Proposal to Participate in RoboCup 2010 Standard Platform League ...

When a camera is located at a fixed position, the real positions of the objects inside its field of view
will have a relation with the positions of them in the picture the camera captures. Consider a camera
as a simple convex lens, for most cases; the objects are beyond the camera’s focus length which
indicates that a real image is formed in the camera’s CMOS. For a 2-D system, regardless an object’s
geometry, i.e. regard it as a point and take the camera as the original point, the relation between the
real object and the image should be as follows.
Figure 5. Vision computation in NAO
The position of the real object A lies in the line determined by the origin and the image A’, and the
relation of the coordinates are
where α is the magnification of the lens of the camera (negative value), which is determined by the
focus length of the lens when the focus length is far less than the object length.
For a 3-D situation, viewing the match from the top, the situation is similar to a 2-D one. The
coordinates system can be changed with a polar coordinate system with the relation remains. Based on
this relation, we can change the configuration of the face detection function such that it detects other
NAO robots’ rather than human face, simultaneously, the configuration of logo detection can also be
change into the detection of balls in the match. The result of the detections can thus be taken from
NAO’s memory and used to analysis the position of ball and other robot.
For the case above, when the ball is detected, the position of the cross is stored in the memory. With a
resolution of 640x480, the vector between the center of the image and the center of the cross can be
obtained by math operation. The horizontal portion thus indicate the direction the robot need to turn
and the magnitude can be used to calculated the angle to turn by the relation below:
=
where the result is in degree, the constant 320 is half of the horizontal resolution and 28 is half of the
view of field of the camera in NAO. The vertical portion is related to distance the NAO need to walk.
Assume the NAO is looking horizontally; the position will always fall below the center line of the
image, which means the vertical portion of the vector is always negative. However, in this case the
position of the ball is hard to found by performing a simple math calculation. If the angle between the
axis of NAO’s camera and the horizontal line is α, given the height of the camera h, the distance
between the bottom of the image and the center can be found by
where h/tan(α) is the distance from the feet of the robot to the point where the axis of the camera meet
the ground, the constant of 17.25 is half the camera’s vertical view range, thus the second part is the
distance between the robot’s feet to the view limit of the camera. The distance traveled then can be set
as every resolution in the vector roughly is 1/240 of d.