A technique without feedback control is theoretically discussed for the swing-up of the free link from the downward vertical position to the upright position and for the stabilization at the upright position. The averaged equation governing motion of the free link is deduced by introducing three time scales when the free joint is excited with high-frequency. By performing bifurcation analysis for the averaged equation, variation of the equilibrium states of the free link is shown depending on the configuration of the active link and the control strategy is analytically proposed. Furthermore, experimental results indicate the validity of the proposed method for an underactuated tow-link manipulator.
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