assigned the portions

documentation/Ahmed/approach.tex

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+\section{Ball Approach}
+\label{p sec approach}
+
+\subsection*{Approach from the Side}
+
+The first possibility is that in the approach planning stage, described in the
+section \ref{j sec approach planning}, the decision was taken to approach the
+ball from the side. In this case the robot will walk the calculated distance in
+the calculated direction. Normally, after the movement the robot should lose
+the sight of the ball. However, the approximate angle, where the ball should be
+relative to the robot after the movement, is known. Therefore, the robot will
+rotate by that angle and will then try to detect the ball and turn to it, using
+the \textbf{Turn to Ball} algorithm, described in the section \ref {j sec
+  turning to ball}. Once this was done, the approach planning stage is
+repeated. Normally, the distance to the ball should now be small, and the ball
+and the goal should lie in the same direction, which means that only short
+direct approach at this point will be necessary. That might not always be the
+case, so in rare situations another step of the approach from the side might be
+required.
+
+\begin{figure}[ht]
+  \includegraphics[width=\textwidth]{\fig after-sideways}
+  \caption{After approach from the side}
+  \label{p figure after-sideways}
+\end{figure}
+
+\subsection*{Direct Approach}
+
+It is also possible that the decision will be taken to approach the ball
+directly, either from the start or after the robot already has approached the
+ball from the side. In this stage the robot will walk towards the ball trying
+to stay centered at it. To do so, it will be constantly checked that the ball
+stays within some tolerance angle from the center of the camera frame. If the
+ball moves from the center further than by the tolerance angle, then the robot
+will stop moving, will adjust the movement direction and then will go further.
+The robot will continue moving until the ball is close enough to start the goal
+alignment. Do determine if that is the case, we don't use trigonometry, but
+simply define a threshold, which the image of the ball in the robot's lower
+camera should reach. The threshold is visualized in figure \ref{p figure
+  direct-approach}. Once this has happened, the approach stage is over and the
+robot will start aligning itself to the goal.
+
+\begin{figure}[ht]
+  \includegraphics[width=\textwidth]{\fig direct-approach}
+  \caption{Approach termination condition}
+  \label{p figure direct-approach}
+\end{figure}

documentation/Ahmed/galign.tex

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+\section{Goal Alignment}
+\label{p sec goal align}
+
+After the approach, described in the section \ref{p sec approach}, is finished,
+the robot is facing the ball, and the ball is at a short distance. In the stage
+of goal alignment, the task is to ensure that from the robot's point of view
+the ball lies between the goalposts. This means, that when the robot is
+centered at the ball, the goalposts should lie on either side of the center of
+the camera image. So the robot will first detect the goal and determine if that
+is the case. If that is not the case, the robot will go around the ball in a
+circle in the appropriate direction, until the ball is indeed between the
+goalposts.
+
+The walk in circle was implemented in the following way: the robot will step
+several steps sideways, then will turn to ball, as described in the section
+\ref{j sec turning to ball}, and finally will adjust the distance to the ball
+by stepping forwards or backwards, so that the ball is neither too close nor
+too far. The distance to the ball, similarly to the stage of the direct
+approach, is not measured explicitly, but is approximated through the position
+of the ball image in the camera frame. After performing these steps, the check
+is performed, if the goal alignment is completed. Otherwise, the steps will be
+repeated until alignment is achieved. The figure \ref{p figure goal-alignment}
+depicts the successful completion of this stage.
+
+\begin{figure}[ht]
+  \includegraphics[width=\textwidth]{\fig goal-alignment}
+  \caption{Successful goal alignment}
+  \label{p figure goal-alignment}
+\end{figure}