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Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation

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  • Control Theory
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Abstract

In this paper, the robust stabilization problem is addressed for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation. Firstly, a continuous, time varying, saturated controller is presented for the kinematic system of the robots. Secondly, for the dynamic feedback system, a special derivable, saturated kinematic controller with slope restrictions is selected as a virtual control law that can be tracked by the real generalized velocity in a finite time, furthermore, the dynamic input signals are continuous and saturated at any time. The systematic strategy combines the theory of finite-time stability with the virtual-controller-tracked method. Finally, the simulation results show the effectiveness of the proposed controller design approach.

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References

  1. R. W. Brockett, “Asymptotic stability and feedback stabilization,” in: R. W. Brockett, R. S. Millman, and H. J. Sussmann (Eds.), Differential Geometric Control Theory, Birkhauser, Boston, pp. 181–208, 1983.

    Google Scholar 

  2. R. M. Murray and S. S. Sastry, “Nonholonomic motion planning: Steering using sinusoids,” IEEE Trans. Automat. Control., vol. 38, no. 5, pp. 700–716, May 1993.

    Article  MATH  MathSciNet  Google Scholar 

  3. Y. P. Tian and S. Li, “Exponential stabilization of nonholonomic dynamic systems by smooth timevarying control,” Automatica, vol. 38, no. 7, pp. 1139–1146, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Teel, R. Murry, and G. Walsh, “Nonholonomic control systems: from steering to stabilization with sinusoids,” Proc. of IEEE Conf. Decision Control, pp. 1603–1609, 1992.

    Google Scholar 

  5. A. Astolfi, “Discontinuous control of nonholonomic systems,” Syst. Control Lett., vol. 27, no. 1, pp. 37–45, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. M. Bloch and S. Drakunov, “Stabilization of a nonholonomic systems via sliding modes,” Proc. of IEEE Conf. Decision Control, pp. 2961–2963, 1995.

    Google Scholar 

  7. C. Canudas de Wit and O. J. SZrdalen, “Exponential stabilization of mobile robots with nonholonomic constraints,” IEEE Trans. Automat. Control, vol. 37, no. 11, pp. 1791–1797, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  8. O. J. Sordalen and O. Egeland, “Exponential stabilization of nonholonomic chained systems,” IEEE Trans. Automat. Control, vol. 40, no. 1, pp. 35–49, 1995.

    Article  MathSciNet  Google Scholar 

  9. C. L. Wang, “Semiglobal practical stabilization of nonholonomic wheeled mobile robots with saturated inputs,” Automatica, vol. 44, no. 3, pp. 816–822, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  10. Z. P. Jiang, E. Lefeber, and H. Nijmeijer, “Saturated stabilization and tracking of a nonholonomic mobile robot,” Syst. Control Lett., vol. 42, no. 5, pp. 327–332, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Luo and P. Tsiotras, “Control design of chained form systems with bounded inputs,” Syst. Control Lett., vol. 39, no. 2, pp. 123–131, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  12. H. L. Yuan and Z. H. Qu, “Saturated control of chained nonholonomic systems,” European Journal of Control, vol. 17, no. 2, pp. 172–179, 2011.

    Article  MATH  MathSciNet  Google Scholar 

  13. H. Chen, M. M. Ma, H. Wang, Z. Y. Liu, and Z. X. Cai, “Moving horizon ℋ∞ tracking control of wheeled mobile robots with actuator saturation,” IEEE Trans. Control Syst. Technol., vol. 17, no. 2, pp. 449–457, 2009.

    Article  Google Scholar 

  14. B. S. Park, J. B. Park, and Y. H. Choi, “Adaptive formation control of electrically driven nonholonomic mobile robots with limited information,” IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 41, no. 4, pp. 1061–1075, 2011.

    Article  MathSciNet  Google Scholar 

  15. P. G. Park, D. Banjerdpongchai, and T. Kailath, “The asymptotic stability of nonlinear (Lur’e) systems with multiple slope restrictions,” IEEE Trans. Automat. Control., vol. 43, no. 7, pp. 979–982, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  16. D. H. Nguyen and D. Banjerdpongchai, “A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties,” Automatica, vol. 47, no. 9, pp. 2039–2043, 2011.

    Article  MATH  MathSciNet  Google Scholar 

  17. I. Kolmanovsky and N. H. McClamvoch, “Developments in nonholonomic control problems,” IEEE Contr. Syst. Mag., vol. 15, no. 6, pp. 20–36, 1995.

    Article  Google Scholar 

  18. C. Canudas de Wit, B. Siciliano, and G. Bastin (Eds.), Theory of Robot Control, Springer, London, 1996.

    MATH  Google Scholar 

  19. Z. P. Jiang, “Robust exponential regulation of nonholonomic systems with uncertainties,” Automatica, vol. 36, no. 2, pp. 189–209, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  20. J. P. Hespanha, D. Liberzon, and A. S. Morse, “Logic-based switching control of a nonholonomic system with parametric modeling uncertainty,” Syst. Control Lett., vol. 38, no. 3, pp. 167–177, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  21. Y. Hong, J. Wang, and Z. Xi, “Stabilization of uncertain chained form systems within finite settling time,” IEEE Trans. Automat. Control., vol. 50, no. 9, pp. 1379–1384, September 2005.

    Article  MathSciNet  Google Scholar 

  22. Z. P. Jiang and H. Nijmeijer, “Tracking control of mobile robots: a case study in backstepping,” Automatica, vol. 33, no. 7, pp. 1393–1399, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  23. H. Chen, C. Wang, B. Zhang, and D, Zhang, “Saturated tracking control for nonholonomic mobile robots with dynamic feedback,” Trans. of the Institute of Measurement and Control, vol. 35, no. 2, pp. 105–116, 2013.

    Article  Google Scholar 

  24. Y. Hong, Z. P. Jiang, and G. Feng, “Finite-time input-to-state stability and applications to finite-time control design,” SIAM J. Control and Optimization, vol. 48, no. 7, pp. 4395–4418, 2010.

    Article  MATH  MathSciNet  Google Scholar 

  25. G. Hardy, J. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge, 1952.

    MATH  Google Scholar 

  26. J.-B. Pomet, “Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift,” Syst. Control Lett., vol. 18, no. 2, pp. 147–158, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  27. R. T. M’Closkey and R. M. Murray, “Exponential stabilization of driftless nonlinear control systems using homogeneous feedback,” IEEE Trans. Automat. Control., vol. 42, no. 5, pp. 614–628, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  28. J. Berg, P. Abbeel, and K. Goliberg, “LQG-MP: optimized path planning for robots with motion uncertainty and imperfect state information,” The International Journal of Robotics Research, vol. 30, no. 7, pp. 895–913, 2011.

    Article  Google Scholar 

  29. E. Todorov and W. Li, “A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic system,” Proc. of American Control Conference, pp. 300–306, 2005.

    Google Scholar 

  30. M. F. Silva, J. A. T. Machado, and A. M. Lopes, “Fractional order control of a hexapod robot,” Nonlinear Dynamics, vol. 38, no. 1–4, pp. 417–433, 2004.

    Article  MATH  Google Scholar 

  31. M. R. Soltanpour and M. H. Khooban, “A particle swarm optimization approach for fuzzy sliding mode control for tracking the robot manipulator,” Nonlinear Dynamics, vol. 74, no. 1–2, pp. 467–478, 2013.

    Article  MATH  MathSciNet  Google Scholar 

  32. B. L. Ma and S. K. Tso, “Robust discontinuous exponential regulation of dynamic nonholonomic wheeled mobile robots with parameter uncertainties,” International Journal of Robust and Nonlinear Control, vol. 18, no. 9, pp. 960–974, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  33. M. Y. Ou, S. H. Li, and C. L. Wang, “Finite-time tracking control for multiple nonholonomic mobile robots based on visual servoing,” International Journal of Control, vol. 86, no. 12, pp. 2175–2188, 2013.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematics and Physics Department, Hohai University, Changzhou Campus, 213022, Nanjing, P. R. China

    Hua Chen

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  1. Hua Chen
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Correspondence to Hua Chen.

Additional information

Recommended by Associate Editor Wonjong Kim under the direction of Editor Zengqi Sun.

This work was supported by the Natural Science Foundation of China (61304004), the China Postdoctoral Science Foundation funded project (2013M531263), and the Jiangsu Planned Projects for Postdoctoral Research Funds (1302140C).

Hua Chen received his B.S. degree from the Department of Mathematics at Yangzhou University, China, an M.S. degree from the Department of Management Sciences and Engineering at Nanjing University, China, and a Ph.D. degree from the Department of Control Science and Engineering at University of Shanghai for Science and Technology, China, in 2001, 2009, and 2012, respectively. His main research interests include saturated control for nonlinear systems, motion control of nonholonomic mobile robots, analysis and control of fractional-order systems.

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Chen, H. Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation. Int. J. Control Autom. Syst. 12, 1216–1224 (2014). https://doi.org/10.1007/s12555-013-0492-z

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  • DOI: https://doi.org/10.1007/s12555-013-0492-z

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