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

The reachable and stabilizable area of a two-link underactuated manipulator is clarified theoretically and experimentally. The manipulator consists of an active (first) link attached to an actuator and a free (second) link connected to the first link with a joint that lacks not only an actuator but also a sensor. In this circumstance the motion of the second (free) link can be controlled without state feedback of the free link, using the nonlinear characteristics of the bifurcations produced in the free link under the high-frequency excitation of the active (first) link attached to the actuator. It is theoretically shown according to the bifurcation theory that the stable equilibrium states of the free link vary depending on the configuration of the active link with respect to the direction of gravity. Then, the set of positions where the tip of the free link can reach and be stable, i.e., the reachable and stabilizable area, is theoretically clarified under the combination of the excitation frequency and the configuration of the active link. Furthermore, experimental results show the validity of the theoretically predicted reachable and stabilizable area.