
  26. Koza, J. R., Andre, D., Keane, M. A., & Bennett III, F. H. (1999). Genetic programming III: Darwinian invention and problem solving (Vol. 3). Morgan Kaufmann. (doi:
  27. AnĎelić, N., Šegota, S. B., Lorencin, I., Jurilj, Z., Šušteršič, T., Blagojević, A., ... & Car, Z. (2021). Estimation of covid-19 epidemiology curve of the united states using genetic programming algorithm. International Journal of Environmental Research and Public Health, 18(3), 959.. (doi:
  28. AnĎelić, N., Baressi Šegota, S., Lorencin, I., & Car, Z. (2020). Estimation of gas turbine shaft torque and fuel flow of a CODLAG propulsion system using genetic programming algorithm. Pomorstvo, 34(2), 323-337. (doi:
  29. Lorencin, I., AnĎelić, N., Mrzljak, V., & Car, Z. (2019). Genetic algorithm approach to design of multi-layer perceptron for combined cycle power plant electrical power output estimation. Energies, 12(22), 4352. (doi:
  30. Ozer, D. J. (1985). Correlation and the coefficient of determination. Psychological bulletin, 97(2), 307. (doi:
  31. Nagelkerke, N. J. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78(3), 691-692. (doi:
  32. Baressi Šegota, S., Lorencin, I., Šercer, M., & Car, Z. (2021). Determining residuary resistance per unit weight of displacement with Symbolic Regression and Gradient Boosted Tree algorithms. Pomorstvo, 35(2), 287-296. (doi:

Article full text

Download PDF