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Journal of Systems Science and Complexity

, Volume 32, Issue 5, pp 1393–1403 | Cite as

Adaptive Tracking Control for Mobile Manipulators with Stochastic Disturbances

  • Wei SunEmail author
  • Jianwei XiaEmail author
  • Yuqiang WuEmail author
Article
  • 62 Downloads

Abstract

This paper investigates adaptive tracking control for mobile manipulators with stochastic disturbances and parametric uncertainties. Based on an appropriate reduced dynamic model and an adaptive law, a controller, which is provided by incorporating stochastic control theory with related adaptive technique, overcomes the problem of over-parametrization. It is shown that the designed state-feedback controllers can guarantee that the mean square of the tracking errors can be made arbitrarily small by choosing suitable design parameters. Simulation studies on the control of 2-DOF mobile manipulator shows the effectiveness of the proposed scheme.

Keywords

Holonomic and noholonomic constraints mobile manipulators stochastic disturbances tracking control 

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References

  1. [1]
    Zhang W H and Chen B S, H-Representation and applications to generalized lyapunov equations and linear stochastic systems, IEEE Trans. Automatic Control, 2012, 57(12): 3009–3002.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Zhao X Y and Deng F Q, Moment stability of nonlinear stochastic systems with time-delays based on H-Representation technique, IEEE Trans. Automatic Control, 2013, 59(3): 814–819.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Gao F Z and Wu Y Q, Global finite-time stabilisation for a class of stochastic high-order timevarying nonlinear systems, International Journal of Control, 2016, 89(12): 2453–2465.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Xie X J and Liu L, A homogeneous domination approach to state feedback of stochastic highorder nonlinear systems with time-varying delay, IEEE Trans. Automatic Control, 2013, 58(2): 494–499.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Tong S C, Li Y, Li Y M, et al., Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems, IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics, 2011, 41(6): 1693–1704.CrossRefGoogle Scholar
  6. [6]
    Lzaro C and Ortega J P, Stochastic Hamiltonian dynamical systems, Reports on Mathematical Physics, 2008, 61(1): 65–122.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Wu Z J, Cui M Y, and Shi P, Backstepping control in vector form for stochastic Hamiltonian systems, SIAM Journal on Control and Optimization, 2012, 50(2): 925–942.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Cui M Y, Wu Z J, Xie X J, et al., Modeling and adaptive tracking for a class of stochastic Lagrangian control systems, Automatica, 2013, 49(3): 770–779.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Liu Z G and Wu Y Q, Modelling and adaptive tracking control for flexible joint robots with random noises, International Journal of Control, 2014, 87(12): 2499–2510.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Li Z J, Yang C G, and Su C Y, Adaptive fuzzy-based motion generation and control of mobile under-actuatedmanipulators, Engineering Applications of Artificial Intelligence, 2014, 30: 86–95.CrossRefGoogle Scholar
  11. [11]
    Xiao L and Zhang Y N, A new performance index for the repetitive motion of mobile manipulators, IEEE Trans. Cybernetics, 2014, 44(2): 280–292.CrossRefGoogle Scholar
  12. [12]
    Zhai D H and Xia Y Q, Adaptive fuzzy control of multilateral asymmetric teleoperation for coordinated multiple mobile manipulators, IEEE Trans. Fuzzy Systems, 2016, 24(1): 57–70.CrossRefGoogle Scholar
  13. [13]
    Pham C V and Wang Y N, Robust adaptive trajectory tracking sliding mode control based on neural networks for cleaning and detecting robot manipulators, Journal of Intelligent Robotic Systems, 2015, 79(1): 101–114.CrossRefGoogle Scholar
  14. [14]
    Li Z J, Ge S S, Adams M, et al., Robust adaptive control of uncertain force/motion constrained nonholonomic mobile manipulators, Automatica, 2008, 44(3): 776–784.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Sun W and Wu Y Q, Adaptive motion/force tracking control for a class of mobile manipulators, Asian Journal of Control, 2014, 17(6): 2409–2416.MathSciNetCrossRefGoogle Scholar
  16. [16]
    Tan J D, Xi N, and Wang Y C, Integrated task planning and control for mobile manipulators, The International Journal of Robotics Research, 2003, 22(5): 337–354.CrossRefGoogle Scholar
  17. [17]
    Tanner H G, Loizou S G, and Kyriakopoulos K J, Nonholonomic navigation and control of cooperating mobile manipulators, IEEE Trans. Robotics and Automation, 2003, 19(1): 53–64.CrossRefGoogle Scholar
  18. [18]
    Wu Y Q, Zhao Y, and Yu J B, Global asymptotic stability controller of uncertain nonholonomic systems, Journal of the Franklin Institute, 2013, 350(5): 1248–1263.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Sun N, Yang T, Chen H, et al., Adaptive anti-swing and positioning control for 4-DOF rotary cranes subject to uncertain/unknown parameters with hardware experiments, IEEE Trans. Systems, Man, and Cybernetics: Systems, in press, DOI: 10.1109/TSMC.2017.2765183.Google Scholar
  20. [20]
    Wu Y Q, Gao F Z, and Liu Z G, Finite-time state-feedback stabilization of non-holonomic systems with low-order non-linearities, IET Control Theory and Applications, 2015, 9(10): 1553–1560.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Sun N, Fang Y C, Chen H, et al., Nonlinear stabilizing control for ship-mounted cranes with ship roll and heave movements: Design, analysis, and experiments, IEEE Trans. Systems, Man, and Cybernetics: Systems, 2018, 48(10): 1781–1793.Google Scholar
  22. [22]
    Wu Y Q and Liu Z G, Output feedback stabilization for time-delay nonholonomic systems with polynomial conditions, ISA Transactions, 2015, 58: 1–10.CrossRefGoogle Scholar
  23. [23]
    Sun N, Wu Y M, Fang Y C, et al., Nonlinear antiswing control for crane systems with doublependulum swing effects and uncertain parameters: Design and experiments, IEEE Trans. Automation Science and Engineering, 2018, 15(3): 1413–1422.CrossRefGoogle Scholar
  24. [24]
    Liu S J, Zhang J F, and Jiang Z P, Decentralized adaptive output feedback stabilization for large-scale stochastic nonlinear systems, Automatica, 2007, 42(2): 238–251.MathSciNetCrossRefGoogle Scholar
  25. [25]
    Dong W J, On trajectory and force tracking control of constrained mobile manipulators with parameter uncertainty, Automatica, 2002, 38(9): 1475–1484.MathSciNetCrossRefGoogle Scholar
  26. [26]
    Mcclamroch N H and Wang D, Feedback stabilization and tracking of constrained robots, IEEE Trans. Automatic Control, 1988, 33(5): 419–426.MathSciNetCrossRefGoogle Scholar
  27. [27]
    SunWandWu Y Q, Modeling and finite-time tracking control for mobile manipulators with affine and holonomic constraints, Journal of Systems Science and Complexity, 2016, 29(3): 589–601.MathSciNetCrossRefGoogle Scholar
  28. [28]
    Khas’minskii R Z, Stochastic Stability of Differential Equations, Springer-Verlag, Berlin, Heidelberg, 2012.CrossRefGoogle Scholar

Copyright information

© The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.School of Mathematics ScienceLiaocheng UniversityLiaochengChina
  2. 2.Key laboratory of Measurement and Control of CSE, Ministry of Education, School of AutomationSoutheast UniversityNanjingChina
  3. 3.Institute of AutomationQufu Normal UniversityQufuChina

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