Backstepping Control of Nonholonomic Car-like Mobile Robot in Chained Form

  • Norsuryani Zainal Abidin
  • Nurul Ain Mohamed
  • Zainah Md. ZainEmail author
  • Maziyah Mat Noh
  • Norhafizah Md. Zain
  • Dwi Pebrianti
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 538)


This project is attempts to stabilize an underactuated system based on the backstepping approach. The discontinuous time-invariant state feedback controller is designed for exponential stabilization of underactuated nonholonomic systems in chained form. System dynamic of the car-like robot with nonholonomic constraints were employed. The validity of the proposed approaches is tested through simulation on a car-like vehicle using Matlab software.


Backstepping control Underactuated system Mobile robot 



The authors would like to thank for the support given to this research by Universiti Malaysia Pahang (UMP) under grant RDU170366.


  1. 1.
    Brockett, R.W.: Asymptotic stability and feedback stabilization. In: Brockett, R.W., Milman, R.S., Sussman, H.J. (eds.) Differential Geometric Control Theory, pp. 181–191. Birkhäuser Boston Inc, USA (1983)Google Scholar
  2. 2.
    Walsh, G., Tilbury, D., Sastry, S., Murray, R., Laumond, J.P.: Stabilization of trajectories for system with nonholonomic constraints. IEEE Trans. Autom. Control 39(1), 216–222 (1994)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Panimadai Ramaswamy, S.A., Balakrishnan, S.N.: Formation control of car-like mobile robots: a Lyapunov function based approach. In: 2008 American Control Conference (2008)Google Scholar
  4. 4.
    Klomanovsky, I., Mc-Clamroch, N.H.: Developments in nonholonomic control problem. IEEE Control Syst. Mag. 15(6), 20–36 (1995)CrossRefGoogle Scholar
  5. 5.
    Tayebi, A., Rachid A.: Discontinuous control design for stabilization of nonholonomic systems in chained form using backstepping approach. In 36th Proceeding of the IEEE CDC, pp. 3089–3090 (1997)Google Scholar
  6. 6.
    Tanner, H.G., Kyriakopoulos, K.: Discontinuous backstepping for stabilization of nonholonomic mobile robot. In: Proceedings of the IEEE ICRA, pp. 3948–3953 (2002)Google Scholar
  7. 7.
    Dierks, T., Jagannathan, S.: Control of nonholonomic mobile robot formations: backstepping kinematics into dynamics. Thesis Dissertation, UMR (2007)Google Scholar
  8. 8.
    Francisco, V., Francisco, R., Carlos, L., Juan, I.C.: Influence of the friction coefficient on the trajectory performance for a car-like robot. In: Mathematical Problems in Engineering, Article ID 4562647 (2017)Google Scholar
  9. 9.
    Mnif, F.: On the reduction and control for a class of nonholonomic underactuated systems. J. Electr. Eng. 54(1–2), 22–29 (2003)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Norsuryani Zainal Abidin
    • 1
  • Nurul Ain Mohamed
    • 1
  • Zainah Md. Zain
    • 1
    Email author
  • Maziyah Mat Noh
    • 1
  • Norhafizah Md. Zain
    • 2
  • Dwi Pebrianti
    • 1
  1. 1.Robotics and Unmanned Research Group (RUS), Instrument and Control Engineering (ICE) Cluster, Faculty of Electrical and Electronics EngineeringUniversiti Malaysia PahangPekanMalaysia
  2. 2.Faculty of Agro-Based IndustryUniversity of Malaysia KelantanJeliMalaysia

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