An adaptive backstepping observer-controller design for manipulators cooperating flexible payload

Two manipulators cooperating a flexible payload are studied based on adaptive backstepping theory. Different from the traditional studies of manipulators cooperating a flexible load which concentrated on the structural analysis and stability, this paper studies the cooperative control and vibration control problem based on observer. 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. The controllers are designed for each subsystem, respectively. The stability of the overall system composed of the observer system and the controller system can be guaranteed by using Lyapunov stability theory. The validity of the proposed scheme is demonstrated by simulations.