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Discrete-time modeling and control of robotic manipulators

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Abstract

A general approach is presented to derive discrete-time models of robotic manipulators. Such models are obtained by applying numerical discretization techniques directly to the problem of the minimization of the Lagrange action functional. Although these models are in implicit form, they own a dynamic structure that allows us to design discrete-time feedback linearizing control laws. The proposed models and control algorithms are validated by simulation with reference to a three link robot.

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References

  1. Paul, R.P., Robot Manipulators: Mathematics, Programming and Control, MIT Press, Cambridge (1981).

    Google Scholar 

  2. Hollerbach, J.M., A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity, IEEE Trans. Systems, Man and Cybernetics SMC- 10, 730–736 (1980).

    Google Scholar 

  3. Luh, J.Y.S., Walker, M.W. and Paul, R.P., On-line computational scheme for mechanical manipulators, ASME J. Dynamics Systems, Measurement, and Control 102, 69–76 (1980).

    Google Scholar 

  4. Freund, E., Fast nonlinear control with arbitrary pole-placement for industrial robots and manipulators, Int. J. Robotics Res. 1, 65–78 (1982).

    Google Scholar 

  5. Chen, Y., Frequency response of discrete-time robot systems — Limitations of PD controllers and improvements by lag-lead compensation, Proc. IEEE Int. Conf. Robotics and Automation, Raleigh, pp. 464–472 (1987).

  6. Landau, Y.D., Adaptive control techniques for robotic manipulators — The status of the art, IFAC Symp. Robot Control, Barcelona (1985).

  7. Tomizuka, M., Horowitz, R. and Landau, Y.D., On the use of MRAC techniques for mechanical manipulators, 2nd IASTED Int. Symp. Modelling, Identification, Control and Robotics, Davos (1982).

  8. Nicosia, S. and Tomei, P., A discrete-time MRAS control for industrial robots, Proc. 7th IASTED Int. Symp. Robotics and Automation, Lugano, pp. 83–89 (1985).

  9. Neuman, C.P. and Tourassis, V.D., Discrete dynamic robot models, IEEE Trans. Systems, Man, and Cybernetics SMC- 15, 193–204 (1985).

    Google Scholar 

  10. Monaco, S. and Normand-Cyrot, D., Discrete time models for robot arm control, IFAC Symp. Robot Control, Barcelona (1985).

  11. Goldstein, H., Classical Mechanics, Addison-Wesley (1950).

  12. Koivo, J.A. and Guo, T., Adaptive linear controller for robotic manipulators, IEEE Trans. Automatic Control AC- 28, 162–170 (1983).

    Google Scholar 

  13. Monaco, S. and Normand-Cyrot, D., Sur le commande non interactive des systèmes non lineaires en temps discret, Lectures Notes in Control and Information Sciences No. 63, Springer-Verlag (1984).

  14. Grizzle, J.W., Feedback Linearization of Discrete Time Systems, Lectures Notes in Control and Information Sciences No. 83, Springer-Verlag (1986).

  15. Jakubczyk, B., Feedback linearization of discrete time systems, Systems and Control Lett. 9, 411–416 (1987).

    Google Scholar 

  16. Lee, H. and Marcus, S.I., On input-output linearization of discrete-time nonlinear systems, Systems and Control Lett. 8, 249–259 (1987).

    Google Scholar 

  17. Nicosia, S., Nicoló, F. and Lentini, D., Dynamical control of industrial robots with elastic and dissipative joints, 8th IFAC Triennial World Congress, Kyoto (1981).

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Nicosia, S., Tomei, P. & Tornambè, A. Discrete-time modeling and control of robotic manipulators. J Intell Robot Syst 2, 411–423 (1989). https://doi.org/10.1007/BF00247916

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  • DOI: https://doi.org/10.1007/BF00247916

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