Adaptive backstepping control of a dual-manipulator cooperative system handling a flexible payload

Two manipulators handling a flexible payload are studied based on adaptive backstepping control theory. Considering the complexity of the dynamic model, the obtained model is divided into a slow subsystem describing the large rigid motion and a fast subsystem expressing the elastic vibration by singular perturbation theory. A cooperative controller is designed based on adaptive backstepping control. The slow subsystem can complete system trajectory tracking performance. The fast subsystem can suppress the elastic vibration of the system. Stability of the system is proved by using Lyapunov stability theory. The validity of the proposed scheme is demonstrated by simulations.