From 0fb875c77705e9d5b313cbfe73167797eab61a0a Mon Sep 17 00:00:00 2001 From: Connor Date: Wed, 23 Mar 2022 08:23:37 -0600 Subject: [PATCH] Finalized. Wish me luck! --- LaTeX/presentation.tex | 93 ++++++++++++++++++------------------------ 1 file changed, 40 insertions(+), 53 deletions(-) diff --git a/LaTeX/presentation.tex b/LaTeX/presentation.tex index 224a2cc..ee367c2 100644 --- a/LaTeX/presentation.tex +++ b/LaTeX/presentation.tex @@ -35,10 +35,10 @@ \subsection{Motivation} - \begin{frame} \frametitle{Motivation} - How can we leverage existing technologies and techniques to determine - optimally-controlled trajectories to targets in interplanetary space? - \end{frame} + % \begin{frame} \frametitle{Motivation} + % How can we leverage existing technologies and techniques to determine + % optimally-controlled trajectories to targets in interplanetary space? + % \end{frame} \note{Today I'll be discussing my research in determining optimal trajectories for interplanetary mission objectives. Numerous scientific and engineering advances have @@ -96,50 +96,17 @@ thrust nature changes the underlying system dynamics that would have been used to optimize a mission such as Voyager, which did not employ low-thrust engines.} - % \begin{frame} \frametitle{Current tools} - % Indirect Methods: - % \begin{itemize} - % \item CHEBYTOP - % \item NEWSEP - % \item SEPTOP - % \item VARITOP - % \end{itemize} - - % Direct Methods: - % \begin{itemize} - % \item EMTG - % \item GALLOP - % \item MALTO - % \item PAGMO - % \end{itemize} - % \end{frame} - - % \note{However, many interesting techniques have been developed to combat this issue, - % particularly in recent years. A number of different algorithms have been developed } - - % \subsection{Scope} - - % \begin{frame} \frametitle{First Frame} - % \begin{itemize} - % \item Item 1 - % \item Item 2 - % \end{itemize} - % \end{frame} - - % \subsection{Problem Statement} - - % \begin{frame} \frametitle{First Frame} - % \begin{itemize} - % \item Item 1 - % \item Item 2 - % \end{itemize} - % \end{frame} + \begin{frame} \frametitle{Problem Statement} + For a given low-thrust engine, spacecraft parameters, and planetary flyby selections, + what is the optimal control thrusting profile, launch conditions, and flyby parameters + to arrive at a target outer planet? + \end{frame} \section{Trajectory Optimization Background} \subsection{System Dynamics} - \begin{frame} \frametitle{Two Body Problem} + \begin{frame} \frametitle{Dynamical Model: Two Body Problem} \begin{columns} \begin{column}{0.45\paperwidth} Assumptions: @@ -167,7 +134,7 @@ which it is orbiting. Secondly, both of these bodies are modeled as point masses with constant mass. This removes the need to account for non-uniform densities and asymmetry.} - \begin{frame} \frametitle{Two Body Problem} + \begin{frame} \frametitle{Dynamical Model: Two Body Problem} \begin{columns} \begin{column}{0.45\paperwidth} \begin{align*} @@ -187,7 +154,7 @@ \note{From Newton's second law and the law of universal gravitation, we can then model this force with this equation. Where...} - \begin{frame} \frametitle{Two Body Problem} + \begin{frame} \frametitle{Dynamical Model: Two Body Problem} \begin{columns} \begin{column}{0.45\paperwidth} \begin{equation*} @@ -206,7 +173,7 @@ \note{Dividing by the mass, we can derive the acceleration...} - \begin{frame} \frametitle{Two Body Problem} + \begin{frame} \frametitle{Dynamical Model: Two Body Problem} \begin{columns} \begin{column}{0.45\paperwidth} \begin{align*} @@ -228,7 +195,7 @@ parameter as a function of the planetary mass alone, rather than both combined. With this assumption, we can model the system dynamics with this analytically solvable equation} - \begin{frame} \frametitle{Kepler's Laws} + \begin{frame} \frametitle{Dynamical Model: Kepler's Laws} \begin{itemize} \item Each planet's orbit is an ellipse with the Sun at one of the foci. \item The area swept out by the imaginary line connecting the primary and secondary @@ -241,7 +208,7 @@ \note{In the early 1600s, Johannes Kepler determined three laws in order to describe the motion of a satellite. These are:} - \begin{frame} \frametitle{Kepler's Laws} + \begin{frame} \frametitle{Dynamical Model: Kepler's Laws} \begin{equation*} r = \frac{\sfrac{h^2}{\mu}}{1 + e \cos(\theta)} \end{equation*} @@ -263,7 +230,7 @@ actually take them a step further, producing the following extremely useful equations for representing spacecraft motion:} - \begin{frame} \frametitle{Kepler's Equation} + \begin{frame} \frametitle{Dynamical Model: Kepler's Equation} \begin{equation*} \frac{\Delta t}{T} = \frac{E - e \sin E}{2 \pi} \end{equation*} @@ -295,7 +262,7 @@ \subsection{Interplanetary Trajectories} - \begin{frame} \frametitle{Patched Conics} + \begin{frame} \frametitle{Interplanetary Trajectories: Patched Conics} \begin{figure}[H] \centering \includegraphics[height=0.7\paperheight]{LaTeX/fig/patched_conics} @@ -310,7 +277,7 @@ sub-trajectories, each governed by a distinct single body when the spacecraft is within the sphere of influence of that particular body...} - \begin{frame} \frametitle{Gravity Assist} + \begin{frame} \frametitle{Interplanetary Trajectories: Gravity Assist} \begin{figure}[H] \centering \includegraphics[height=0.7\paperheight]{LaTeX/fig/flyby} @@ -326,7 +293,7 @@ \subsection{Low Thrust Trajectories} - \begin{frame} \frametitle{Sims-Flanagan Transcription} + \begin{frame} \frametitle{Low Thrust Trajectories: Sims-Flanagan Transcription} \begin{columns} \begin{column}{0.45\paperwidth} \begin{itemize} @@ -351,7 +318,7 @@ trajectories with a single impulsive thrust in the center of each. Effectively, this allows...} - \begin{frame} \frametitle{Control Vector Description} + \begin{frame} \frametitle{Low Thrust Trajectories: Control Vector Description} \begin{columns} \begin{column}{0.45\paperwidth} \begin{align*} @@ -607,6 +574,26 @@ \section{Conclusion} + \begin{frame} \frametitle{Conclusion} + \begin{itemize} + \item Validation of direct approach to optimizing interplanetary, low-thrust + trajectories as non-linear programming problems + \item Validation of Monotonic Basin Hopping algorithm for finding global optima in the + same scenario + \item Application in a realistic sample mission revealed two effective trajectory + possibilities + \end{itemize} + \end{frame} + + \begin{frame} \frametitle{Future Work} + \begin{itemize} + \item Outer loop which chooses optimal flyby trajectories for increased automation + \item Parallelization would be effective for this problem + \item Better quantification of search space ``coverage'' by the monotonic basin hopping + algorithm + \end{itemize} + \end{frame} + \begin{frame} \begin{center} \begin{Huge}