Abstract: Nonlinear dynamic equations of a free-floating space robot with two manipulators and a flexible end-manipulator are established based on Lagrange and assumed mode methods.Its new global dynamic model in terms of measured joints is derived by coordinate transformation,and the decoupled control equations for joint relative angles and elastic parts of the flexible manipulator are obtained with the model-based nonlinear decoupling feedback control method.Trajectory tracking control of the free floating space robot with flexible manipulators is discussed,and the numerical simulation shows that the proposed model transformation and control method is efficient in trajectory tracking control of free floating space robot with flexible manipulators.