In the present paper, we consider a three-link underactuated manipulator, the first joint of which is active and the second and third joints of which exhibit passive motion, on a plane inclined at slight angle from horizontal the plane. We analytically investigate changes in the stability of equilibrium points of the free links connected to the passive joints using high-frequency horizontal excitation of the first link. We derive autonomous averaged equations from the dimensionless equations of motion using the method of multiple scales. We clarify that the two free links can be swung up through pitchfork bifurcations and stabilized at some configurations by producing nontrivial and stable equilibrium points due to the high-frequency excitation. Furthermore, it is experimentally verified that increasing the excitation frequency multiplies stable and nontrivial equilibrium points.
Swing-Up Control of a Three-Link Underactuated Manipulator by High-Frequency Horizontal Excitation
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 20, 2011; final manuscript received February 28, 2012 published online June 14, 2012. Assoc. Editor: Yoshiaki Terumichi.
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Endo, K., and Yabuno, H. (June 14, 2012). "Swing-Up Control of a Three-Link Underactuated Manipulator by High-Frequency Horizontal Excitation." ASME. J. Comput. Nonlinear Dynam. January 2013; 8(1): 011002. https://doi.org/10.1115/1.4006251
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