Reachable and stabilizable area of an underactuated manipulator without state feedback control

In this paper, we investigate the reachable and stabilizable area of the tip of an underactuated manipulator (the first joint has an actuator and the second joint has no actuator), which is movable in a vertical plane. In the previous research, we proposed the open-loop control method (which is using the bifurcation phenomena occurred in the second link by high-frequency excitation of the active link sinusoidally) for the underactuated manipulator in order to swing up and stabilize at the upright position of its unactuated link. Applying the method more globally, we realize many configurations of the manipulator without state feedback. The reachable and stabilizable positions of the tip of the underactuated link are theoretically shown. Furthermore, the validity of the theoretical results are experimentally confirmed.