Lyapunov-based Low-thrust Optimal Orbit Transfer: An approach in Cartesian coordinates

TL;DR

This paper introduces a Lyapunov-based approach in Cartesian coordinates for low-thrust optimal orbit transfer, simplifying trajectory optimization by overcoming oscillation issues and enabling easier polynomial approximation compared to orbital elements.

Contribution

The paper proposes a novel Lyapunov-based initial guess method in Cartesian coordinates for low-thrust orbit transfer optimization, improving solution robustness and simplicity over traditional orbital element approaches.

Findings

Lyapunov-based initial guess improves optimization convergence.

Cartesian coordinates facilitate easier polynomial approximation.

Method successfully solves multiple low-thrust transfer problems.

Abstract

This paper presents a simple approach to low-thrust optimal-fuel and optimal-time transfer problems between two elliptic orbits using the Cartesian coordinates system. In this case, an orbit is described by its specific angular momentum and Laplace vectors with a free injection point. Trajectory optimization with the pseudospectral method and nonlinear programming are supported by the initial guess generated from the Chang-Chichka-Marsden Lyapunov-based transfer controller. This approach successfully solves several low-thrust optimal problems. Numerical results show that the Lyapunov-based initial guess overcomes the difficulty in optimization caused by the strong oscillation of variables in the Cartesian coordinates system. Furthermore, a comparison of the results shows that obtaining the optimal transfer solution through the polynomial approximation by utilizing Cartesian coordinates is easier than using orbital elements, which normally produce strongly nonlinear equations of motion. In this paper, the Earth's oblateness and shadow effect are not taken into account.