Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Steering Control for a Rigid Body with two Torque Actuators using Adaptive Back Stepping

Journal of Applied Nonlinear Dynamics 6(3) (2017) 369--377 | DOI:10.5890/JAND.2017.09.005

Abdul Baseer Satti

Griffith University, School of engineering, Australia

Download Full Text PDF



This paper presents a simple steering control algorithm for a rigid body model, which is a famous example of non-holonomic control systems with drift. The controllability Lie Algebra of a rigid body model contains Lie brackets of depth two. We propose a back-stepping-based adaptive controller design under the strict-feedback form. We analyze two cases for continuous steering. In the first case, the parameters of the model are assumed to be known while in the second case these are estimated by considering them unknown. This approach does not necessitate the conversion of the system model into a “chained form”, and thus does not rely on any special transformation techniques. The practical effectiveness of the controller is illustrated by numerical simulations and graceful stabilization.


  1. [1]  Brockett, R.W. (1983), Asymptotic stability and feedback stabilization, Differential Geometric Control Theory (Birkhauser, Boston, USA) (Brockett, R.W , Millman, R.S, and Sussman, S.J, eds.), 181-191.
  2. [2]  Kolmanovsky, I. and McClamroch, N.H, (1995), Developments in nonholonomic control problems, IEEE Control Systems Magazine, 15, 20-36.
  3. [3]  Pomet, J.B. (1992), Explicit design of time-varying control laws for a class of controllable systems without drift, Systems & Control Letters, 18, 147-158.
  4. [4]  Samson, C. (1995), Control of Chained Systems: Application to path following and time-varying pointstabilization of mobile robots, IEEE Trans. on Automatic Control, 40(1), 64-77.
  5. [5]  Astolfi, A. (1998), Discontinuous control of the Brockett integrator, European Journal of Control, 4(1), 49-63.
  6. [6]  Lucibello, P. and Oriolo, G. (2001), Robust stabilization via iterative state steering with application to chained form systems, Automatica, 37(1), 71-79.
  7. [7]  Branicky, M.S (1998), Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control, 43(4), 475-482.
  8. [8]  Fang, F. andWei, L. (2011), Backstepping based nonlinear adaptive control for coal-fired utility boiler-turbine units, Appl. Energy, 88(3), 814-824.
  9. [9]  Sun, L.Y., Tong, S.C., and Liu, Y. (2011), Adaptive backstepping sliding mode H∞ control of static var compensator, IEEE Trans. Control Syst. Technol., 19(5), 1178-1185.
  10. [10]  Zhou, J. and Wen, C. (2008), Adaptive Backstepping Control of Uncertain Systems, Nonsmooth Nonlinearities, Interactions or Time-Variations. New York, USA: Springer-verlag.
  11. [11]  Rehman, F. (2005), Discontinuous Steering Control for Nonholonomic Systems with drift, Nonlinear Analysis, An International Multidisciplinary Journal, 63(3), November 2005.