Gain Design of Quasi-Continuous Exponential Stabilizing Controller for a Nonholonomic Mobile Robot

Open access

Abstract

The control of nonholonomic canonical form using an invariant manifold is investigated to apply to a mobile robot steered by two independent driving wheels. A quasi-continuous exponential stabilizing controller is designed by using another input pattern. Additionally, the control gain designing method is proposed for this controller. Modified error system of nonholonomic double integrator model is used as nonholonomic canonical form. Generally, the gain cannot be calculated due to the non-linear transform of system. Owing to complicated relation of several parameters, the controller behavior is inconstant by gain pattern. We propose a method of designing gain which uses desired settling time. An approximate equation to obtain designed gains is derived based on the evaluation function. The design method to determine gains of the assumed actual system is simulated. The effectiveness of the proposed method is confirmed by these simulations.

References

  • [1] T.-C. Lee, Exponential stabilization for nonlinear systems with applications to nonholonomic systems, Automatica, vol. 39, no. 6, pp. 1045-1051, 2003.

  • [2] A. Bloch, S. Drakunov, Stabilization and tracking in the nonholonomic integrator via sliding modes, Systems and Control Letters, vol. 29, no. 2, pp. 91-99, 1996.

  • [3] G. Escobar, M. Reyhanglu, Regulation and tracking of the nonholonomic double integrator: A fieldoriented control approach, Automatica, vol. 34, no. 1, pp. 125-131, 1998.

  • [4] R. W. Brockett, Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, pp. 181-191, 1983.

  • [5] J. Luo, P. Tsiotras, Control design for chained-form systems with bounded inputs, System and Control Letters, vol. 39, no. 2, pp. 123-131, 2000.

  • [6] Z. Sun, S.S. Ge, W. Huo, T.H. Lee, Stabilization of nonholonomic chained systems via nonregular feedback linearization, System and Control Letters, vol. 44, no. 4, pp. 279-289, 2001.

  • [7] N. Marchand, M. Alamir, Discontinuous exponential stabilization of chained form systems, Automatica, vol. 39, no. 2, pp. 343-348, 2003.

  • [8] K. Cao, Global -exponential tracking control of nonholonomic systems in chained-form by output feedback, Acta Automatica Sinica, vol. 35, no. 5, pp. 568-576, 2009.

  • [9] O. J. Sordalen, O. Egeland, Exponential stabilization of nonholonomic chained systems, IEEE Trans. on Automatica Control, vol. 40, no. 1, pp. 35-49, 1995.

  • [10] A. Astolfi, Discontinuous control of nonholonomic systems, Systems and Control Letters, vol. 27, no. 1, pp. 37-45, 1996.

  • [11] A. Astolfi, Discontinuous control of the brockett integrator, Proc. of the 36th IEEE Conference on Decision and Control, vol. 5, pp. 4334-4339, 1997.

  • [12] J. P. Hespanha, A. S. Morse, Stabilization of nonholonomic integrators via logic-based switching, Automatica, vol. 35, no. 3, pp. 385-393, 1999.

  • [13] R. N. Banavar, Switched control strategies for underactuated Systems, Manuscripts of Invited talk, ACODS07, 2007.

  • [14] H. Khennouf and C. Canudas de Wit, On the construction of stabilizing discontinuous controllers for nonholonomic systems, Proc. of IFAC Nonlinear Control Systems Design, pp. 747-752, 1995.

  • [15] H. Khennouf, C. Canudas de Wit, Quasicontinuous exponential stabilizers for nonholonomic systems, Proc. of IFAC 13th TriennialWorld Congress, pp. 49-54, 1996.

  • [16] S. Nonaka, T. Tsujimura and K. Izumi: Modified error system of nonholonomic double integrator model using invariant manifold control, Proceedings of SICE Annual Conference 2014, pp. 42-47, 2014.

Journal of Artificial Intelligence and Soft Computing Research

The Journal of Polish Neural Network Society, the University of Social Sciences in Lodz & Czestochowa University of Technology

Journal Information

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 17 17 13
PDF Downloads 3 3 1