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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 105298, 11 pages
Research Article

Stability Problem of Wave Variable Based Bilateral Control: Influence of the Force Source Design

Key Laboratory of Airborne Optical Imaging and Measurement, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China

Received 29 August 2013; Accepted 18 October 2013

Academic Editor: Hui Zhang

Copyright © 2013 Dapeng Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The wave variable has been proposed to achieve robust stability against the time delay in bilateral control system. However, the influence of the force source on the overall system is still not clear. This paper analyzes this problem and proposes a supplement to the stability analysis for wave variable based bilateral control. Based on the scattering theory, it is pointed out that the design of force source decides the passivity of the two-port network of slave robot. This passivity influences the stability of overall system. Based on the characteristic equation and small gain theorem, it is clear that inappropriate designed force source in encoding the wave variable destroys the stability in the presence of time delay. A wave domain filter makes up for the broken stability. The principle of this reparation is explained in this paper. A reference is also provided by the analysis to design the parameter of the wave domain filter. Experiments prove the correctness and validity.