Fractional Dynamics in Mechanical Manipulation

This paper analyzes the signals captured during the movement of a mechanical manipulator carrying a liquid container. In order to study the signals, an experimental setup is implemented. The system acquires data from the sensors, in real time, and, in a second phase, processes them through an analysis package. The analysis package runs offline and handles the recorded data. The results show that the Fourier spectrum of several signals presents a fractional behavior. The experimental study provides useful information that can assist in the design of a control system to be used in reducing or eliminating the effect of vibrations.

[1]  J. Machado.  Analysis and design of fractional-order digital control systems , 1997 .

[2]  Xavier Moreau,et al.  From fractal robustness to non-integer approach in vibration insulation: the CRONE suspension , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[3]  F. Harris.  On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

[4]  J. A. Tenreiro Machado,et al.  Tuning of PID Controllers Based on Bode’s Ideal Transfer Function , 2004 .

[5]  Wayne J. Book,et al.  Filtering micro-manipulator wrist commands to prevent flexible base motion , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[6]  Warren P. Seering,et al.  Using acausal shaping techniques to reduce robot vibration , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[7]  Vasily E. Tarasov,et al.  Conservation laws and Hamilton’s equations for systems with long-range interaction and memory , 2008 .

[8]  Dennis Gabor,et al.  Theory of communication , 1946 .

[9]  Gary W. Bohannan,et al.  Interpretation of complex permittivity in pure and mixed crystals , 2001 .

[10]  A. Papoulis.  Signal Analysis , 1977 .

[11]  Clark R. Dohrmann,et al.  Control for slosh-free motion of an open container , 1997 .

[12]  J.A.T. Machado,et al.  Windowed Fourier Transform of Experimental Robotic Signals with Fractional Behavior , 2006, 2006 IEEE International Conference on Computational Cybernetics.

[13]  J. A. Tenreiro Machado,et al.  FRACTIONAL ORDER FOURIER SPECTRA IN ROBOTIC MANIPULATORS WITH VIBRATIONS , 2006 .

[14]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[15]  W. Rumold.  Modeling and Simulation of Vehicles Carrying Liquid Cargo , 2001 .

[16]  Maria da Graça Marcos,et al.  Fractional dynamics in the trajectory control of redundant manipulators , 2008 .

[17]  Tsuneo Yoshikawa,et al.  Dynamic trajectory tracking control of flexible manipulator macro-micro manipulator system , 1993, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[18]  Vasily E. Tarasov,et al.  Coupled oscillators with power-law interaction and their fractional dynamics analogues , 2007 .

[19]  G. Zaslavsky,et al.  Fractional dynamics of systems with long-range interaction , 2006, 1107.5436.

[20]  Wayne J. Book,et al.  Experimental study on micro/macro manipulator vibration control , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[21]  M. S. Evans,et al.  Micro manipulator motion control to suppress macro manipulator structural vibrations , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[22]  Mattias Grundelius,et al.  Methods for Control of Liquid Slosh , 2001 .