1. Maryam Alizadeh Feb 4 th 2011 1

2.  Introduction  Characterizing the error › Initial position › Sampling rate of camera › ECG  Future work 2

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4. Purpose:  Servoing and Tracking the moving object (ball) using a 2-dof model helicopter 4

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6.  This model is able to match centroid of the ball and the desired point regardless of the distance between the camera and the blue background and also the initial position of the ball.  There is an error between the desired point and ball center.  This error is much more in ‘X’ direction than ‘Y’ direction 6

7.  Following figures show the Ball centroid pixel coordinate error vs Time.  In these experiments, the ball does not move. (Servoing Mode)  In upper graphs, distance between camera and background is 25 inches and in lower ones, this distance is equal to 35 inches. 7

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9. Characterizing the error which exist between the desired point and centroid of the ball Parameters which are changed:  Initial position  Sampling rate of camera  ECG 9

10.  Firstly, some random locations were chosen in order to find the effect of “Ball Initial Position”.  Graphs show the square root of sum of squares of Errors in X and Y direction VS Time in different initial positions,[ (e x 2 + e y 2 ) 0.5 ]. 10

11. Initial position: 97, 277 Initial position: 219, 12 11

12. Initial position: 212, 231 Initial position: 184, 232 12

13.  Then, locations were selected that are in the same line with the desired point, in X direction or in Y direction.  These case’s graphs are approximately similar to graphs which are related to a random initial position 13

14. Initial position: 119, 36 Initial position: 121, 245 Initial position: 45, 101 14

15. Initial position: 27, 163 15 Trajectory of centroid of the ball Total error

16.  Initial position does not have any effect on existing error  The most part of error is related to difference in X direction 16

17.  This camera is able to produce up to 30 frames per second  All of these sampling rates are tried: 2,3,4,…..,15,.....30  Following plots illustrate the total error VS time for different sampling rates (FPS) 17

18. SR = 1/2SR = 1/7 SR = 1/12 18 FPS=2 FPS=12 FPS=7

19. SR = 1/17SR = 1/22 SR = 1/27 19 FPS=17FPS=22 FPS=27

20.  Next graph shows RMS(Root Mean Square) of total error VS Sampling Rate (FPS)  It is obvious that there is no specific treatment by increasing sampling rate. 20

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22.  By increasing ECG, the helicopter fluctuates very much around the centroid of the ball and doesn’t courage to it. (for ECG greater than 0.1) 22

23. 23 ECG = 0.2 Trajectory of centroid of the ball Total error

24. ECG = 0.25 24 Trajectory of centroid of the ball Total error

25.  And by decreasing ECG, nevertheless, the fluctuation disappear around the centroid of ball, the race of helicopter decreases.  Total error VS time for different values of ECG is shown in following plots. (ECG less than 0.1) 25

26. ECG = 0.1 ECG = 0.08 ECG = 0.06 26

27. ECG = 0.04 ECG = 0.01 27

28.  Assuming this system as a second order system  Finding poles of that system  Designing another controller to optimize the results 28