Relative orbit transfer using constant-vector thrust acceleration

This study proposes a rapid algorithm to achieve relative orbit transfer based on constant-vector thrust acceleration control, where the magnitude and direction of the thrust acceleration are constant in the tangential–normal–out-of-plane (TNH) frame. Based on the presented linearized thrust-control matrix, which is used to construct the first-order relationships between the relative position, velocity, and the constant-vector thrust acceleration, two analytical approximate solutions are presented for two types of relative orbit transfer problems: the one-vector thrust acceleration solution to the relative orbit transfer problem, which only requires the final relative position, and the double-vector thrust acceleration solution to the relative orbit transfer problem, which requires the final relative position and velocity. Furthermore, for the cases where the magnitude constraint of the thrust provided by the engine is required, fast-iterative algorithms are proposed to obtain the one-vector acceleration solution and the double-vector acceleration solution that satisfy the magnitude constraint strictly. The simulation results showed that the proposed methods are rapid, accurate, and easy to implement, demonstrating their wide application potential for engineering practice.