On the optimality of uniform velocity–deceleration separation scheme for tethered satellite systems

For mitigating the libration angle fluctuation of the tethered satellite system, this paper discusses how to make the uniform velocity–deceleration separation scheme achieve the best effect. First, a judgment condition is established to determine the tether state by comparing the tether length and the relative distance of the sub-satellite and the parent satellite. Based on the tethered satellite system dynamics equation and Clohessy–Wiltshire equation, dynamic models are given for four cases of tether states. Second, the influence of the uniform velocity–deceleration separation scheme on the libration angle is analyzed by taking the libration angle at the separation ending time and the mean absolute value of the libration angle as index functions. Then, the optimality problem of the uniform velocity–deceleration separation scheme is formulated as an optimization problem with constraints, and an approximate solution algorithm is given by combining the back propagation neural network and Newton–Raphson method of multiple initial values. Finally, the effectiveness of the proposed method is verified by a numerical simulation.