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Robust simultaneous tracking and stabilization of wheeled mobile robots not satisfying nonholonomic constraint

  • Zhu Xiao-cai  (祝晓才)Email author
  • Dong Guo-hua  (董国华)
  • Cai Zi-xing  (蔡自兴)
  • Hu De-wen  (胡德文)
Article

Abstract

A robust unified controller was proposed for wheeled mobile robots that do not satisfy the ideal rolling without slipping constraint. Practical trajectory tracking and posture stabilization were achieved in a unified framework. The design procedure was based on the transverse function method and Lyapunov redesign technique. The Lie group was also introduced in the design. The left-invariance property of the nominal model was firstly explored with respect to the standard group operation of the Lie group SE(2). Then, a bounded transverse function was constructed, by which a corresponding smooth embedded submanifold was defined. With the aid of the group operation, a smooth control law was designed, which fulfills practical tracking/stabilization of the nominal system. An additional component was finally constructed to robustify the nominal control law with respect to the slipping disturbance by using the Lyapunov redesign technique. The design procedure can be easily extended to the robot system suffered from general unknown but bounded disturbances. Simulations were provided to demonstrate the effectiveness of the robust unified controller.

Key words

wheeled mobile robot robust control Lie group transverse function Lyapunov redesign 

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References

  1. [1]
    BROCKETT R W. Asymptotic stability and feedback stabilization[C]// BROCKETT R W, MILLMAN R S, SUSSMANN H J. Differential Geometric Control Theory. Boston: Birkhauser, 1983: 181–191.Google Scholar
  2. [2]
    KOLMANOVSKY I, MCCLAMROCH N H. Developments in nonholonomic control systems[J]. IEEE Control System Mag, 1995, 15(6): 20–36.CrossRefGoogle Scholar
  3. [3]
    LUCA A D, ORIOLO G, VENDITTELLI M. Control of wheeled mobile robots: An experimental overview[C]// NICOSIA S, SICILIANO B, BICCHI A, et al. RAMSETE—Articulated and Mobile Robotics for Services and Technologies. Berlin: Springer, 2001: 181–226.Google Scholar
  4. [4]
    ORIOLO G, LUCA A D, VENDITTELLI M. WMR control via dynamic feedback linearization: Design, implementation and experimental validation[J]. IEEE Transactions on Control Systems Technology, 2002, 10(6): 835–852.CrossRefGoogle Scholar
  5. [5]
    LEE T C, SONG K T, LEE C H, et al. Tracking control of unicycle-modeled mobile robots using a saturation feedback controller[J]. IEEE Transactions on Control Systems Technology, 2001, 9(2): 305–318.CrossRefGoogle Scholar
  6. [6]
    DO K D, JIANG Z P, PAN J. A global output-feedback controller for simultaneous tracking and stabilization of unicycle-type mobile robots[J]. IEEE Trans on Robotics and Automation, 2004, 20(3): 589–594.CrossRefGoogle Scholar
  7. [7]
    de CANUDAS WIT C, KHENNOUF H. Quasi-continuous stabilizing controllers for nonholonomic systems: Design and robustness considerations[C]// Proc 3rd Euro Contr Conf Rome, Italy: IEEE Press, 1995: 2630–2635.Google Scholar
  8. [8]
    D’ANDREA-NOVEL B, CAMPION G, BASTIN G. Control of wheeled mobile robots not satisfying ideal velocity constraints: A singular perturbation approach[J]. International Journal of Robust and Nonlinear Control, 1995, 5(2): 243–267.MathSciNetCrossRefGoogle Scholar
  9. [9]
    LEROQUAIS W, D’ANDREA-NOVEL B. Modeling and control of wheeled mobile robots not satisfying ideal velocity constraints: the unicycle case[C]// Proc 35th Conf Decision Control. Kobe, Japan: IEEE Press, 1996: 1437–1442.Google Scholar
  10. [10]
    MOTTE I, CAMPION G. A slow manifold approach for the control of mobile robots not satisfying the kinematic constraints[J]. IEEE Transactions on Robotics and Automation, 2000, 16(6): 875–880.CrossRefGoogle Scholar
  11. [11]
    DIXON W, DAWSON D, ZHANG F, et al. Global exponential tracking control of mobile robot system via a PE condition[J]. IEEE Trans Syst Man Cybern B, 2000, 30(1): 129–142.CrossRefGoogle Scholar
  12. [12]
    DIXON W E, DOWSON D M, ZERGEROGLU E, et al. Robust tracking and regulation control for mobile robots[J]. International Journal of Robust and Nonlinear Control, 2000, 10(2): 199–216.MathSciNetCrossRefGoogle Scholar
  13. [13]
    DIXON W E, de QUEIRROZ M S, DOWSON D M, et al. Adaptive tracking and regulation of a wheeled mobile robot with controller/update law modularity[J]. IEEE Transactions on Control Systems Technology, 2004, 12(1): 138–147.CrossRefGoogle Scholar
  14. [14]
    MORIN P, SAMSON C. Practical stabilization of a class of nonlinear systems: Application to chain systems and mobile robots[C]// Proc 39th IEEE Conf Decision Contr. Sydney, Australia: IEEE Press, 2000: 2989–2994.Google Scholar
  15. [15]
    MORIN P, POMET J B, SAMSON C. Design of homogeneous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of Lie brackets in closed loop[J]. SIAM Journal on Control and Optimization, 2000, 38(1): 22–49.MathSciNetCrossRefGoogle Scholar
  16. [16]
    MORIN P, SAMSON C. Practical stabilization of driftless systems on Lie groups: The transverse function approach[J]. IEEE Transactions on Automatic Control, 2003, 48(9): 1496–1508.MathSciNetCrossRefGoogle Scholar
  17. [17]
    MORIN P, SAMSON C. A characterization of the Lie algebra rank condition by transverse periodic functions[J]. SIAM Journal on Control and Optimization, 2002, 40(4): 1227–1249.MathSciNetCrossRefGoogle Scholar
  18. [18]
    MORIN P, SAMSON C. Practical and asymptotic stabilization of chained systems by the transverse function control approach[J]. SIAM Journal on Control and Optimization, 2004, 43(1): 32–57.MathSciNetCrossRefGoogle Scholar
  19. [19]
    KHALIL H K. Nonlinear Systems[M]. 2nd ed. Upper Saddle River: Prentice-Hall, 1996.Google Scholar
  20. [20]
    ISIDORI A. Nonlinear Control Systems[M]. 3rd ed. Berlin: Springer-Verlag, 1995.CrossRefGoogle Scholar
  21. [21]
    LIZARRAGA D A. Obstructions to the existence of universal stabilizers for smooth control systems[J]. Mathematics of Control, Signals, and Systems, 2003, 16: 255–277.MathSciNetCrossRefGoogle Scholar
  22. [22]
    ZHENG Da-zhong. Linear System Theory[M]. 2nd ed. Beijing: Tsinghua University Press, 2002. (in Chinese)Google Scholar
  23. [23]
    SPIVAK M. A Comprehensive Introduction to Differential Geometry[M]. 2nd ed. vol. I. Houston: Perish Inc, 1979.zbMATHGoogle Scholar

Copyright information

© Central South University Press, Sole distributor outside Mainland China: Springer 2007

Authors and Affiliations

  • Zhu Xiao-cai  (祝晓才)
    • 1
    Email author
  • Dong Guo-hua  (董国华)
    • 1
  • Cai Zi-xing  (蔡自兴)
    • 2
  • Hu De-wen  (胡德文)
    • 1
  1. 1.College of Mechatronic Engineering and AutomationNational University of Defense TechnologyChangshaChina
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaChina

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