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Analytical modelling and nonlinear strain feedback control of a flexible robot ARM

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Abstract

In this paper, a full nonlinear analytical model of a single link flexible manipulator consisting of a rotary joint and a flexible link, handling uniform payload at the tip considering its inertia is developed based on extended Hamilton-assumed mode method. Due to model nonlinearities, a nonlinear control strategy directly based on the strain gauges measurements attached in some locations of the link is investigated. Effectiveness of the controller in vibration suppressing and fast motion duration tracking capability is shown through simulation.

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References

  1. Siciliano, B., Control in Robotics: Open Problems and Future Directions, Proc. IEEE Int. Conf. on Control Applications, 1998, pp. 81–85,.

  2. Book, W.J., Maizzo-Neto, O., and Whiteny, D.E., Feedback Control of Two Beam, Two Joint Systems with Distributed Flexibility, ASME J. Dynamics Systems Measurements and Control, 1975, vol. 97, pp. 424–431.

    Google Scholar 

  3. Book, W.J., Recursive Lagrangian Dynamics of Flexible Manipulator Arms, Int. J. Robotic Res., 1984, vol. 3, no. 3, pp. 87–101.

    Article  Google Scholar 

  4. Cannon, R.H., Jr. and Schmitz, E., Initial Experiments on the End Point Control of a Flexible One Link Robot, Int. J. Robotic Res., 1984, vol. 3, no. 3.

  5. Okley, C.M. and Cannon, R.H., Anatomy of an Experimental Two-Link Flexible Manipulator Under End Point Control, Proc. IEEE Conf. on Decision and Control, 1990, pp. 507–513.

  6. Hasting, G.G. and Book, W.J., Verification of a Linear Dynamic Model for Flexible Robotic Manipulator, Proc. IEEE Conf. on Robotics and Automation, 1986, pp. 1024–1029.

  7. Hasting, G.G. and Book, W.J., A Linear Model for Flexible Robotic Manipulator, IEEE Control System Magazine, 1987, vol. 7, no. 1, pp. 61–64.

    Article  Google Scholar 

  8. Nicosia, S., Tomi, D., and Tornambe, A., Dynamic Modelling of a Flexible Manipulator, Proc. IEEE Conf. on Robotics and Automation, 1986, pp. 365–372.

  9. Sooraksa, P. and Chen, G., Mathematical Modelling of a Flexible Robot Arm, Proc. IEEE Conf. on Control Applications, 1996, pp. 960–964.

  10. Saad, M., Saydy, L., and Akhrif, O., Noncollocated Passive Transfer Functions for a Flexible Link Robot, IEEE Int. Conf. on Control Applications, September, 2000.

  11. Martins, J.M., Mohamed, Z., and Tokhi, M.O., Approaches for Dynamic Modelling of Flexible Manipulator Systems, IEEE Proc. on Control Theory and Applications, 2003, vol. 150, no. 4, pp. 401–411.

    Article  Google Scholar 

  12. Mohamed, Z. and Tokhi, M.O., A Symbolic Manipulation Approach for Modelling and Performance Analysis of Flexible Manipulator Systems, Int. J. Acoustic and Vibration, 2002, pp. 27–37.

  13. Tokhi, M.O., Mohamed, Z., and Shaheed, M.H., Dynamic Modelling of a Flexible Manipulator System Incorporating Payload: Theory and Experiments, J. Low Frequency Noise, Vibration and Active Control, 2000, pp. 209–229.

  14. Tokhi, M.O., Mohamed, Z., and Azad, A.K.M., Finite Difference and Finite Element Approach to Dynamic Modelling of a Flexible Manipulator, J. System and Control Eng., 1997, pp. 145–156.

  15. Kotnic, P.T., Yurkovich, S., and Ozguner, U., Acceleration Feedback for Control of a Flexible Manipulator Arm, J. Robotic and System, 1988, pp. 181–195.

  16. Nelson, W.L. and Mitra, D., Load Estimation and Load Adaptive Optimal Control for a Flexible Robot Arm, IEEE Conf. Decision Control, 1986, pp. 206–211.

  17. Chen, J.S., and Menq, C.H., Modelling and Adaptive Control of a Flexible One Link Manipulator, Robotica, 1990, vol. 8, pp. 339–345.

    Google Scholar 

  18. Feliu, V., Rattan, K.S., and Brown, B.H., Adaptive Control of a Single Link Flexible Manipulator, IEEE Control Magazine, pp. 29–33.

  19. Siciliano, B., Yuan, B.S., and Book, W.J., Model Reference Adaptive Control of a One Link Flexible Arm, Proc. Conf. on Decision and Control, 1986.

  20. Yuh, J., Application of Discrete Time Model Reference Adaptive Control to a Single Link Flexible Robot Arm, J. Robotic System, 1987, vol. 4, no. 5.

  21. Fraser, A.R. and Daniel, R.W., Perturbation Techniques for Flexible Manipulators, Netherlands: Kluwer Academic, 1991.

    MATH  Google Scholar 

  22. Lewis, F.L. and Vandegrift, M., Flexible Robot Arm Control by a Feedback Linearization-Singular Perturbation Approach, Proc. IEEE Conf. on Robotic and Automation, vol. 3, pp.729–736.

  23. Singh, S.N. and Schy, A.A., Control of Elastic Robotic Systems by Nonlinear Inversion and Modal Damping, ASME J. Dynamic, System, Measurement and Control, 1986, vol. 108, pp. 180–183.

    MATH  Google Scholar 

  24. Asada, H., Ma, Z.D., and Tokumaro, H., Inverse Dynamics of Flexible Robot Arms: Modeling and Trajectory Control, ASME J. Dynamic, System, Measurement and Control, 1990, vol. 112, pp. 177–185.

    Article  MATH  Google Scholar 

  25. Pham, C.M., Khalil, W., and Chevallereau, C., A Nonlinear Model Based Control of Flexible Robots, Robotica, 1992, vol. 11, pp. 73–82.

    Article  Google Scholar 

  26. Chevallereau, C. and Aoustin, Y., Nonlinear Control Laws for a 2 Link Flexible Robot: Comparison of Applicability Domains, Proc. IEEE Conf. on Robotic and Automation, 1992, pp. 718–753.

  27. De Luca, A., Panzieri, S., and Ulivi, G., Stable Inversion Control for Flexible Link Manipulators, Proc. IEEE Int. Conf. on Robotics and Automation, 1998, pp. 799–805.

  28. Madhavan, S.K. and Singh, S.N., Variable Structure Trajectory Control of an Elastic Robotic Arms, J. Robotic Systems, 1993, pp. 23–44.

  29. Zuo, K. and Wang, D., Closed Loop Shaped-Input Control of a Class of Manipulators with a Single Flexible Link, Proc. IEEE Conf. on Robotic and Automation, 1992, pp. 782–787.

  30. Singer, N.C. and Seering, W.P., An Extension of Command Shaping Methods for Controlling Residual Vibrations Using Frequency Sampling, Proc. IEEE Conf. on Robotic and Automation, 1992, pp. 800–806.

  31. Wang, F.Y. and Guang, G.G., Influence of Rotary Inertia, Shear Deformation and Loading on Vibration Behaviours of Flexible Manipulators, J. Sound and Vibrations, 1994, vol. 171, no. 4, pp. 433–452.

    Article  MATH  Google Scholar 

  32. Wang, F.Y., Zhou, P., and Lever, P., Dynamic Effects of Rotary Inertia and Shear Deformation on Flexible Manipulators, Proc. IEEE, 1996, pp. 2315–2320.

  33. Meirovitch, L., Dynamics and Control of Structures, New York: John Wiley and Sons 1990.

    Google Scholar 

  34. Bolandi, H. and Esmaeilzadeh, S.M., Nonlinear Dynamical Modelling of Flexible Manipulator System, Int. Conf. on Mechanical Eng. (ISME), 2008.

  35. Yang, J.H., Lian, F.L. and Fu, L.C., Adaptive Robust Control for Flexible Manipulators, Proc. IEEE Conf. on Robotics and Automation, 1995, pp. 1223–1228.

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Correspondence to H. Bolandi.

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Bolandi, H., Esmaeilzadeh, S.M. Analytical modelling and nonlinear strain feedback control of a flexible robot ARM. Aut. Conrol Comp. Sci. 42, 236–248 (2008). https://doi.org/10.3103/S0146411608050027

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  • DOI: https://doi.org/10.3103/S0146411608050027

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