Simultaneous rotation-nutation suppression for a tumbling satellite via a flexible rod

Effectively capturing a malfunctioning tumbling satellite by a servicing spacecraft is nowadays a worldwide challenge. Because of the potential collision between the chaser and the target spacecraft, it is risky to directly capture the tumbling satellite. An innovative approach is to use a flexible brush/rod as the end-effector of a chaser to tackle the tumbling target. However, almost all studies are confined to reducing the pure rotational motion without considering the inevitable nutation motion. To ensure safe capture, it is necessary to suppress both the nutation and rotation simultaneously to the desired low level. There are two difficulties with the simultaneous suppression problem: i) the ideal contact point between the rod and the target is difficult to pinpoint for simultaneous suppression, and ii) the solution of the rod-target dynamic system (described by nonlinear partial differential equations) is extremely time-consuming especially with the limited computing capability of the on-board computer. To conquer these difficulties, a simultaneous rotation-nutation suppression (SRNS) method based on the equal ratio principle is proposed to simultaneously reduce angular velocity and nutation angle. Besides, a highly efficient simplified rod-target model is established based on machine learning. Numerical simulations have been carried out to verify the effectiveness and efficiency of the proposed method.