Coplanar Low-Thrust Transfer with Eclipses Using Analytical Costate Guess

TL;DR

This paper introduces an analytical costate guess for optimizing coplanar low-thrust orbital transfers with eclipses, simplifying the process and ensuring global optimality across various thrust levels and eclipse scenarios.

Contribution

It proposes a novel analytical costate guess that reduces the optimal control problem to an unconstrained minimization, enabling efficient and global solutions without prior guess dependence.

Findings

The method works for a wide range of thrust levels.

It handles any eclipse configuration effectively.

The approach achieves solutions in a few minutes.

Abstract

Low-thrust orbital transfers are difficult to optimize by indirect methods. The main issues come from the costate guess and from the numerical propagation accuracy required by the shooting method. In the case of a coplanar minimum-time low-thrust transfer with eclipses, an analytical costate guess is proposed. The optimal control problem reduces to an unconstrained minimization problem with two unknowns. A derivative-free algorithm yields a quasi-optimal solution from scratch in a few minutes. No specific guess is necessary and the algorithm properties ensure finding the global minimum of the unconstrained problem. The method is applicable to thrust levels from large to very low and to any eclipse configuration, as exemplified on a transfer towards the geostationary orbit.