\section{Guidance, Navigation and Control}
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\begin{frame}

  \frametitle{Rocket steering}
  
  Autonomous steering (of anything) requires 3 things:
  \begin{itemize}
    \item {\bf G}uidance - Where am I going?
    \item {\bf N}avigation - Where am I now?
    \item {\bf C}ontrol - How do I get from here to there?
  \end{itemize}
  
\end{frame}
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\begin{frame}

  \frametitle{Guidance: Where are we going, and why are we in a handbasket?}
  
  \begin{itemize}
    \item The trajectory (path) from ground to orbit.
    \item Plain old vanilla rocket science:
      \begin{itemize}
        \item Figure out the least energy solution to get you to orbit.
        \item 25 cent phrase: ``optimal orbital insertion trajectory''.
      \end{itemize}
    \item Mostly calculated in advance, depends on:
      \begin{itemize}
        \item Launch site location.
        \item Orbit you're trying to acheive.
        \item How your rocket works.
        \item The current atmospheric conditions (``weather'')
      \end{itemize}
  \end{itemize}
  
\end{frame}
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\begin{frame}

  \frametitle{Navigation: where are we really?}
  
  \begin{itemize}
    \item More precisely, what is the full inertial state of the rocket?
      \begin{itemize}
        \item position, velocity, acceleration
        \item attitude, rotational velocity, rotational acceleration
      \end{itemize}
    \item That's easy to figure out, right?
  \end{itemize}
  
\end{frame}
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\begin{frame}

  \frametitle{Navigation: No, this is the \emph{hard} part}
  
  \begin{itemize}
    \item Knowing your inertial state accurately is really, really, hard.
    \item \emph{This} is the problem we're most interested in trying to solve.
  \end{itemize}
 
  \begin{figure}
        \centering
        \includegraphics[width=0.5\textwidth]{images/broken_missile.jpg}
   \end{figure}   

\end{frame}
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\begin{frame}

  \frametitle{Navigation: IMU}
  
  \begin{block}{{\bf I}nertial {\bf M}easurment {\bf U}nit}
    \begin{itemize}
      \item 6 degrees of freedom (6 DOF) of movement
        \begin {itemize}
          \item 3 linear accelerometers (X, Y, Z)
          \item 3 rotational gyroscopes (roll, pitch, yaw)
        \end{itemize}
      \item But really {\bf 18} variables: $x$, $\dot{x}$, $\ddot{x}$, $y$, $\dot{y}$, $\ddot{y}$, $z$...
    \end{itemize}
  \end{block}
  
  \begin{itemize}
    \item Comercial strategic grade IMU's - Forget it.
    \item Comercial tactical grade IMU's - \$250,000.
    \item Roll your own extremely crappy IMU! Only \$200!!
        \begin {itemize}
          \item Crappy = drifts over time (integrates noise like $t^{2}$)
          \item Position accuracy is gone within 10's of seconds.
        \end{itemize}
  \end{itemize}
  
\end{frame}
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\begin{frame}

  \frametitle{Navigation: GPS}
  
  \begin{block}{{\bf G}lobal {\bf P}ositioning {\bf S}ystem}
    \begin{itemize}
      \item Provides relatively slow absolute position updates.
      \item Doesn't provide attitude
      \item Could lose signal and/or signal lock.
    \end{itemize}
  \end{block}
  
\end{frame}
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\begin{frame}

  \frametitle{Navigation: Other sensors}

  \begin{itemize}
    \item Magnetometers: 3D compasses, gives attitude but not position.
    \item Barometric altimeters: gives height above ground only.
    \item Image processing: Gives attitude, but probably not position.
  \end{itemize}

\end{frame}
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\begin{frame}

  \frametitle{Navigation: Each of these sensors... well... they suck.}

  \begin{itemize}
    \item No way to robustly get inertial state using individual sensors.
    \item But what if you could \emph{combine all} of the sensors?
  \end{itemize}

\end{frame}
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\begin{frame}

  \frametitle{Navigation: Data fusion, the magic sauce}

  \begin{itemize}
    \item Data fusion techniques allow us to optimally combine navigation sensors
      \begin{itemize}
        \item Absolute position of GPS corrects for IMU drift.
        \item Inertial state from IMU aids GPS correlator lock.
        \item Magneometer attitude aid gyroscope drift.
        \item barometric altimeter aid GPS and inertial height estimates.
       \end{itemize}
    \item Example data fusion techniques: Kalman filtering, particle filters, etc.
    \item Currently using Bayesian Particle Filters
  \end{itemize}

\end{frame}
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\begin{frame}

  \frametitle{Control: How do you steer this thing?}

  \begin{itemize}
    \item People with actual resources use thrust vector control (TVC).
      \begin{itemize}
        \item Gymballed nozzles, like on the space shuttle.
      \end{itemize}
    \item Poeple without so many resources use more crude methods:
      \begin{itemize}
        \item In the lower atmosphere, how about fins?
        \item In space, how about cold gas jets?
      \end{itemize}
  \end{itemize}
  
\end{frame}
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\begin{frame}

  \frametitle{Control: Who's got the steering wheel?}

  \begin{itemize}
    \item Control ``Closes the loop'' from navigation to guidance: from where we are to where we want to go.
    \item Inertial and aerodynamic models help predict what to do (e.g., model preditive control).
  \end{itemize}
  
\end{frame}
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