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Nonlinear Regulation of End-Effector Motion for a Flexible Robot Arm

  • Alessandro De Luca
  • Leonardo Lanari
  • Giovanni Ulivi
Part of the Progress in Systems and Control Theory book series (PSCT, volume 7)

Abstract

In this paper we consider the problem of controlling via state-feedback the end-effector motion of a one-link flexible robot arm described by a nonlinear dynamic model. Due to the non-minimum phase nature of the system zero-dynamics, use of pure inversion-based techniques is unfeasible. In order to obtain stable tracking of desired tip trajectories, a nonlinear regulation approach is followed. Alternate general design procedures that exploit system invertibility are presented, leading to regulators of different complexity and realtime demand. Issues about the generation of output reference trajectories and the off-line computation of the associated steady-state trajectories are discussed, using the one-link flexible arm as a case study. Simulation results obtained for a spline trajectory and for a point-to-point motion show the achievable tracking accuracy and the wide applicability of the presented control technique.

Keywords

Input Torque Output Tracking Nonlinear Regulation Flexible Robot Asymptotic Tracking 
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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References

  1. [1]
    R.M. Hirschorn, “Output tracking in multivariable nonlinear systems,” IEEE Trans. on Automatic Control, vol. AC-26, no. 2, pp. 593–595, 1981.CrossRefGoogle Scholar
  2. [2]
    S.N. Singh, “Generalized functional reproducibility condition for nonlinear systems,” IEEE Trans, on Automatic Control, vol. AC-27, no. 4, pp. 958–960, 1982.CrossRefGoogle Scholar
  3. [3]
    T.J. Tarn, A.K. Bejczy, A. Isidori, and Y. Chen, “Nonlinear feedback in robot arm control,” Proc. 23rd Conf. on Decision and Control (Las Vegas, NV, Dec. 12–14, 1984), pp. 736–751.Google Scholar
  4. [4]
    A. De Luca, “Dynamic control of robots with joint elasticity,” Proc. 1988 IEEE Int. Conf. on Robotics and Automation (Philadelphia, PA, Apr. 24–29, 1988), pp. 152–158.Google Scholar
  5. [5]
    A. Isidori, C.H. Moog, and A. De Luca, “A sufficient condition for full linearization via dynamic state feedback,” Proc. 25th IEEE Conf. on Decision and Control (Athens, GR, Dec. 10–12, 1986), pp. 203–208.Google Scholar
  6. [6]
    C. Byrnes and A. Isidori, “Local stabilization of critically minimum phase nonlinear systems,” Systems and Control Lett., vol. 11, no. 1, pp. 9–17, 1988.CrossRefGoogle Scholar
  7. [7]
    A. Isidori and C. Byrnes, “Output regulation of nonlinear systems,” IEEE Trans, on Automatic Control, vol. AC-35, no. 2, pp. 131–140, 1990.CrossRefGoogle Scholar
  8. [8]
    A. De Luca and B. Siciliano, “Joint-based control of a non-linear of a flexible arm,” Proc. 1988 American Control Conf. (Atlanta, GA, Jun. 15–17, 1988), pp. 935–940.Google Scholar
  9. [9]
    R.H. Cannon, Jr. and E. Schmitz, “Initial experiments on the end-point control of a flexible one-link robot,” Int. J. of Robotics Research, vol. 3, no. 3, pp. 62–75, 1984.CrossRefGoogle Scholar
  10. [10]
    A. De Luca, P. Lucibello, and G. Ulivi, “Inversion techniques for trajectory control of flexible robot arms,” J. of Robotic Systems, vol. 6, no. 4, pp. 325–344, 1989.CrossRefGoogle Scholar
  11. [11]
    E. Bayo, “A finite-element approach to control the end-point motion of a single-link flexible robot,” J. of Robotic Systems, vol. 4, no. 1, pp. 63–75, 1985.CrossRefGoogle Scholar
  12. [12]
    A. De Luca, L. Lanari, and G. Ulivi, “Output regulation of a flexible robot arm,” Proc. 9th INRIA Int. Conf. on Analysis and Optimization of Systems (Antibes, F, Jun. 12–15, 1990), pp. 833–842.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Alessandro De Luca
    • 1
  • Leonardo Lanari
    • 1
  • Giovanni Ulivi
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaUniversità degli Studi di Roma “La Sapienza”RomaItaly

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