All tracking is done in pixel coordinates, but the behavior control needs the positions of the objects in a standard coordinate system. The origin of that system is located in the middle of the field and its length corresponds to the interval [-1, 1]. The width of the standard system is chosen such that the aspect ratio of the field is preserved.
A linear coordinate transformation is not sufficient, since the camera produces distortions. We model them for the four quadrants of the field using eight positions located at the fields corners and in the middle of the walls (see Figure 4). The central point is computed from the intersection of the two lines connecting the wall centers that become the axis of the standard system.
In each quadrant, we perform a bilinear interpolation between its corners. We also account for the different heights of the objects by multiplying the transformed coordinates with a suitable factor. The described transformation models the non-linearities of the camera sufficiently.
