Abstract: In order to analyze the dynamic simulation and movement control of space robot under the influence of full flexible of base, links and joints, as well as the active vibration suppression of base, links and joints, an input limited repetitive learning controller with integration of motion and vibration is proposed. The design of the algorithm is not based on the system model information. The flexible base and the flexible joints are regarded as linear spring and torsion springs. The flexible links are analyzed by the Eulerian Bernoulli model, and the dynamic equation is established by the Lagrange equation and the assumed mode method. Based on the singular perturbation theory, the model is decomposed into a slow subsystem including the system rigid variables and the link flexible vibration, and a fast subsystem including the base and joint flexible vibration. The corresponding sub controllers are designed for the slow and fast subsystems to form the general controller with joint flexible compensation. For the slow subsystem, an input limited repetitive learning controller is proposed, which is composed of hyperbolic tangent function, saturation function and repetitive learning term. The hyperbolic tangent function and saturation function realize the requirement of limited input torque. The repetitive learning term compensates the periodic system error to complete the gradual stable tracking of the expected trajectory of base attitude and joint. However, in order to suppress the flexible vibration of the links of the slow subsystem, a hybrid trajectory reflecting the flexible vibration of the links and the rigid motion of the system is constructed by using virtual force conception, and an input limited repetitive learning controller on virtual force conception is proposed to ensure the accurate tracking of the trajectory of the base and joint, while actively suppressing the flexible vibration of the links. For the fast subsystem, the linear quadratic optimal control algorithm is used to suppress the flexible vibration of the base and joints. The simulation results show that the controller is suitable for general flexible nonlinear system, meets the requirements of limited input torque, realizes high-precision tracking of periodic signal, effectively suppresses the flexible vibration of base, links and joints, and verifies the feasibility of the algorithm.