First Test

This first test was made to assure that all the procedures are getting rightly done. This test was made with linear movement with total of 500 mm, horizontal to the camera sensor. The distance from the tip of optics to the "ground" was 200 mm and the velocity of the movement was 200 mm/s with a phase of acceleration at the beginning and deceleration at the end. The positions of the manipulator and the instants are registered through a Ethernet connection and simultaneously another computer does the frame's acquisition. The acquisition was set at 5000 Hz line rate. 

The texture used as "ground" was a piece of cork, as shown on figure 1, this texture is composed mostly of fine grain and should, in theory, represent a hard texture to find matches.

Figure 1 - Texture used as ground.

The calibration was done using the pattern described in the previous post. In the figure 2 there is presented one of the trials of the calibration process, the camera was adjusted until the spaces between the pairs of lines were all equal to assure that the sensor is truly horizontal to the movement of the robot. The field of view in this experiment was 51 mm.

Figure 2 - Process of the camera calibration

Two methods of correlation between consecutive frames were implemented. The Pearson product-moment correlation coefficient, used by [1] and the cross-correlation method using Fast Fourier transform, highly used in signal processing. Both the methods showed good results, although Pearson's correlation method has a high computational cost, so the cross-correlation method is the most suitable to process high quantity samples.

Results with the camera

With the sample of 5000 Hz were made various tests, one using the full sample at 5000 Hz, one at 2500 Hz, 1000 Hz, 500 Hz and 100 Hz.

At 5000 Hz the velocity calculated at all instants was zero, this is due to the very high sampling rate which caused the consecutive line to be very similar to the previous one and thus the pixel displacement to be zero. 

The results of the other tests made with the camera are shown below:

Velocity (mm/s) Vs Time (s) calculated at 2500 Hz

Velocity (mm/s) Vs Time (s) calculated at 1000 Hz

Velocity (mm/s) Vs Time (s) calculated at 500 Hz

Velocity (mm/s) Vs Time (s) calculated at 100 Hz

And the total displacement calculated is listed in the following table, the real displacement measured by the robotic manipulator was 500 mm.

Sample Rate [Hz]	Total Displacement [mm]
5000	0
2500	602.8706
1000	498.0863
500	498.0365
100	488.6283

[1] - "On modeling and control of omnidirectional wheels" by Viktor Kálmán