Experimental Signal Analysis of Robot Impacts in a Fractional Calculus Perspective

Miguel F. M. Lima; J. A. Tenreiro Machado; Manuel Crisóstomo

doi:10.20965/jaciii.2007.p1079

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JACIII Vol.11 No.9 pp. 1079-1085

doi: 10.20965/jaciii.2007.p1079

(2007)

Paper:

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Experimental Signal Analysis of Robot Impacts in a Fractional Calculus Perspective

Miguel F. M. Lima^, J. A. Tenreiro Machado^,
and Manuel Crisóstomo^

^*Dept. of Electrotechnical Engineering, Superior School of Technology, Polytechnic Institute of Viseu, 3504-510 Viseu, Portugal

^**Dept. of Electrotechnical Engineering, Institute of Engineering, Polytechnic Institute of Porto, 4200-072 Porto, Portugal

^***Institute of Systems and Robotics, University of Coimbra, Polo II, 3030-290 Coimbra, Portugal

Received:

February 5, 2007

Accepted:

June 14, 2007

Published:

November 20, 2007

Keywords:

windowed Fourier transform, vibrations, impacts, robotics, fractional order systems

Abstract

This paper presents a study of the signals captured during impacts and vibrations of a mechanical manipulator. In order to acquire and study the signals an experimental setup is implemented. The system acquires data from the sensors, in real time, and processes it through an off-line analysis package. The study is developed based on a set of signal processing tools, such as the Fast Fourier Transform and the windowed Fourier transform. The signals whose Fourier spectrum presents a non integer behavior are pointed out and analyzed using several time windows. The experimental results provide useful information that can assist in the design of a control system to deal with the unwanted effects of vibrations.

Cite this article as:

M. Lima, J. Machado, and M. Crisóstomo, “Experimental Signal Analysis of Robot Impacts in a Fractional Calculus Perspective,” J. Adv. Comput. Intell. Intell. Inform., Vol.11 No.9, pp. 1079-1085, 2007.

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References

[1] R. L. Allen and D. W. Mills, “Signal Analysis,” Wiley, 2004.
[2] R. S. Barbosa, J. A. T. Machado, and I. M. Ferreira, “Tuning of PID Controllers Based on Bode’s Ideal Transfer Function,” In Nonlinear Dynamics, pp. 305-321, 2005.
[3] G. W. Bohannan, “Analog Realization of a Fractional Control Element-Revisited,”
In mechatronics.ece.usu.edu/foc/cdc02tw/cdrom/aditional/FOC_Proposal_Bohannan.pdf ,
2002.
[4] D. W. Cannon, D. P. Magee, W. J. Book, and J. Y. Lew, “Experimental Study on Micro/Macro Manipulator Vibration Control,” In Proc. IEEE Int. Conf. on Robotics & Automation, 1996.
[5] D. Gabor, “Theory of communication,” J. IEE 1946, 1946.
[6] M. F. M. Lima, J. T. Machado, and M. Crisóstomo, “Experimental Set-Up for Vibration and Impact Analysis in Robotics,” WSEAS Trans. on Systems, 4(5), pp. 569-576, 2005.
[7] M. F. M. Lima, J. T. Machado, and M. Crisóstomo, “Fractional Order Fourier Spectra In Robotic Manipulators With Vibrations,” In Second IFAC Workshop on Fractional Differentiation and its Applications, pp. 386-391, 2006.
[8] J. A. T. Machado, “A Probabilistic Interpretation of the Fractional-Order Differentiation,” In Journal of Fractional Calculus & Applied Analysis, pp. 73-80, 2003.
[9] D. P. Magee and W. J. Book, “Filtering Micro-Manipulator Wrist Commands to Prevent Flexible Base Motion,” In Proc. American Control Conf., 1995.
[10] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, “Discrete-Time Signal Processing,” Prentice Hall, 1989.
[11] A. Oustaloup, X. Moreau, and M. Nouillant, “From fractal robustness to non integer approach in vibration insulation: the CRONE suspension,” In Proc. of the 36th Conf. on Decision & Control, 1997.
[12] I. Podlubny, “Geometrical and physical interpretation of fractional integration and fractional differentiation,” Journal of Fractional Calculus & Applied Analysis, 5(4), pp. 357-366, 2002.
[13] N. C. Singer and W. P. Seering, “Using Acausal Shaping Techniques to Reduce Robot Vibration,” In Proc. IEEE Int. Conf. on Robotics & Automation, 1988.
[14] T. Yoshikawa, K. Hosoda, T. Doi, and H. Murakami, “Quasi-static Trajectory Tracking Control of Flexible Manipulator by Macromicro Manipulator System,” In Proc. IEEE Int. Conf. on Robotics & Automation, pp. 210-215, 1993.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] R. L. Allen and D. W. Mills, “Signal Analysis,” Wiley, 2004.

[2] [2] R. S. Barbosa, J. A. T. Machado, and I. M. Ferreira, “Tuning of PID Controllers Based on Bode’s Ideal Transfer Function,” In Nonlinear Dynamics, pp. 305-321, 2005.

[3] [3] G. W. Bohannan, “Analog Realization of a Fractional Control Element-Revisited,”
In mechatronics.ece.usu.edu/foc/cdc02tw/cdrom/aditional/FOC_Proposal_Bohannan.pdf ,
2002.

[4] [4] D. W. Cannon, D. P. Magee, W. J. Book, and J. Y. Lew, “Experimental Study on Micro/Macro Manipulator Vibration Control,” In Proc. IEEE Int. Conf. on Robotics & Automation, 1996.

[5] [5] D. Gabor, “Theory of communication,” J. IEE 1946, 1946.

[6] [6] M. F. M. Lima, J. T. Machado, and M. Crisóstomo, “Experimental Set-Up for Vibration and Impact Analysis in Robotics,” WSEAS Trans. on Systems, 4(5), pp. 569-576, 2005.

[7] [7] M. F. M. Lima, J. T. Machado, and M. Crisóstomo, “Fractional Order Fourier Spectra In Robotic Manipulators With Vibrations,” In Second IFAC Workshop on Fractional Differentiation and its Applications, pp. 386-391, 2006.

[8] [8] J. A. T. Machado, “A Probabilistic Interpretation of the Fractional-Order Differentiation,” In Journal of Fractional Calculus & Applied Analysis, pp. 73-80, 2003.

[9] [9] D. P. Magee and W. J. Book, “Filtering Micro-Manipulator Wrist Commands to Prevent Flexible Base Motion,” In Proc. American Control Conf., 1995.

[10] [10] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, “Discrete-Time Signal Processing,” Prentice Hall, 1989.

[11] [11] A. Oustaloup, X. Moreau, and M. Nouillant, “From fractal robustness to non integer approach in vibration insulation: the CRONE suspension,” In Proc. of the 36th Conf. on Decision & Control, 1997.

[12] [12] I. Podlubny, “Geometrical and physical interpretation of fractional integration and fractional differentiation,” Journal of Fractional Calculus & Applied Analysis, 5(4), pp. 357-366, 2002.

[13] [13] N. C. Singer and W. P. Seering, “Using Acausal Shaping Techniques to Reduce Robot Vibration,” In Proc. IEEE Int. Conf. on Robotics & Automation, 1988.

[14] [14] T. Yoshikawa, K. Hosoda, T. Doi, and H. Murakami, “Quasi-static Trajectory Tracking Control of Flexible Manipulator by Macromicro Manipulator System,” In Proc. IEEE Int. Conf. on Robotics & Automation, pp. 210-215, 1993.

Experimental Signal Analysis of Robot Impacts in a Fractional Calculus Perspective

Miguel F. M. Lima*, J. A. Tenreiro Machado**, and Manuel Crisóstomo***

Miguel F. M. Lima^, J. A. Tenreiro Machado^,
and Manuel Crisóstomo^