Motion control of an underactuated manipulator without feedback control

A technique without state feedback control of the free link is proposed for the swing-up and the stabilization at the upright position of the free link in a two-link underactuated manipulator (the first and second links are active and free, respectively) moving in the plane inclined from the horizontal plane. The proposed method is based on the utilization of the bifurcation phenomena in the second link under high-frequency sinusoidal excitation for the first link. By the change of the configuration of the first link with respect to the direction of the gravity effect, various bifurcation phenomena (super-critical and sub-critical pitchfork bifurcations and their perturbations) emerge in the second link. An appropriate actuation of the perturbations of the bifurcations by the change of the configuration realizes the swing-up and stabilization without feedback control. Experimental results indicate the validity of the proposed method for the underactuated manipulator.