Dynamics and Control

, Volume 4, Issue 1, pp 59–71 | Cite as

Global stability of trajectory tracking of robot underPD control

  • Zhihua Qu


It is shown for the first time that, even if there exist nonlinear unknown dynamics, aPD feedback control without higher-order nonlinear compensation can guarantee global stability for the trajectory following problem of a robot manipulator. ThePD control under investigation is a position and velocity feedback control with a time-varying gain, and does not contain any higher-order nonlinearity. The proposed control is in general continuous and does not require any knowledge of robotic systems except size bounding function on nonlinear dynamics. Asymptotic stability of velocity tracking error and arbitrarily small position tracking error are guaranteed. Another novel and interesting result shown in this paper is that a measure on protection against saturation of actuators has been incorporated into consideration of control design and robustness analysis.


Feedback Control Asymptotic Stability Tracking Error Robotic System Global Stability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    J.J. Craig,Adaptive Control of Mechanical Manipulators. Addison-Wesley Publishing Co.: New York, NY, 1988.Google Scholar
  2. 2.
    J.J. Craig,Introduction to Robotics. Addison Wesley: Boston, MA, 1986.Google Scholar
  3. 3.
    N.V. Dunskaya and E.S. Pyatnitskii, “Stabilization of mechanical and electromechanical systems,”Automation and Remote Control, pp. 1565–1574, 1989.Google Scholar
  4. 4.
    D.M. Dawson, Z. Qu, F.L. Lewis, and J.F. Dorsey, “Robust control for the tracking of robot motion,”Int. J. Control, vol. 52, pp. 581–595, 1990.Google Scholar
  5. 5.
    S.V. Gusev, “Linear stabilization of nonlinear systems program motion,”Systems Control Lett., vol. 11, pp. 409–412, 1988.Google Scholar
  6. 6.
    S. Kawamura, F. Miyazaki, and S. Arimoto, “Is a local linearPD feedback control law effective for trajectory tracking of robot motion?” inProc. of 1988 IEEE Conf. on Robotics and Automation, pp. 1345–1340.Google Scholar
  7. 7.
    V. I. Matyukhin, “Nominal stability of manipulator robots in a decomposition mode,”Automation and Remote Control, pp. 314–323, 1989.Google Scholar
  8. 8.
    E.S. Pyatnitskii, “Design of hierarchical control systems for mechanical and electromechanical plants with the aid of decomposition,”Automation and Remote Control, pp. 64–73, 1989.Google Scholar
  9. 9.
    Z. Qu and J. Dorsey, “Robust tracking control of robots by a linear feedback law,”IEEE Trans. Automat. Control, vol. 36, pp. 1081–1084, 1991.Google Scholar
  10. 10.
    Z. Qu and J. Dorsey, “RobustPID control of robots,”Int. J. of Robotics and Automation, vol. 6, pp. 228–235, 1991.Google Scholar
  11. 11.
    Z. Qu, J. Dorsey, Z. Zhang, and D. Dawson, “Robust control of robots by computed torque law,”Systems Control Lett. vol. 16, pp. 25–32, 1991.Google Scholar
  12. 12.
    Z. Qu, D. Dawson, and J. Dorsey, “Exponentially stable trajectory following of robotic manipulators under a class of adaptive control,”Automatica, vol. 28, pp. 579–586 1992.Google Scholar
  13. 13.
    C. Samson, “Robust nonlinear control of robotic manipulators,”Proceeding of 22nd IEEE CDC, pp. 1211–1216, 1983.Google Scholar
  14. 14.
    C. Samson, “Robust control of a class of nonlinear systems and applications to robotics,”Int. J. Adaptive Control and Signal Processing, vol. 1, pp. 49–68, 1987.Google Scholar
  15. 15.
    J.J. Slotine and W. Li,Applied Nonlinear Control, Prentice-Hall: Englewood Cliffs, NJ, 1991.Google Scholar
  16. 16.
    X. Wang and L.-K. Chen, “Proving the uniform boundedness of some commonly used control schemes for robots,”Proc. of 1989 IEEE Conf. on Robotics and Automation, pp. 1491–1496.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Zhihua Qu
    • 1
  1. 1.Department of Electrical EngineeringUniversity of Central FloridaOrlandoUSA

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