Skip to main content
SpringerLink
Log in

Finite-Time Adaptive Interval Type-2 Fuzzy Tracking Control for Mecanum-Wheel Mobile Robots

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Aiming at the tracking problem of a four-mecanum-wheel omnidirectional mobile robot, a finite-time adaptive interval type-2 fuzzy controller is proposed by a backstepping technique. An interval type-2 fuzzy approximator is utilized to approximate the complicated dynamics of the mobile robot, of which the output is calculated through an improved Begian–Melek–Mendel (BMM) reduction algorithm. The proposed controller only relies on the length, width and wheel radius of the robot, which are easily available and time-invariant, therefore it is very convenient to apply and has a wide range of applicability. The stability is proved by the practical semi-global finite-time stability theory. Comparative simulation results between adaptive interval type-2 fuzzy controller, adaptive type-1 fuzzy controller and PID controller are given to illustrate the effectiveness of the proposed controller.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Lu, X., Zhang, X., Zhang, G., Jia, S.: Design of adaptive sliding mode controller for four-Mecanum wheel mobile robot. In: 2018 37th Chinese Control Conference (CCC), pp. 3983–3987. IEEE (2018)

  2. Gfrerrer, A.: Geometry and kinematics of the Mecanum wheel. Comput. Aided Geom. Des. 25(9), 784–791 (2008)

    Article  MathSciNet  Google Scholar 

  3. Yuan, Z., Tian, Y., Yin, Y., Wang, S., Liu, J., Ligang, W.: Trajectory tracking control of a four Mecanum wheeled mobile platform: an extended state observer-based sliding mode approach. IET Control Theory Appl. 14(3), 415–426 (2019)

    Article  Google Scholar 

  4. Galicki, M., Banaszkiewicz, M.: Optimal trajectory tracking control of omni-directional mobile robots. In: 2019 12th International Workshop on Robot Motion and Control (RoMoCo), pp. 137–142. IEEE (2019)

  5. Santos, J., Conceição, A., Santos, T., Araújo, H.: Remote control of an omnidirectional mobile robot with time-varying delay and noise attenuation. Mechatronics 52, 7–21 (2018)

    Article  Google Scholar 

  6. Sun, H., Zhao, H., Zhen, S., Huang, K., Zhao, F., Chen, X., Chen, Y.-H.: Application of the Udwadia-Kalaba approach to tracking control of mobile robots. Nonlinear Dyn. 83(1–2), 389–400 (2016)

    Article  MathSciNet  Google Scholar 

  7. Cui, M., Liu, W., Liu, H., Jiang, H., Wang, Z.: Extended state observer-based adaptive sliding mode control of differential-driving mobile robot with uncertainties. Nonlinear Dyn. 83(1), 667–683 (2016)

    Article  MathSciNet  Google Scholar 

  8. Alakshendra, V., Chiddarwar, S.: Adaptive robust control of Mecanum-wheeled mobile robot with uncertainties. Nonlinear Dyn. 87(4), 2147–2169 (2017)

    Article  MathSciNet  Google Scholar 

  9. Conceição, A.G.S., Dórea, C.E.T., Martinez, L., de Pieri, E.R., et al.: Design and implementation of model-predictive control with friction compensation on an omnidirectional mobile robot. IEEE/ASME Trans. Mechatron. 19(2), 467–476 (2013)

    Google Scholar 

  10. Watson, M.T., Gladwin, D.T., Prescott, T.J., Conran, S.O.: Dual-mode model predictive control of an omnidirectional wheeled inverted pendulum. IEEE/ASME Trans. Mechatron. 24(6), 2964–2975 (2019)

    Article  Google Scholar 

  11. Jeong, S., Chwa, D.: Sliding-mode-disturbance-observer-based robust tracking control for omnidirectional mobile robots with kinematic and dynamic uncertainties. IEEE/ASME Trans. Mechatron. 26(2), 741–752 (2020)

    Article  Google Scholar 

  12. Ren, C., Li, X., Yang, X., Ma, S.: Extended state observer-based sliding mode control of an omnidirectional mobile robot with friction compensation. IEEE Trans. Ind. Electron. 66(12), 9480–9489 (2019)

    Article  Google Scholar 

  13. Ovalle, L., Ríos, H., Llama, M., Santibáñez, V., Dzul, A.: Omnidirectional mobile robot robust tracking: sliding-mode output-based control approaches. Control Eng. Pract. 85, 50–58 (2019)

    Article  Google Scholar 

  14. Huang, J.-T., Van Hung, T., Tseng, M.-L.: Smooth switching robust adaptive control for omnidirectional mobile robots. IEEE Trans. Control Syst. Technol. 23(5), 1986–1993 (2015)

    Article  Google Scholar 

  15. Sun, L., He, W., Sun, C.: Adaptive fuzzy relative pose control of spacecraft during rendezvous and proximity maneuvers. IEEE Trans. Fuzzy Syst. 26(6), 3440–3451 (2018)

    Article  Google Scholar 

  16. Tong, S., Li, Y., Sui, S.: Adaptive fuzzy tracking control design for siso uncertain nonstrict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 24(6), 1441–1454 (2016)

    Article  Google Scholar 

  17. Ma, M., Wang, T., Jianbin, Q., Karimi, H.R.: Adaptive fuzzy decentralized tracking control for large-scale interconnected nonlinear networked control systems. IEEE Trans. Fuzzy Syst. 29, 3186 (2020)

    Article  Google Scholar 

  18. Yousef, H., Hamdy, M., El-Madbouly, E., Eteim, D.: Adaptive fuzzy decentralized control for interconnected mimo nonlinear subsystems. Automatica 45(2), 456–462 (2009)

    Article  MathSciNet  Google Scholar 

  19. Fang, L., Ding, S., Ju, H., Ma, L.: Adaptive fuzzy control for nontriangular stochastic high-order nonlinear systems subject to asymmetric output constraints. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3000920

    Article  Google Scholar 

  20. Chen, B., Liu, X.P., Ge, S.S., Lin, C.: Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 20(6), 1012–1021 (2012)

    Article  Google Scholar 

  21. Xin, L.-P., Bo, Y., Zhao, L., Jinpeng, Y.: Adaptive fuzzy backstepping control for a two continuous stirred tank reactors process based on dynamic surface control approach. Appl. Math. Comput. 377, 125138 (2020)

    MathSciNet  MATH  Google Scholar 

  22. Dongrui, W.: Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons. IEEE Trans. Fuzzy Syst. 21(1), 80–99 (2012)

    Google Scholar 

  23. Begian, M.B., Melek, W.W., Mendel, J.M.: Stability analysis of type-2 fuzzy systems. In: 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), pp. 947–953. IEEE (2008)

  24. Li, C., Yi, J, Wang, T.: Stability analysis of sirms based type-2 fuzzy logic control systems. In: International Conference on Fuzzy Systems, pp. 1–7. IEEE (2010)

  25. Zeghlache, S., Djerioui, A., Benyettou, L., Benslimane, T., Mekki, H., Bouguerra, A.: Fault tolerant control for modified quadrotor via adaptive type-2 fuzzy backstepping subject to actuator faults. ISA Trans. 95, 330–345 (2019)

    Article  Google Scholar 

  26. Lin, T.-C., Liu, H.-L., Kuo, M.-J.: Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems. Eng. Appl. Artif. Intell. 22(3), 420–430 (2009)

    Article  Google Scholar 

  27. Bibi, Y., Bouhali, O., Bouktir, T.: Petri type 2 fuzzy neural networks approximator for adaptive control of uncertain non-linear systems. IET Control Theory Appl. 11(17), 3130–3136 (2017)

    Article  MathSciNet  Google Scholar 

  28. Dian, S., Yi, H., Zhao, T., Han, J.: Adaptive backstepping control for flexible-joint manipulator using interval type-2 fuzzy neural network approximator. Nonlinear Dyn. 97(2), 1567–1580 (2019)

    Article  Google Scholar 

  29. Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(5), 678–682 (1998)

    Article  MathSciNet  Google Scholar 

  30. Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)

    Article  MathSciNet  Google Scholar 

  31. Wang, F., Chen, B., Liu, X., Lin, C.: Finite-time adaptive fuzzy tracking control design for nonlinear systems. IEEE Trans. Fuzzy Syst. 26(3), 1207–1216 (2017)

    Article  Google Scholar 

  32. Ren, Z., Zhao, B., Nguyen, D.T.: Finite-time backstepping of a nonlinear system in strict-feedback form: proved by Bernoulli inequality. IEEE Access 8, 47768–47775 (2020)

    Article  Google Scholar 

  33. Li, Y., Li, K., Tong, S.: Finite-time adaptive fuzzy output feedback dynamic surface control for mimo nonstrict feedback systems. IEEE Trans. Fuzzy Syst. 27(1), 96–110 (2018)

    Article  Google Scholar 

  34. Tsai, C-C., Wu, H-L.: Nonsingular terminal sliding control using fuzzy wavelet networks for Mecanum wheeled omni-directional vehicles. In: International Conference on Fuzzy Systems, pp. 1–6. IEEE (2010)

  35. Ma, L., Zong, G., Zhao, X., Huo, X.: Observed-based adaptive finite-time tracking control for a class of nonstrict-feedback nonlinear systems with input saturation. J. Frankl. Inst. 357(16), 11518–11544 (2020)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work is supported by the Sichuan Science and Technology Program (Grant No. 2020YFG0115) and Chengdu Science and Technology Program (2019-YF05-00958-SN).

Author information

Authors and Affiliations

  1. College of Electrical Engineering, Sichuan University, Chengdu, 610065, China

    Xuegen Zou, Tao Zhao & Songyi Dian

Authors
  1. Xuegen Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tao Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Songyi Dian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tao Zhao.

Ethics declarations

Conflict of interest

No potential conflict of interest was reported by the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zou, X., Zhao, T. & Dian, S. Finite-Time Adaptive Interval Type-2 Fuzzy Tracking Control for Mecanum-Wheel Mobile Robots. Int. J. Fuzzy Syst. 24, 1570–1585 (2022). https://doi.org/10.1007/s40815-021-01211-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-021-01211-w

Keywords

Search

Navigation