Submitted version of the thesis - Airlab, the Artificial Intelligence ...

124 Appendix B. Documentation of the programming
position=inv(K)∗image point ;
l=sqrt(xˆ2+yˆ2);
%l the distance of the origin point selected in the image to the robot
%% center
Dreal=200; %diameter of the ball in mm
Dpx=29; %pixel counter of diameter in image
%the f∗ constant pixel/unit (mm)
fstar = Dpx ∗ l / Dreal ;
%the position should be normalized since position (3) is not 1
position= position/norm( position );
Pc=[( fstar∗Dreal/Dpx)∗ position ;1];
inv(T cw∗T rw)∗Pc;
result= T wr∗T wc∗Pc;
result
%ans gives the position of the ball in real world in mm
% ans(1) x;ans(2) y;ans(3) z ; coordinates in real world
%% 2−) Calibration for the object at Ground
%tranlastion matrix−coming from image toolbox
Tc ext = [ 160.700069 27.498986 492.532634 ];
%rotation matrix−coming from image toolbox
Rc ext = [ −0.009783 −0.999883 −0.011800
−0.428525 0.014854 −0.903408
0.903477 −0.003781 −0.428620 ];
%transformation of camera to chess board
T cch=[Rc ext Tc ext ’];
% K internal camera parameters−from image toolbox
K=[191.71462 0 80.35911
0 191.27299 61.27650
0 0 1 ];
% x,y,z the distance of the chess board from the robots center in mm.
x=550;