\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}