Numerical methods for low-thrust trajectory optimization

The spacecraft trajectory design process frequently includes the optimization of a quantity of importance such as propellant consumption or time of flight. A variety of methods for trajectory optimization are available, however the efficiency of an approach is dependent on the problem scenario it is applied to. Indirect and direct trajectory optimization methods are examined in this investigation with the goal of assessing the characteristics of each approach, and thereby determining the problem scenarios each is best suited for. Insight is gained from application of each optimization method to three sample problems; a circular-to-circular orbit transfer as well as two variants of a halo-to-halo orbit transfer, one that leverages manifold arcs and one that does not. The analytical theory underlying indirect optimization methods is presented as is the adjoint control transformation for determining initial costate values. Results from application of the indirect optimization approach to each of the sample problems are offered. The framework of a direct optimization scheme employing collocation is described including a mesh refinement process based on the de Boor update method. The direct optimization method is applied to the three sample problems and results are supplied. Quantitative comparisons of the results of the optimization methods are made based on the categories of accuracy, robustness, and efficiency. Findings from quantitative and qualitative comparisons of the optimization methods are employed to formulate guidelines on the problem scenarios each technique is most applicable to