An Adaptive Backstepping Trajectory Tracking Control of a Tractor Trailer Wheeled Mobile Robot

  • Nguyen Thanh Binh
  • Nguyen Anh Tung
  • Dao Phuong NamEmail author
  • Nguyen Hong Quang
Regular Papers Robot and Applications


The considered Tractor Trailer Wheeled Mobile Robot (TTWMR) is type of Mobile Robot including a master robot – Tractor and slave robots – Trailers which moves along Tractor to track a given desired trajectory. The main difficulties of the stabilization and the tracking control of TTWMR are due to nonlinear and underactuated systems subjected to nonholonomic constraints. In order to overcome these problems, firstly, we develop the model of TTWMR and transform the tracking error model to the triangular form to propose a control law and an adaptive law. Secondly, the varying time state feedback controllers are designed to generate actuator torques by using Backstepping technique and Lyapunov direct’s method, in that these are able to guarantee the stability of the whole system including kinematics and dynamics. In addition, the Babarlat’s lemma is used to prove that the proposed tracking errors converge to the origin and the proposed adaptive law is carried on to tackle unknown parameter problem. The simulations are implemented to demonstrate the effective performances of the proposed adaptive law and the proposed control law.


Adaptive control backstepping design tracking control tractor trailer wheeled mobile robot 


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  1. [1]
    K. D. Do, Z. P. Jiang, and J. Pan, “Simultaneous tracking and stabilization of mobile robots: an adaptive approach,” IEEE Trans. on Automatic Control, vol. 49, no. 7, pp. 1147–1152, 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    T. Fukao, H. Nakagawa, and N. Adachi, “Adaptive tracking control of a nonholonomic mobile robot,” IEEE Trans. on Robotics and Automation, vol. 16, no. 5, pp. 609–615, 2000.CrossRefGoogle Scholar
  3. [3]
    S. S. Ge, Z. Wang, and T. H. Lee, “Adaptive stabilization of uncertain nonholonomic systems by state and output feedback,” Automatica, vol. 39, no. 8, pp. 1451–1460, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Huang, C. Wen, W. Wang, and Z. P. Jiang, “Adaptive output feedback tracking control of a nonholonomic mobile robot,” Automatica, vol. 50, no. 3, pp. 821–831, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    R. M. Murray and S. S. Sastry, “Nonholonomic motion planning: steering using sinusoids,” IEEE Trans. on Automatic Control, vol. 39, no. 5, pp. 700–716, 1993.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Z. P. Jiang and H. Nijmeijer, “A recursive technique for tracking control of nonholonomic systems in chained form,” IEEE Trans. on Automatic Control, vol. 44, no. 2, pp. 265–279, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    A. K. Khalaji and S. A. A. Moosavian, “Robust adaptive controller for a tractor–trailer mobile robot,” IEEE/ASME Trans. on Mechatronics, vol. 19, no. 3, pp. 943–953, 2013.CrossRefGoogle Scholar
  8. [8]
    E. Kayacan and E. Kayacan, “Robust tube–based decentralized nonlinear model predictive control of an autonomous tractor–trailer system,” IEEE/ASME Trans. on Mechatronics, vol. 20, no. 1, pp. 447–456, 2014.CrossRefGoogle Scholar
  9. [9]
    E. Kayacan, E. Kayacan, H. Ramon, and W. Saeys, “Learning in centralized nonlinear model predictive control: application to an autonomous tractor–trailer system,” IEEE Trans. on Control Systems Technology, vol. 23, no. 1, pp. 197–205, 2014.CrossRefGoogle Scholar
  10. [10]
    R. Fierro and F. L. Lewis, “Control of a nonholonomic mobile robot: backstepping kinematics into dynamics,” Proc. of the 34th IEEE Conference on Decision and Control, pp. 3805–3810, 1995.Google Scholar
  11. [11]
    W. He, Y. Dong, and C. Sun, “Adaptive neural impedance control of a robotic manipulator with input saturation,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 46, no. 3, pp. 334–344, 2016.CrossRefGoogle Scholar
  12. [12]
    W. He, Y. Chen, and Z. Yin, “Adaptive neural network control of an uncertain robot with full–state constraints,” IEEE Trans. on Cybernetics, vol. 46, no. 3, pp. 620–629, 2016.CrossRefGoogle Scholar
  13. [13]
    W. He and Y. Dong, “Adaptive fuzzy neural network control for a constrained robot using impedance learning,” IEEE Trans. on Neural Networks and Learning Systems, vol. 29, no. 4, pp. 1174–1186, 2018.CrossRefGoogle Scholar
  14. [14]
    W. He, Z. Yan, C. Sun, and Y. Chen, “Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer,” IEEE Trans. on Cybernetics, vol. 47, no. 10, pp. 3542–3465, 2017.Google Scholar
  15. [15]
    D.–P. Li, Y.–J. Liu, S. Tong, C. L. P. Chen, and D.–J. Li, “Neural networks–based adaptive control for nonlinear state constrained systems with input delay,” IEEE Trans. on Cybernetics, to be published. DOI: 10.1109/TCYB.2018.2799683Google Scholar
  16. [16]
    Y. J. Liu and S. Tong, “Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems,” Automatica, vol. 76, pp. 143–152, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Y. J. Liu, S. Lu, S. Tong, X. Chen, C. L. P. Chen, and D. J. Li, “Adaptive control–based Barrier Lyapunov Functions for a class of stochastic nonlinear systems with full state constraints,” Automatica, vol. 87, pp. 83–93, 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Y. J. Liu, M. Gong, S. Tong, C. L. P. Chen, and D. J. Li, “Adaptive fuzzy output feedback control for a class of nonlinear systems with full state constraints,” IEEE Trans. on Fuzzy Systems, vol. 26, no. 5, pp. 2607–2617, 2018.CrossRefGoogle Scholar
  19. [19]
    M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.zbMATHGoogle Scholar
  20. [20]
    H. K. Khalil, Nonlinear Systems, 3rd ed., Prentice–Hall, NJ, 2002.zbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Nguyen Thanh Binh
    • 1
  • Nguyen Anh Tung
    • 2
  • Dao Phuong Nam
    • 2
    Email author
  • Nguyen Hong Quang
    • 3
  1. 1.School of Electrical EngineeringUniversity of UlsanUlsanKorea
  2. 2.Department of Automatic ControlHanoi University of Science and TechnologyHanoiVietnam
  3. 3.Departement of AutomationThai Nguyen University of TechnologyThaiVietnam

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