Low-thrust spacecraft trajectories optimization by linearization method

Mathematica modeling, numerical technique and program complexes


Аuthors

Vernigora L. V.*, Kasmerchuk P. V.**

Lavochkin Research and Production Association, NPO Lavochkin, 24, Leningradskay str., Khimki, Moscow region, 141400, Russia

*e-mail: vlv@laspace.ru
**e-mail: pavel.kazmerchuk@gmail.com

Abstract

Problems of a low thrust spacecraft trajectories optimization are rather complicated problems of nonlinear optimization in the presence of constrains. The authors suggest applying linearization method modified for compound dynamic systems optimization for solving them. The Modified Method of a Linearization (MML) is quite a general method of nonlinear optimization problems solution. However, specifics of trajectory optimization problems of a low thrust spacecraft require confirmation of the MML application possibility to solve them. Two problems are being solved in this work:

- A flat flight optimization of a spacecraft with electric propulsion unit (EPU) and a solar sail between the Earth and Mars orbits;

- An optimization problem of a flight between two arbitrary non-coplanar near-Earth orbits.

The obtained results were compared to the results obtained by other authors.

The flat flight optimization problem of a spacecraft with EPU and a solar sail between the Earth and Mars orbits was solved for the two values of dimensionless initial acceleration of 1.0 and 0.02. An error of 0.37% in term of criterion, and 0.32% in the flight range angle was obtained for the first problem. In the second problem, the flight range angle error was 4.9%. The criterion value agreed within the put forward significant figures. In the flat flight optimization problem of a spacecraft with EPU and a solar sail between the Earth and Mars the results obtained with MML are better than the results obtained by the majority of other authors in the sense of criterion value. In the optimization problem of elliptic-to-geostationary orbit transfer for minimum time the obtained error in the criterion value was 0.05%, and control and trajectory nature coincided with the considered work.

Based on a number of the well-known examples the article demonstrates the MML steady work while solving the offered problems of trajectory optimization of a low thrust spacecraft with EPU and solar sail. A close agreement of the results with the results of other authors was obtained. This allows make conclusion on the possibility of MML application for solving the regarded classes of the trajectory optimization problems for low thrust spacecraft. The main advantages of the method are the large area of the solution convergence, which allows selecting trivial initial approximations, operating in terms of the loop problem without the necessity of obtaining additional structures of the transversability condition type etc. Rather slow convergence in the problem of transfering a spacecraft with EPU between two noncoplanar orbits, associated with the necessity of selecting a small-size area of the acceptable variations (the area in which the linear programming problem is being solved) to ensure the acceptable linearization level may be related to the shortcomings.

Keywords:

linearization method, low thrust, nonlinear optimization

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