Optimal Elliptic Orbital Maneuver with Continuous Radial Thrust on the Chaser Using Generating Functions

Abstract

This paper solves the time-fixed optimal elliptic orbital maneuver problem with continuous radial thrust on the chaser based on the generating function technique. Firstly, by using the relative direction cosine matrix, the two-body nonlinear relative motion equations with a continuous radial acceleration on the chaser are obtained in the target’s local-vertical-local-horizontal frame. Secondly, considering that the relative range is small, a dimension of the system is weakly controllable by analyzing the controllability of the system, and then the problem is simplified into a two-dimensional optimal control problem with integral and terminal constraints. Thirdly, the optimal control problem is transformed into a two-point boundary value problem by using the Pontryagin’s minimum principle. Then a proper form of the generating function is proposed, and the differential equations associated with initial conditions are derived. Finally, the initial value of the adjoint variable is obtained by solving an initial value problem. Two numerical examples are presented to illustrate the effectiveness of the proposed method, which has higher computational efficiency when compared with the direct optimization method.