Mapped Adjoint Control Transformation for Low-Thrust Space Mission Design

Abstract

Spacecraft trajectory optimization is an essential task in space mission design. The propulsion system of the spacecraft can affect the type of trajectories that can be realized by a spacecraft. In the past few decades, electric propulsion systems (with their characteristic high specific impulse values, but low thrust magnitudes) have revolutionized space trajectories. Low-thrust trajectory design can be converted into boundary-value problems, which are typically challenging to solve because of a small domain of convergence and lack of knowledge about the initial costates when indirect formalism of optimal control is adopted. Estimating missing values of the non-intuitive costates is an important step in solving the resulting boundary-value problems. In this thesis, the initial costates are obtained using two methods: 1) random initialization, and 2) when costate initial values are constrained to lie on a unit 8-dimensional hypersphere. Minimum-fuel trajectories are designed for a heliocentric maneuver from Earth to comet 67P/Churyumov–Gerasimenko. The two costate initialization methods are compared against each other in terms of the percent of convergence and accuracy of the results of the associated boundary-value problems. After this analysis, the Adjoint Control Transformation costate initialization method is considered. By leveraging costate vector mapping theorem, the method of Adjoint Control Transformation (ACT) is extended to alternative sets of coordinates/elements for solving low-thrust trajectory optimization problems, called Mapped Adjoint Control Transformation (MACT). The development of MACT is the main contribution of this thesis. In particular, this extension is applied to the set of modified equinoctial elements and an orbital element set based on the specific angular momentum and eccentricity vectors (h-e). The computational and robustness efficiency of the MACT method is compared against the traditionally used random initialization of costates by solving 1) interplanetary rendezvous maneuvers, 2) an Earth-centered, orbit-raising problem with and without the inclusion of J2 perturbation, and 3) an Earth-centered, orbit-raising problem with a relatively large number of revolutions around the central body. For the considered problems, numerical results indicate two to three times improvement in the percent of convergence of the resulting boundary-value problems when the MACT method is used compared to the random initialization method. Results also indicate that the h-e set is a contender and suitable choice for solving low-thrust trajectory optimization problems.