A trajectory optimization method to solve a problem of spacecraft insertion into geostationary orbit using electric thrusters

Аuthors

Konstantinov M. S.^*, Min T. ^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: mkonst@bk.ru
**e-mail: minnntheino@gmail.com

Abstract

This paper describes the trajectory optimization method for spacecraft insertion into geostationary orbit (GSO) with the use oj electric propulsion. Special efforts are made to provide regularization for the solving of the boundary value problems of optimal control. By applying the Pontryagin 's maximum principle, the low-thrust trajectory optimization problem is reduced to the boundary value problem for the ordinary differential equations system. The core sense of the boundary value problem is the solution of the non-linear system of equations. To solve the non-linear system of equations, we offer to use the hybrid method which combines the Levenberg — Markquardt method with the quasi-Newton method. We compare the effectiveness of this method with the use of the continuation method on parameter which offered in the works by V.G. Petukhov. The numerical results of the spacecraft's trajectory into GSO and the effectiveness of the electric propulsion application for such insertion are presented. Two factors are considered as the criteria of optimization — the time of flight (which is minimized for minimum-time transfer problem) and terminal mass of the spacecraft (which is maximized for fixed-time transfer problem).

Keywords:

spacecraft, geostationary orbit, boundary value problem, electric propulsion