Motion control of a flexible underactuated manipulator using resonance in a flexible active arm

Abstract Underactuated manipulators have a free joint without an actuator and a free arm connected to the free joint. Of the many existing control methods, we focus on a method based on the utilization of the pitchfork bifurcation produced by a high-frequency excitation of an active arm with an actuator; this method is also applicable to the case in which the free joint lacks not only an actuator but also a sensor because it does not rely on the state feedback of the free joint. In this study, we consider an underactuated two-arm manipulator in which the first arm is active and flexible and the second arm is free and rigid. By producing resonance in the flexible arm, we control the motion without high-frequency excitation. The equations governing the elastic behavior and the rigid motion of the first and second arms, respectively, are analyzed theoretically and the nonlinear characteristics of the bifurcations produced in the second arm are analytically examined. Then, we propose a motion control method for swinging up the free second arm from the downward vertical direction to the upright position without the use of high-frequency excitation. Experiments using a corresponding simple apparatus demonstrate the validity of the proposed method.