HIGHER ORDER SLIDING MODE STABILIZATION OF A CAR-LIKE MOBILE ROBOT

F. Hamerlain, K. Achour, T. Floquet, W. Perruquetti

Abstract

This paper deals with the robust stabilization of a car-like mobile robot given in a perturbed chained form. A higher order sliding mode control strategy is developed. This control strategy switches between two different sliding mode controls: a second order one (super-twisting algorithm) and a new third order sliding mode control that performs a finite time stabilization. The proposed third sliding mode controller is based on geometric homogeneity property with a discontinuous term. Simulation results show the control performance.

References

  1. Astolfi A. (1996). Discontinuous control of nonholonomic systems, Systems & Control Letters Vol. 27, pp. 37- 45.
  2. Barbot J.-P., Djemai M., Floquet T. and Perruquetti W. (2003). Stabilization of a unicycle-type mobile robot using higher order sliding mode control. In Proc. of the 41st IEEE Conference on Decision and Control.
  3. Bhat, S. and Bernstein, D. (2005). Geometric Homogeneity with applications to finite time stability. Mathematics of Control, Signals and Systems, Vol. 17, pp. 101-127.
  4. Brockett, R. (1983). Asymptotic stability and feedback stabilization. In Differential geometric control theory, pp. 181-191, Birkhauser.
  5. Djemai M. and Barbot J.-P. (2002). Smooth manifolds and high order sliding mode control. In Proc. of the 41st IEEE Conference on Decision and Control.
  6. Edwards C. and Spurgeon S. (1998). Sliding mode control: theory and applications. Taylor and Francis Eds.
  7. Emel'yanov S.V., Korovin S.V., and Levantovsky L.V. (1993). Higher order sliding modes in control systems. Differential Equations, Vol. 29, pp. 1627-1647.
  8. Floquet T., Barbot J.-P. and Perruquetti W. (2000). Onechained form and sliding mode stabilization for a nonholonomic perturbed system. American Control Conference, Chicago, USA.
  9. Floquet T., Barbot J.-P. and Perruquetti W. (2003). Higher order sliding mode stabilization for a class of non holonomic perturbed system. Automatica, Vol. 39, pp. 1077-1083.
  10. Fliess M., Levine J., Martin P. and Rouchon P. (1995). Flatness and defect of non-linear systems: Introductory theory and examples. International Journal on Control, Vol.61, pp. 1327-1361.
  11. Fridman L. and Levant A. (2002). Higher order sliding modes. In Sliding Mode Control in Engineering, W. Perruquetti and J. P. Barbot (Eds), Marcel Dekker, pp. 53-101.
  12. Huo W. and Ge S. (2001). Exponential stabilization of nonhononomic systems: an ENI approach. International Journal of Control, Vol. 74, 1492-1500.
  13. Jiang, Z. and Nijmeijer, H. (1999). A recursive technique for tracking control of nonholonomic systems in chained form. IEEE Tansactions on Automatic Control, Vol. 44, pp. 265-279.
  14. Laghrouche S., Smaoui M. and Plestan F. (2004). Thirdorder sliding mode controller for electropneumatic actuators. In Proc. of the 43rd IEEE Conference on Decision and Control.
  15. Levant, A. (2001). Universal SISO sliding-mode controllers with finite-time convergence. IEEE Transactions on Automatic Control, Vol. 46, pp. 1447-1451.
  16. Levant, A. (2003). Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control, Vol. 76, pp. 924-941.
  17. Murray R. and Sastry S. (1993). Nonholonomic motion planning :steering using sinusoids. IEEE. Tansactions On Automatic Control, Vol. 38, pp. 77-716.
  18. Murray R., Li Z. and Sastry S. (1994). A Mathematical Introduction to Robotic Manipulation. CRC Press, Inc., Florida, USA.
  19. Perruquetti W. and Barbot J.-P. (Editors) (2002), Sliding Mode Control in Engineering, Marcel Dekker.
  20. Samson C. (1995). Control of chained systems. Application to path following and time-varying point stabilization of mobile robots. IEEE Tansactions on Automatic Control, Vol. 40, pp. 64-77.
Download


Paper Citation


in Harvard Style

Hamerlain F., Achour K., Floquet T. and Perruquetti W. (2007). HIGHER ORDER SLIDING MODE STABILIZATION OF A CAR-LIKE MOBILE ROBOT . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO, ISBN 978-972-8865-83-2, pages 195-200. DOI: 10.5220/0001639901950200


in Bibtex Style

@conference{icinco07,
author={F. Hamerlain and K. Achour and T. Floquet and W. Perruquetti},
title={HIGHER ORDER SLIDING MODE STABILIZATION OF A CAR-LIKE MOBILE ROBOT},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,},
year={2007},
pages={195-200},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001639901950200},
isbn={978-972-8865-83-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,
TI - HIGHER ORDER SLIDING MODE STABILIZATION OF A CAR-LIKE MOBILE ROBOT
SN - 978-972-8865-83-2
AU - Hamerlain F.
AU - Achour K.
AU - Floquet T.
AU - Perruquetti W.
PY - 2007
SP - 195
EP - 200
DO - 10.5220/0001639901950200