Adaptive control of a rigid manipulator holding a flexible payload driven by an unknown force

This paper presents an adaptive control method for trajectory tracking of a rigid manipulator which holds a flexible payload driven by an unknown force. First, kinematics and dynamics of the payload is derived. After the analysis of the interaction force in the whole system, a model of manipulator is then combined with the payload model, by which the model of the whole system is obtained. The unknown force exerted on the left end of the payload could be identified by some sensors equipped at the wrist of the manipulator. The measurement error of the force is considered when the control scheme is designed. The proposed controller makes the position and orientation of the flexible payload track a desired trajectory while suppressing its vibration in the absence of the gravity force. A control scheme and a parameter update law are derived so that the reference states are guaranteed to converge to a closed ball. Stability of the system is proved by using Lyapunov stability theory. The validity of the proposed scheme is demonstrated by simulations.