The dynamics modeling, algorithm design of motion control and step active suppression of joint- link double flexible vibration of free-floating flexible space robot are discussed. The system dynamic equations are established according to system momentum conservation, angular momentum conservation and Lagrange- assumed mode method. Based on singular perturbation method, the system is decomposed into a slow subsystem (represents the system's rigid motion), a fast subsystem 1 (represents the system's flexible motion caused by flexible-link), and a fast subsystem 2 (represents the system's flexible motion caused by flexible-joint). For the slow subsystem, a robust controller is proposed to compensate the uncertain parameters and rotation errors, and to realize the asymptotic tracking of the system's motion trajectory. For the fast subsystem 1, linear quadric regulator (LQR) is used to suppress the flexible vibration caused by flexible-link. For the fast subsystem 2, a feedback controller based on the velocity difference between the link and the motor is used to suppress the flexible vibration caused by flexible-joint. So the system's controller is a synthesize controller by the three controllers. The simulation results prove the controller's efficiency.%讨论了漂浮基柔性空间机器人系统的动力学建模、运动控制算法设计以及关节、臂双重柔性振动的分级主动抑制问题．利用系统动量、动量矩守恒关系和拉格朗日一假设模态法对系统进行动力学分析，建立系统动力学方程．基于奇异摄动法，将系统分解为表示系统刚性运动部分的慢变子系统，表示由柔性臂引起的系统柔性运动部分的快变子系统i和表示由柔性关节引起的系统柔性运动部分的快变子系统2．针对慢变子系统提出一种鲁棒控制方法来补偿系统参数的不确定性和柔性关节引起的转动误差，实现系统期望运动轨迹的渐近跟踪；针对快变子系统1采用线性二次型最优控制器来抑制由柔性臂引起的系统柔性振动；针对快变子系统2设计了基于机械臂和电机转子的转角速度差值的反馈控制器来抑制由柔性关节引起的系统柔性振动．因此，系统的总控制律为以上3个子系统控制律的综合．最后通过仿真实验证明了所提出的混合控制方法的有效性．
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