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This work studies the maneuver control and vibration suppression of a flexible free-flying space robot using variable-speed control moment gyros as actuators. A novel flexible space manipulator is designed. The dynamics of the flexible multibody system is derived by using Kane method. Based on the singular perturbation approach, the dynamics of the flexible manipulator is decoupled into a slow subsystem and a fast subsystem. The slow subsystem is associated with the rigid motion dynamics, and the fast subsystem is related to the link flexible dynamics. A composite control strategy is proposed as a combination of two controllers for these subsystems. An adaptive sliding mode controller is designed for the slow subsystem, and an adaptive controller is designed for the fast subsystem. Uncertainty estimation can be achieved by the adaptive terms of the composite controller. A weighted robust pseudo-inverse steering law is proposed for the variable-speed control moment gyros. Numerical results demonstrate that the proposed composite controller is robust to parameter uncertainties and external disturbances. [ABSTRACT FROM AUTHOR]