Motion Control of an Under-Actuated Manipulator : Analysis and Application of Bifurcation Phenomena

Abstract

We have proposed an position control method for a two-joint manipulator with the second joint free under gravitational effect. The control objective is to swing the free link from the gravitational direction to the opposite position and then to stabilize the free link at the inverted position without feedback control. In this paper, the theoretical procedure for the realization of the control is provided. The averaged equation governing the motion of the free joint is derived by using the method of multiple scales. The bifurcation analysis for the equation shows the variation of the stable equilibrium states under changing the configuration of the actuated joint. Finally, experimental results confirm the validity of the proposed control method.