178 lines
7.9 KiB
TeX
178 lines
7.9 KiB
TeX
\documentclass{article}
|
|
|
|
\usepackage{graphicx}
|
|
\usepackage{mathtools}
|
|
\usepackage{geometry}
|
|
\usepackage{setspace}
|
|
|
|
\geometry{left=1in, right=1in, top=1in, bottom=1in}
|
|
\doublespacing
|
|
|
|
\begin{document}
|
|
|
|
\title{This Will Be The Title Page}
|
|
\author{Richard Connor Johnstone}
|
|
|
|
\maketitle
|
|
|
|
\newpage
|
|
|
|
This will be the copyright page.
|
|
|
|
\newpage
|
|
|
|
This will be the signature page.
|
|
|
|
\newpage
|
|
|
|
This will be the Acknowledgments.
|
|
|
|
\newpage
|
|
|
|
\begin{abstract}
|
|
|
|
This will be the overview/summary/abstract page
|
|
|
|
\end{abstract}
|
|
|
|
\newpage
|
|
|
|
\tableofcontents
|
|
|
|
\newpage
|
|
|
|
\section{Introduction}
|
|
Provide some historical background, motivations, and discussion of the basic problems being investigated. Also a brief overview how the thesis will be laid out.
|
|
|
|
\section{Trajectory Optimization}
|
|
This section will outline the foundational problem of trajectory optimization.
|
|
|
|
\subsection{The Two-Body Problem}
|
|
Propose the two-body problem as a differential equation.
|
|
|
|
\subsubsection{Kepler's Equations}
|
|
Detail Kepler's equations for astrodynamics.
|
|
|
|
\subsection{Analytical Solutions to Kepler's Equations}
|
|
Discuss how, since the 2BP is analytically solveable, there exists algorithms for solving these equations.
|
|
|
|
\subsubsection{LaGuerre-Conway Algorithm}
|
|
Step through the LaGuerre-Conway algorithm, as it's used in this implementation.
|
|
|
|
\subsection{Non-Linear Problem Optimization}
|
|
Discuss the concept of a non-linear problem as it related to the study of optimization.
|
|
|
|
\subsubsection{Non-Linear Solvers}
|
|
Mention common non-linear solvers (Ipopt, SNOPT, etc.).
|
|
|
|
\subsubsection{Newton Trust-Region Method}
|
|
Discuss how the Newton Trust-Region method works.
|
|
|
|
\subsubsection{Linesearch Method}
|
|
I may take this section out, because I'm not currently using a linesearch. But I would cover the additions of linesearch methods.
|
|
|
|
\section{Low-Thrust Considerations}
|
|
Highlight the differences between high and low-thrust mission profiles.
|
|
|
|
\subsection{Low Thrust Overview}
|
|
Dive deeper into the concept of low thrust trajectories, highlighting the added trouble with propagation/integration.
|
|
|
|
\subsection{Sims-Flanagan Transcription}
|
|
Reveal the advantages of Sims-Flanagan transcription as an alternative to higher-fidelity propagation models. Be sure to mention its uses in many legitimate places.
|
|
|
|
\section{Interplanetary Trajectory Considerations}
|
|
Highlight the problems with the 2BP in co-ordinating influences of extra bodies over an interplanetary journey.
|
|
|
|
\subsection{Patched Conics}
|
|
Describe the method of patched conics.
|
|
|
|
\subsection{Gravity Assist Maneuvers}
|
|
Describe how a gravity assist maneuver would work in the framework of patched conics. Also discuss the advantages of such a maneuver.
|
|
|
|
\subsection{Multiple Gravity Assist Techniques}
|
|
Discuss the advantages of chaining together multiple gravity assists and highlight the difficulties in choosing these assists. Here I can mention porkchop plots, Lambert's problem, etc. Here I can also talk about Hybrid Optimal Control Problems.
|
|
|
|
\subsection{Ephemeris Considerations}
|
|
I can quickly mention SPICE here and talk a bit about validation.
|
|
|
|
\section{Genetic Algorithms}
|
|
I will probably give only a brief overview of genetic algorithms here. I don't personally know that much about them. Then in the following subsections I can discuss the parts that are relevant to the specific algorithm that I'm using.
|
|
|
|
\subsection{Decision Vectors}
|
|
Discuss what a decision vector is in the context of an optimization problem.
|
|
|
|
\subsection{Selection and Fitness Evaluation}
|
|
Discuss the costing being used as well as the different types of fitness evaluation that are common. Also discuss the concept of generations and ``survival''.
|
|
|
|
\subsubsection{Tournament Selection}
|
|
Dive deeper into the specific selection algorithm being used here.
|
|
|
|
\subsection{Crossover}
|
|
Discuss the concept of crossover and procreation in a genetic algorithm.
|
|
|
|
\subsubsection{Binary Crossover}
|
|
Discuss specific crossover algorithm used here.
|
|
|
|
\subsubsection{Mutation}
|
|
Discuss both the necessity for mutation and the mutation algorithm being used.
|
|
|
|
\section{Algorithm Overview}
|
|
Highlight the algorithm at a high-level. This is likely where flowcharts and diagrams will go to give a high-level overview.
|
|
|
|
\subsection{Trajectory Composition}
|
|
Discuss briefly the nomenclature used in defining these trajectories. Currently this isn't ``baked in'' to the code, so I have some freedom to adopt Englander's notation or use my own (since my intended use case is a little simpler).
|
|
|
|
\subsection{Inner Loop Implementation}
|
|
Give a better overview of the inner loop specifically. Probably this section will have a more in-depth flowchart.
|
|
|
|
\subsubsection{LaGuerre-Conway Kepler Solver}
|
|
Discuss how the LaGuerre-Conway algorithm is used in the code to provide a fundamental ``natural trajectory'' between two quantized, but not necessarily close points. Mention validation.
|
|
|
|
\subsubsection{Sims-Flanagan Propagator}
|
|
Discuss how this algorithm can then be expanded by using SFT to propagate any number of low-thrust steps over a specific arc. Mention validation. Here I can also mention the ``Sc'' object and talk about how those parameters were chosen and effected the propagator.
|
|
|
|
\subsubsection{Non-Linear Problem Solver}
|
|
Mention the package being used to solve NLPs and how it works, highlighting the trust region method used and error-handling. Mention validation.
|
|
|
|
\subsubsection{Monotonic Basin Hopping}
|
|
Outline the MBH algorithm, going into detail at each step. Mention the long-tailed PDF being used and go into quite a bit of detail. Englander's paper on the MBH algorithm specifically should be a good guide. Mention validation.
|
|
|
|
\subsection{Outer Loop Implementation}
|
|
Overview the outer loop. This may require a final flowchart, but might potentially be too simple to lend itself to one.
|
|
|
|
\subsubsection{Inner Loop Calling Function}
|
|
The primary reason for including this section is to discuss the error handling.
|
|
|
|
\subsubsection{Genetic Algorithm Description}
|
|
Similar to the MBH section, there are a lot of implementation details to go over here. Many will have already been discussed in the background sections above. But I can step through each of the decisions, similar to Englander's paper on this.
|
|
|
|
\section{Results Analysis}
|
|
Simply highlight that the algorithm was tested on a sample trajectory to Saturn.
|
|
|
|
\subsection{Sample Trajectory to Saturn}
|
|
Give an overview of the trajectory that was ultimately chosen.
|
|
|
|
\subsubsection{Comparison to Less Optimal Solutions}
|
|
I should have a number of elite but less-optimal solutions. Honestly, I may write the algorithm to keep all of the solutions to provide many points of comparison here.
|
|
|
|
\subsubsection{Cost Function Analysis}
|
|
Give some real-world context for the mass-use, time-of-flight, etc.
|
|
|
|
\subsubsection{Comparison to Impulsive Trajectories}
|
|
I may also remove this section. I could do a quick comparison (using porkchop plots) to similar impulsive trajectories. Honestly, this is a lot of work for very little gain, though, so probably the first place to chop if needed.
|
|
|
|
\section{Conclusion}
|
|
\subsection{Overview of Results}
|
|
Quick re-wording of the previous section in a paragraph or two for reader's convenience.
|
|
|
|
\subsection{Applications of Algorithm}
|
|
Talk a bit about why this work is valuable. Missions that could have benefited, missions that this enables, etc.
|
|
|
|
\subsection{Recommendations for Future Work}
|
|
Recommend future work, obviously. There are a \emph{ton} of opportunities for improvement including parallelization, cluster computing, etc.
|
|
|
|
% \bibliography{biblio}{}
|
|
% \bibliographystyle{plain}
|
|
|
|
\end{document}
|