Finite-Thrust Lambert Transfer Based on Multistage Constant-Vector Thrust Control

Abstract

In this work, an efficient multi-stage constant-vector thrust control algorithm is proposed for spacecraft to achieve finite-thrust Lambert transfer considering <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> perturbation. In contrast to most designs that apply continuous-thrust requiring time-varying direction and the magnitude of the thrust, the proposed control scheme utilizes a multi-stage constant-vector thrust which means the modulus and direction of the thrust are constant in each stage determined by a given set of time nodes dividing the whole transfer time, which reduces the control complexity of the engine. Based on the multi-stage sensitivity matrix, which describes the first-order relationship between the thrust and the change of the orbital elements, a rapid algorithm is presented to obtain the multi-stage constant-vector thrust solution with the required accuracy. Furthermore, the optimization problem of the multi-stage constant-vector thrust solution is established, and the direct optimization method is proposed to obtain an optimal multi-stage constant-vector thrust solution for a given set of time nodes. Based on this approach, the node-sequence optimization method is further proposed to obtain a series of feasible optimized solutions rapidly corresponding to a monotonically increasing time-node sets. Compared with the existing finite-thrust methods, the presented methods balance the fuel consumption and control requirements of the engine because the situation that the engine always needs to change the direction and the magnitude of the thrust could be avoided, which are practical options for engineering applications.