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针对自由浮动空间柔性机械臂,讨论了在笛卡尔坐标系中机械臂对刚性载荷的轨迹跟踪控制和连杆柔性振动主动控制问题。基于拉格朗日法、假设模态法和系统动量守恒定律,推导了一种自由浮动空间柔性机械臂在轨操作刚性载荷的动力学方程。在此基础上,采用奇异摄动法将系统分解为慢变和快变两种尺度时标的子系统,设计模糊终端滑模控制器和Backstepping控制器分别对两个子系统进行控制,由此得到的组合控制使得机械臂按期望轨迹对刚性载荷进行精确在轨操作,同时抑制了柔性连杆的弹性振动。通过数字仿真验证了上述方法的有效性。
Aiming at the flexible manipulator with free floating space, the trajectory tracking control of rigid manipulator and the active control of connecting rod flexible vibration in Cartesian coordinate system are discussed. Based on the Lagrangian method, the modal law and the law of conservation of momentum of the system, a dynamic equation of the rigid load in orbit of a flexible manipulator with free floating space is deduced. On this basis, the singular perturbation method is used to decompose the system into two subsystems, slow and fast subspace scale subsystems. The design of fuzzy terminal sliding mode controller and Backstepping controller respectively control the two subsystems, The combined control allows the robot arm to precisely track the rigid load in the desired trajectory while suppressing the elastic vibration of the flexible link. The effectiveness of the above method is verified by numerical simulation.