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Comparison Between Fuzzy and Non-fuzzy Ordinary If–Then Rule-Based Control for the Trajectory Tracking of a Differential Drive Robot

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Abstract

The paper proposes fuzzy and non-fuzzy controllers as two control techniques for trajectory tracking of a differential drive mobile robot. The first approach relies on fuzzy logic. Fuzzy logic systems represent knowledge via fuzzy rules. The large number of possible rules complicates the controller and has an impact on timing decision. Logic methods like Karnaugh maps and Quine McCluskey's algorithm have been offered as ways to adapt and reduce the amount of fuzzy rules. An approach based on Karnaugh maps to reduce the number of fuzzy rules without binary coding has been proposed. The second technique, on the other hand, is a non-fuzzy approach that employs the same rules as the reduced fuzzy controller, namely, non-fuzzy (ordinary) If–then rules. Simulation tests and a comparison of fuzzy and non-fuzzy controllers were used to test the efficiency of the proposed controllers.

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References

  1. Tiwari, A., Pati, K.C.: Optimal control, stability and numerical integration analysis of unicycle. Int. J. Dyn. Control. 9, 1042–1052 (2021). https://doi.org/10.1007/s40435-020-00726-8

    Article  MathSciNet  Google Scholar 

  2. Mondal, K., Wallace, B., Rodriguez, A. A.: Stability versus maneuverability of non-holonomic differential drive mobile robot: focus on aggressive position control applications. In: 2020 IEEE Conference on Control Technology and Applications (CCTA), Montreal, pp. 388–395 (2020)

  3. Singh, R., Singh, G., Kumar, V.: Control of closed-loop differential drive mobile robot using forward and reverse Kinematics. In: 2020 Third International Conference on Smart Systems and Inventive Technology (ICSSIT), Tirunelveli, India, pp. 430–433 (2020).

  4. Song, H., Wu, Y., Wu, Y., Zhou, G., Luo, C.: Two-vehicle coordination system for omnidirectional transportation based on image processing and deviation prediction. J. Control Autom. Electr. Syst. 32, 875–883 (2021)

    Article  Google Scholar 

  5. Zhang, Z., Cheng, W., Wu, Y.: Trajectory tracking control design for nonholonomic systems with full-state constraints. Int. J. Control Autom. Syst. 19, 1798–1806 (2021)

    Article  Google Scholar 

  6. Okuyama, I.F., Maximo, M.R.O.A., Afonso, R.J.M.: Minimum-time trajectory planning for a differential drive mobile robot considering non-slipping constraints. J. Control Automat. Electric. Syst. 32, 120–131 (2021). https://doi.org/10.1007/s40313-020-00657-x

    Article  Google Scholar 

  7. Martinez-Melchor, J.A., Jimenez-Fernandez, V.M., Vazquez-Lea, H., Filobello-Nino, U.A.: Optimization of collision-free paths in a differential-drive robot by a smoothing piecewise-linear approach. Compt. Appl. Math. 37, 4944–4965 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  8. Resende, C.Z., Carelli, R., Sarcinelli-Filho, M.: A path-following controller for guiding a single robot or a multi-robot system. J. Control Autom. Electr. Syst. 32, 895–909 (2021)

    Article  Google Scholar 

  9. Hirpo, B.D., Zhongmin, W.: Design and control for differential drive mobile robot. Int. J. Eng. Res. Technol (IJERT) 6(10), 327–334 (2017)

    Google Scholar 

  10. Demirbaş, F., Kalyoncu, M.: Differential drive mobile robot trajectory tracking with using pid and kinematic based backstepping controller. Selcuk Univ. J. Eng. Sci. Technol. 5(1), 1–15 (2017)

    Google Scholar 

  11. Khai, T.Q., Ryoo, Y.J., Gill, W.R., Im, D.Y.: Design of kinematic controller based on parameter tuning by fuzzy inference system for trajectory tracking of differential-drive mobile robot. Int. J. Fuzzy Syst. 22, 1972–1978 (2020)

    Article  Google Scholar 

  12. Bouzoualegh, S., Guechi, E., Kelaiaia, R.: Model predictive control of a differential-drive mobile robot. Acta Universitatis Sapientiae 10, 20–41 (2018)

    Google Scholar 

  13. Macias, V., Becerra, I., Martinez, E., Murrieta-Cid, R., Becerrra, H.M.: Single landmark feedback-based time optimal navigation for a differential drive robot. J. Franklin Inst. 358(9), 4761–4792 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  14. Cristofaro, A., Salaris, P., Pallottino, L., Giannoni, F., Bicchi, A.: On the minimum-time control problem for differential drive robots with bearing constraints. J Optim Theory Appl. 173, 967–993 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  15. Abdulwahhab, O.W., Abbas, N.H.: Design and stability analysis of a fractional order state feedback controller for trajectory tracking of a differential drive robot. Int. J. Control Autom. Syst. 16, 2790–2800 (2018). https://doi.org/10.1007/s12555-017-0234-8

    Article  Google Scholar 

  16. Martins, F.N., Sarcinelli-Filho, M., Carelli, R.: A velocity-based dynamic model and its properties for differential drive mobile robots. J. Intell. Robot. Syst. 85, 277–292 (2017). https://doi.org/10.1007/s10846-016-0381-9

    Article  Google Scholar 

  17. Lopez-Padilla, R., Murrieta-Cid, R., Becerra, I., Laguna, G., LaValle, S.M.: Optimal navigation for a differential drive disc robot: a game against the polygonal environment. J. Intell. Rob. Syst. 89, 211–250 (2018)

    Article  Google Scholar 

  18. Xu, X., Su, P., Wang, F., Chen, L., Xie, J., Atindana, V.A.: Coordinated control of dual-motor using the interval type-2 fuzzy logic in autonomous steering system of AGV. Int. J. Fuzzy Syst. 23, 1070–1086 (2021). https://doi.org/10.1007/s40815-020-00886-x

    Article  Google Scholar 

  19. Pan, Y., Li, Q., Liang, H., Lam, H.K.: A novel mixed control approach for fuzzy systems via membership functions online learning policy. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.3130201

    Article  Google Scholar 

  20. Pan, Y., Wu, Y., Lam, H.K.: Security-based fuzzy control for nonlinear networked control systems with DoS attacks via a resilient event-triggered scheme. IEEE Trans. Fuzzy Syst. (2022). https://doi.org/10.1109/TFUZZ.2022.3148875

    Article  Google Scholar 

  21. Carranza, E.J.M.: Fuzzy modeling of surficial uranium prospectivity in british columbia (Canada) with a weighted fuzzy algebraic sum operator. J. Earth Sci. 32, 293–309 (2021). https://doi.org/10.1007/s12583-021-1403-5

    Article  Google Scholar 

  22. Bhanja, S., Metia, S., Das, A.: A hybrid neuro-fuzzy prediction system with butterfly optimization algorithm for PM25 forecasting. Microsyst. Technol. (2022). https://doi.org/10.1007/s00542-022-05252-5

    Article  Google Scholar 

  23. Xian, S., Cheng, Y.: Pythagorean fuzzy time series model based on pythagorean fuzzy c-means and improved Markov weighted in the prediction of the new COVID-19 cases. Soft. Comput. 25, 13881–13896 (2021). https://doi.org/10.1007/s00500-021-06259-2

    Article  Google Scholar 

  24. Xue, Y., Deng, Y.: Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. Appl. Intell. 51, 6224–6233 (2021). https://doi.org/10.1007/s10489-021-02216-6

    Article  Google Scholar 

  25. Sherwani, A.R., Ali, Q.M.: Parametric classification using fuzzy approach for handling the problem of mixed pixels in ground truth data for a satellite image. Ann. Data. Sci. (2022). https://doi.org/10.1007/s40745-022-00383-y

    Article  Google Scholar 

  26. Hung, C. C., Fernandez, B.: Minimizing rules of fuzzy logic system by using a systematic approach. In: Second IEEE International Conference on Fuzzy Systems, pp. 38–44, (1993)

  27. Andone, D.: Fuzzy rule base complexity reduction: a survey. In: 15th International Conference on Control Systems and Computer Science, Bucharest, Romania, DOI: https://doi.org/10.13140/RG.2.1.5021.8326, (2005)

  28. Guillaume, S.: Designing fuzzy inference systems from data: an interpretability-oriented review. IEEE Trans. Fuzzy Syst. 9(3), 426–443 (2001). https://doi.org/10.1109/91.928739

    Article  Google Scholar 

  29. Ciliz, M.K.: Rule base reduction for knowledge-based fuzzy controllers with application to a vacuum cleaner. Expert Syst. Appl. 28, 175–184 (2005)

    Article  Google Scholar 

  30. Alcalá, R., Alcalá-fdez, J., Gacto, M.J., Herrera, F.: Fuzzy rule reduction and tuning of fuzzy logic controllers for a HVAC system. Fuzzy Appl. Ind. Eng. Stud. Fuzzin. Soft Comput. 201, 89–117 (2006)

    Article  MATH  Google Scholar 

  31. Mamaghani, A.S., Pedrycz, W.: Structural optimization of fuzzy rule-based models: towards efficient complexity management. Expert Syst. Appl. 152(15), 113362 (2020)

    Article  Google Scholar 

  32. Gacto, M.J., Alcalá, R., Herrera, F.: Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems. Soft. Comput. 13, 419–436 (2009). https://doi.org/10.1007/s00500-008-0359-z

    Article  Google Scholar 

  33. Chandramohan, A., Rao, M.V.C.: A novel approach for combining fuzzy rules using mean operators for effective rule reduction. Soft. Comput. 10, 1103–1108 (2006). https://doi.org/10.1007/s00500-006-0047-9

    Article  Google Scholar 

  34. Aghaeipoor, F., Eftekhari, M.: EEFR-R: extracting effective fuzzy rules for regression problems, through the cooperation of association rule mining concepts and evolutionary algorithms. Soft. Comput. 23, 11737–11757 (2019). https://doi.org/10.1007/s00500-018-03726-1

    Article  Google Scholar 

  35. Hacene, N., Mendil, B.: Fuzzy behavior-based control of three wheeled omnidirectional mobile robot. Int. J. Autom. Comput. 16(2), 163–185 (2019)

    Article  Google Scholar 

  36. Hacene, N., Mendil, B.: Motion analysis and control of three wheeled omnidirectional mobile robot. J, Control Autom, Electr. Syst. 30(2), 194–213 (2019)

    Article  Google Scholar 

  37. Cococcioni, M., Foschini, L., Lazzerini, B., Marcelloni, F.: Complexity reduction of mamdani fuzzy systems through multi-valued logic minimization. In: 2008 IEEE International Conference on Systems, Man and Cybernetics, Singapore, pp. 1782–1787 (2008)

  38. Jara, L., González, A., Pérez, R.: A preliminary study to apply the Quine McCluskey algorithm for fuzzy rule base minimization. In: 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Glasgow, pp. 1–6 (2020)

  39. Kosheleva, O., Kreinovich, V., Nguyen, T.N.: Why triangular membership functions are successfully used in f-transform applications: a global explanation to supplement the existing local ones. Axioms 8(3), 95 (2019). https://doi.org/10.3390/axioms8030095

    Article  MATH  Google Scholar 

  40. Zhao, J., Bose, B.K.: Evaluation of membership functions for fuzzy logic controlled induction motor drive. In: 2002 IEEE 28th Annual Conference of the Industrial Electronics Society. IECON 02, Seville, pp. 229–234, vol. 1. https://doi.org/10.1109/IECON.2002.1187512

  41. Mandal, S.N., Choudhury, J.P., Chaudhuri, S.R.B.: In search of suitable fuzzy membership function in prediction of time series data. IJCSI Int. J. Comput. Sci. Issues 9(3), 293–302 (2012)

    Google Scholar 

  42. Monicka, J.G., Sekhar, N.O.G., Kumar, K.R.: Performance evaluation of membership functions on fuzzy logic controlled AC voltage controller for speed control of induction motor drive. Int. J. Comput. Appl. 13(5), 8–12 (2011)

    Google Scholar 

  43. Barua, A., Mudunuri, L.S., Kosheleva, O.: Why trapezoidal and triangular membership functions work so well: towards a theoretical explanation. J. Uncert. Syst. 8(3), 164–168 (2014)

    Google Scholar 

  44. Gholamy, A., Kosheleva, O., Kreinovich, V.: How to explain the efficiency of triangular and trapezoid membership functions in applications to design. Oнтoлoгия пpoeктиpoвaния (Ontol. Des.) 9(2), 253–260 (2019). https://doi.org/10.18287/2223-9537-2019-9-2-253-260

    Article  Google Scholar 

  45. Pedrycz, W.: Why triangular membership functions? Fuzzy Sets Syst 64, 21–30 (1994). https://doi.org/10.1016/0165-0114(94)90003-5

    Article  MathSciNet  Google Scholar 

  46. Mai, T.A., Dang, T.S., Duong, D.T., Le, V.C., Banerjee, S.: A combined backstepping and adaptive fuzzy PID approach for trajectory tracking of autonomous mobile robots. J Braz. Soc. Mech. Sci. Eng. 43, 156 (2021). https://doi.org/10.1007/s40430-020-02767-8

    Article  Google Scholar 

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Hacene, N., Mendil, B., Bechouat, M. et al. Comparison Between Fuzzy and Non-fuzzy Ordinary If–Then Rule-Based Control for the Trajectory Tracking of a Differential Drive Robot. Int. J. Fuzzy Syst. 24, 3666–3687 (2022). https://doi.org/10.1007/s40815-022-01365-1

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