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I made some investigation on the trend of this error. The results are shown in in error_trend.png. In the figure, "x_loc" indicate the x coordinate in pixels in the local coordinate system of the camera (i.e. the horizontal one), while "x_glob" is the x coordinate in cm in the global coordinate system. Remember that the axises of the local and the global coordinate systems are inverted. Data where gathered for two cameras.
Solution
I decided to consider the error linear along both direction and try to apply a linear correction to the computed global coordinates error along both direction. The The correction is thus applied in the form err = a*x_loc*y_loc + b*x_loc + c*y_loc + d. The parameters a, b, c, d are computed by the CPS on start by loading a file where the real global coordinates of four points must points must be saved. This is the procedure that must be followed to configure this file. This procedure must be repeated for each camera. It is calibration-independent, meaning that you do not have to repeat it if you have to perform a new instrinsic/extrinsic calibration, but if the camera is moved, the procedure must be done again.
- Set the variable RECORDvariable RECORD_OBJECT_DATA = 1 in the file CPS.h in the computer responsible for the camera that you want to configure and compile it. For information about compiling the CPS, check the the original lab documentation.
- Run CPS.exe. The RECORD_OBJECT_DATA mode was designed to take pictures of the cars symbols so it will ask you the car number and the section number, just put a negative number. The only thing you must insert correctly is the camera number that you want to configure.
- Determine the four points to record. Considering the error trend, the four points should be should be chosen to form the broadest rectangle of interest, that is the rectangle with the biggest area contained in the camera view where the car can be tracked. To To clarify, an example of how to choose the points is found in point_selection.png. Walls, obstacles and the end of the sections limit the rectangle. The console gives you information about the pixel coordinates of the top left corner of the small squared boxes, in the figure it is located close to (x2, y2). You can move that box with keys "a", "s", "d" and "w". Write down the pixel coordinates of those four points.
- Now measure the global position of those four points with a measure tape and record them. You should now have written down 4 pixel coordinates (x1, y1, x2, y2) and 8 global coordinates, 2 for each point of the rectangle. Pay attention when writing down the global coordinates. Since the x and y axises of the local and the global coordinate system are inverted, it is easy to make confusion.
- Open the folder "Desktop/camera_programs/Andrea CPS/calib_data". There 5 files called "error_camx.txt", where "x" is the number of the camera. Open the one that refers to the camera you are configuring. The format of the file is very easy to understand and consistent with this explanation. Write there the pixel coordinates of x1, y1, x2, y2 and the global coordinates of those points.
- Now you can set RECORD_OBJECT_DATA to 0 and you are good to go.
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Figure pwm.png shows the speed of the car obtained by keep the steer constant and varying the PWM. The relationship between PWM and velocity is quite linear. For some reason, when the steer input is high, the speed observed with PWM 140 is slightly lower than I would expect. On On the other hand, the steer effect seems to be a little bit more complicated (see steer.png). Velocities observed for steer 92 and 120 are always very close. This may be due to the fact that curvature radius for the two steer input are very similar (the curvature radius is not linear with respect to the steer signal). Still the speed is not linear w.r.t. the curvature radius because the discrepancy between the speed for steer 36 and 64 (which I measured to have respectively a curvature radius of roughly 200cm and 100cm) tends to be reduced by decreasing the PWM.
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- Experiment 1: the initial voltage was kept constant while varying the pwm signal. The car is run twice in a row for 250 seconds from a starting voltage of 16.8V (turned off). See figure figure experiment1.png. The speed always reaches a peak and then decrease to a steady state value. The second run starts more or less from the steady state value. The PWM does not seem to affect neither the time constant nor the steady state value that is more or less always 200 mm/s below the peak.
- Experiment 2: the pwm was kept constant while varying the initial voltage. The car is run only once. See figure figure experiment2.png. From starting voltage 16.9V to 16.5V the speed has basically the same trend. The steady state value and the constant time becomes lower below 16.4V.
- Experiment 3: the car is run 3 times in a row to check if the third time the speed dynamics changes again. See See experiment 3.png. The third time the car has the same behavior of the previous run.
- Experiment 5: the car is left turned on for 25 minutes before running to check if the capacitor gets discharged even if the car is not running. See See experiment 5.png. The car speed is not affected.
- Experiment 6: the car is run for 200 seconds, then it is left on for other 200 seconds without running and then run for other 200 seconds. See experiment 6.png. The car speed has the same peak as the previous run.
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