Asymptotic tracking control of uncertain nonholonomic wheeled mobile robot with actuator saturation and external disturbances


This paper deals with the asymptotic tracking control for the uncertain nonholonomic wheeled mobile robot system subjected to actuator saturation and external disturbances simultaneously. A dynamic system is introduced to deal with the actuator saturation, radial basis function neural networks (RBF NNs) are employed to approximate the unknown closed-loop system dynamics, and an adaptive sliding mode feedback term is used to compensate for the approximation error as well as external disturbances. Consequently, a novel adaptive neural controller is designed to guarantee the stability of the closed-loop system and the asymptotic convergence of tracking errors. Meanwhile, the convergence of NN weights is verified, which means that accurate approximation of the unknown closed-loop system dynamics can be obtained and the constant weights can be reused to perform the same or similar control tasks. Finally, simulation studies illustrate the effectiveness of the proposed scheme.

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

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


  1. 1.

    Cao Z, Yin L, Fu Y, Dai JS (2014) Adaptive dynamic surface control for vision-based stabilization of an uncertain electrically driven nonholonomic mobile robot. Robotica 34(2):449–467

    Google Scholar 

  2. 2.

    Kayacan E, Chowdhary G (2018) Tracking error learning control for precise mobile robot path tracking in outdoor environment. J Intell Robot Syst.

    Google Scholar 

  3. 3.

    Yang H, Guo M, Xia Y, Cheng L (2018) Trajectory tracking for wheeled mobile robots via model predictive control with softening constraints. IET Control Theory Appl 12(2):206–214

    MathSciNet  Google Scholar 

  4. 4.

    Fu J, Tian F, Chai T, Jing Y, Li Z, Su CY (2018) Motion tracking control design for a class of nonholonomic mobile robot systems. In: IEEE transactions on systems, man, and cybernetics: systems, pp 1–7

  5. 5.

    Li L, Liu Y, Jiang T, Wang K, Fang M (2018) Adaptive trajectory tracking of nonholonomic mobile robots using vision-based position and velocity estimation. IEEE Trans Cybern 48(2):571–582

    Google Scholar 

  6. 6.

    Binh NT, Tung NA, Nam DP, Quang NH (2019) An adaptive backstepping trajectory tracking control of a tractor trailer wheeled mobile robot. Int J Control Autom Syst 17(2):465–473

    Google Scholar 

  7. 7.

    Chiu CH, Lin CM (2018) Control of an omnidirectional spherical mobile robot using an adaptive mamdani-type fuzzy control strategy. Neural Comput Appl 30(4):1303–1315

    Google Scholar 

  8. 8.

    Dang VQ, Nielsen IE, Stegerjensen K, MAdsen O (2014) Scheduling a single mobile robot for part-feeding tasks of production lines. J Intell Manuf 25(6):1271–1287

    Google Scholar 

  9. 9.

    Chen Y, Wu F, Shuai W, Wang N, Chen R, Chen X (2015) KeJia robot—an attractive shopping mall guider. In: International conference on social robotics, Springer, Cham pp 145–154

  10. 10.

    Hassan KM, Alireza A, Maryam ADN (2013) Teaching-learning-based optimal interval type-2 fuzzy pid controller design: a nonholonomic wheeled mobile robots. Robotica 31(7):1059–1071

    Google Scholar 

  11. 11.

    Wen C, Huang J, Wang W, Jiang ZP (2014) Adaptive output feedback tracking control of a nonholonomic mobile robot. Automatica 50(3):821–831

    MathSciNet  MATH  Google Scholar 

  12. 12.

    Alfi A, Farrokhi M (2009) Hybrid state-feedback sliding-mode controller using fuzzy logic for four-wheel-steering vehicles. Veh Syst Dyn 47(3):265–284

    Google Scholar 

  13. 13.

    Huang D, Zhai J, Ai W, Fei S (2016) Disturbance observer-based robust control for trajectory tracking of wheeled mobile robots. Neurocomputing 198:74–79

    Google Scholar 

  14. 14.

    Esmaeili N, Alfi A, Khosravi H (2017) Balancing and trajectory tracking of two-wheeled mobile robot using backstepping sliding mode control: design and experiments. J Intell Robot Syst 87(3):601–613

    Google Scholar 

  15. 15.

    Zhai J-Y, Song Z-B (2018) Adaptive sliding mode trajectory tracking control for wheeled mobile robots. Int J Control.

    MATH  Google Scholar 

  16. 16.

    Yasmine K, Mohamed B, Tarak D (2018) Adaptive sliding mode control for trajectory tracking of nonholonomic mobile robot with uncertain kinematics and dynamics. Appl Artif Intell 32(9–10):924–938

    Google Scholar 

  17. 17.

    Wu X, Jin P, Zou T, Qi Z, Lou P (2019) Backstepping trajectory tracking based on fuzzy sliding mode control for differential mobile robots. J Intell Robot Syst 4:1–13

    Google Scholar 

  18. 18.

    Zeng W, Wang Q, Liu F, Wang Y (2016) Learning from adaptive neural network output feedback control of a unicycle-type mobile robot. ISA Trans 61:337–347

    Google Scholar 

  19. 19.

    Rossomando FG, Soria CM (2015) Identification and control of nonlinear dynamics of a mobile robot in discrete time using an adaptive technique based on neural PID. Neural Comput Appl 26(5):1179–1191

    Google Scholar 

  20. 20.

    Rossomando FG, Soria C, Carelli R (2014) Sliding mode neuro adaptive control in trajectory tracking for mobile robots. J Intell Robot Syst 74(3–4):931–944

    Google Scholar 

  21. 21.

    Peng S, Shi W (2017) Adaptive fuzzy integral terminal sliding mode control of a nonholonomic wheeled mobile robot. Math Probl Eng.

    MathSciNet  MATH  Google Scholar 

  22. 22.

    Boukens M, Boukabou A, Chadli M (2017) Robust adaptive neural network-based trajectory tracking control approach for nonholonomic electrically driven mobile robots. Robot Auton Syst 92:30–40

    Google Scholar 

  23. 23.

    Wang C, Hill DJ (2009) Deterministic learning theory for identification, recognition, and control, 1st edn. CRC Press Inc, Boca Raton

    Google Scholar 

  24. 24.

    Wang H, Chen B, Liu X, Liu K, Lin C (2014) Adaptive neural tracking control for stochastic nonlinear strict-feedback systems with unknown input saturation. Inf Sci 269:300–315

    MathSciNet  MATH  Google Scholar 

  25. 25.

    Wang H, Chen B, Liu X, Liu K, Lin C (2013) Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints. IEEE Trans Syst Man Cybern 43(6):2093–2104

    Google Scholar 

  26. 26.

    Bezzaoucha S, Marx B, Maquin D, Ragot J (2012) Linear feedback control input under actuator saturation: a Takagi–Sugeno approach. In 2nd international conference on systems and control, ICSC 2012

  27. 27.

    Zhou S, Chen M, Ong CJ, Chen PCY (2016) Adaptive neural network control of uncertain MIMO nonlinear systems with input saturation. Neural Comput Appl 27(5):1317–1325

    Google Scholar 

  28. 28.

    Wang F, Zou Q, Zong Q (2017) Robust adaptive backstepping control for an uncertain nonlinear system with input constraint based on Lyapunov redesign. Int J Control Autom Syst 15(1):212–225

    Google Scholar 

  29. 29.

    Li H, Bai L, Zhou Q, Lu R, Wang L (2017) Adaptive fuzzy control of stochastic nonstrict-feedback nonlinear systems with input saturation. IEEE Trans Syst Man Cybern Syst 47(8):2185–2197

    Google Scholar 

  30. 30.

    Cai M, Xiang Z (2018) Adaptive finite-time control of a class of non-triangular nonlinear systems with input saturation. Neural Comput Appl 29(7):565–576

    Google Scholar 

  31. 31.

    Shojaei K (2015) Saturated output feedback control of uncertain nonholonomic wheeled mobile robots. Robotica 33(1):87–105

    Google Scholar 

  32. 32.

    Yue M, Wu G, Wang S, An C (2014) Disturbance observer-based trajectory tracking control for nonholonomic wheeled mobile robot subject to saturated velocity constraint. Appl Artif Intell 28(8):751–765

    Google Scholar 

  33. 33.

    Chen H (2014) Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation. Int J Control Autom Syst 12(6):1216–1224

    Google Scholar 

  34. 34.

    Huang J, Wen C, Wang W, Jiang ZP (2013) Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance. Syst Control Lett 62(3):234–241

    MathSciNet  MATH  Google Scholar 

  35. 35.

    Sun Z, Dai L, Xia Y, Liu K (2018) Event-based model predictive tracking control of nonholonomic systems with coupled input constraint and bounded disturbances. IEEE Trans Autom Control 63(2):608–615

    MathSciNet  MATH  Google Scholar 

  36. 36.

    Shojaei K (2015) Neural adaptive robust output feedback control of wheeled mobile robots with saturating actuators. Int J Adapt Control Signal Process 29(7):855–876

    MathSciNet  MATH  Google Scholar 

  37. 37.

    Good MC, Sweet LM, Strobel KL (1985) Dynamic models for control system design of integrated robot and drive systems. J Dyn Syst Meas Control 107(1):53–59

    Google Scholar 

  38. 38.

    Park BS, Yoo SJ, Park JB, Choi YH (2011) Adaptive output-feedback control for trajectory tracking of electrically driven non-holonomic mobile robots. IET Control Theory Appl 5(6):830–838

    MathSciNet  Google Scholar 

  39. 39.

    Chang W, Tong S, Li Y (2017) Adaptive fuzzy backstepping output constraint control of flexible manipulator with actuator saturation. Neural Comput Appl 28(1):1165–1175

    Google Scholar 

  40. 40.

    Sirouspour MR, Salcudean SE (2001) Nonlinear control of hydraulic robots. IEEE Trans Robot Autom 17(2):173–182

    Google Scholar 

  41. 41.

    Liu T, Wang C, Hill DJ (2009) Learning from neural control of nonlinear systems in normal form. Syst Control Lett 58(9):633–638

    MathSciNet  MATH  Google Scholar 

Download references


The authors thank the associate editor and anonymous reviewers for their useful comments to improve the quality of the manuscript. This work is partially supported by the Guangdong Science and Technology Project under Grant Nos. 2015B010133002 and 2017B090910011.

Author information



Corresponding author

Correspondence to Yu Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wu, Y., Wang, Y. Asymptotic tracking control of uncertain nonholonomic wheeled mobile robot with actuator saturation and external disturbances. Neural Comput & Applic 32, 8735–8745 (2020).

Download citation


  • Asymptotic tracking
  • Adaptive neural controller
  • Nonholonomic wheeled mobile robot
  • Actuator saturation