Optimization of a Low-Thrust Salvage Mission from a Highly Inclined Geostationary Transfer Orbit to a Geostationary Orbit

Abstract

A direct optimization method was used to flnd several three-dimensional minimum fuel trajectories from a highly inclined (51 degree) geostationary transfer orbit (GTO) to a geostationary orbit (GEO). To obtain GEO, two strategies were examined: 1) using an Earth-orbiting transfer, and 2) using a lunar gravity assist to remove the excess inclination. The solutions consisted of an initial non-optimized impulsive high-thrust burn, followed by optimized low-thrust burns. A single-shooting optimization strategy was used to solve the various transfer problems. In order to accommodate the many orbit revolutions of the Earth-orbiting transfer, a multiple-orbit thrust parameterization strategy was used to reduce the problem size. This strategy allows near-optimal solutions to be found for very large transfer problems. For the lunar swingby trajectories, the transfer problems were divided into two subproblems due to complexity involved in the swingby. Additionally, the complex-step derivative approximation was used to obtain high accuracy derivative information for the objective function and nonlinear constraints. This high accuracy derivative information was found to resolve some of the inherent sensitivity and lack of robustness present in the single-shooting method.