The problem of modeling and controlling of a free-floating space manipulator with flexures in both links and joints is addressed in this study. A mathematical model of the system is developed by combining Lagrange’s equations and momentum conservation. The finite element method is introduced to discretize multi-links with complex cross-sections. In order to reduce the dimensions and maintain the precision of a rigid-flexible coupled system, an iterated improved reduction system method is adopted. Then, a novel composite control scheme for the reduced system is presented that uses the concept of integral manifolds and singular perturbation theory. Finally, an augmented computed torque controller is applied to the under-actuated slow subsystem to realize trajectory tracking in joint space, while a linear-quadratic controller is designed to damp out the vibration of joints and links. Numerical simulation results verified that the proposed hybrid controller can successfully suppress vibration and track trajectory at the same time.

本研究解决了在连杆和关节处均具有弯曲的自由浮动空间机械手的建模和控制问题。该系统的数学模型是通过结合拉格朗日方程和动量守恒来开发的。引入有限元方法对具有复杂横截面的多连杆进行离散化。为了减小刚柔耦合系统的尺寸并保持其精度，采用迭代改进的约简系统方法。然后，使用积分流形和奇异摄动理论的概念，提出了一种用于简化系统的新型复合控制方案。最后，将增强计算扭矩控制器应用于欠驱动慢速子系统，以实现关节空间的轨迹跟踪，而线性二次控制器旨在抑制关节和连杆的振动。数值仿真结果验证了所提出的混合控制器可以成功地同时抑制振动和轨道轨迹。