Category Archives: Physics

Setting up the Camera


Camera and image processing are crucial components of a successful soccer robot. Consequently, before we could even start to build our robot we had to make sure the camera of the N9 won’t bring any unexpected surprises. In particular, the important questions were:

  • Is the angle of view of the camera reasonably wide? Can we position the camera to see the whole field?
  • What about camera resolution. If we position a ball at the far end of the field (~5 meters away) will it still be discernible (i.e. at least 3-4 pixels in size)?
  • Can it happen that the frames are too blurry when the robot moves?
  • At what frame rate is it possible to receive and process frames?

Answering those questions is a matter of several simple checks. Here’s how it went back then.

Resolution and Angle of View

The camera at N9 is capable of providing video at a framerate of about 30Hz with different resolutions, starting from 320×240 up to 1280×720. Among those, there three options which make sense for fast video processing: 320×240, 640×480 and 848×480. The first two are essentially equivalent (one is just twice the size of the other). The third option differs in terms of aspect ratio, and its horizontal and vertical angles of view. The difference is illustrated by the picture below, which shows a measure tape shot from a distance of 10cm.

Different angles of view
Different angles of view

We can see that the resolution 848×480 provides just a slightly larger vertical angle of view than 640×480 (102mm vs 97mm) at the price of significantly reduced horizontal angle of view (65mm vs 86mm). Consequently, we decided to stick with the 640×480 resolution.

Camera positioning
Phone mounting angle

From the picture we can also estimate the angle of view, which is 2*arctan(97/200) ~ 52 degrees vertical and 2*arctan(86/200) ~ 46.5 degrees horizontal. Repeating this crude measurement produced somewhat varying results, with the horizontal angle being as low as 40 and the vertical as large as 60 degrees.

Knowledge that the vertical angle of view is 60 degrees suggested that the phone should also be mounted at around 60 degrees – this provided the full view of the field. As we also needed to see the ball in front of the robot, we had to mount the phone somewhat to the back.

Image Processing Speed

The first code we implemented was just reading camera frames and drawing them on the screen. The code could run nicely at 30 frames per second. Additional simple image operations, such as classifying pixels by colors also worked fine at this rate. Something more complicated and requiring multiple passes over the image, however, could easily drag the framerate down to 20 or 10 fps, hence we knew early on that we had to be careful here. So far it seems that we managed to keep our image processing fast enough to be able to work at 25-30 fps, but this is a topic of a future post.

Camera Speed

One reason why the Playstation 3 Eye camera is popular among Robotex teams is that it can produce 120 frames per second. And it is not the framerate itself, which is important (it is fairly hard to do image processing at this rate even on the fastest CPUs). The important part is that the frames are shot faster and thus do not blur as much when the robot moves. So what about our 30 fps camera? Can it be so blurry as to be impractical? We used our NXT prototype robot (at the time, we did not have our “real” robot, not even as a 3D model) and filmed its view as it drove forward (at 0.4 m/s) or rotated (at about 0.7 revolutions per second). The result is shown below:

Moving forward
Moving forward

The results are quite enlightening. Firstly, we see that there is no blurring problems with the forward movement. What concerns rotation, however, it is indeed true that even for a moderate rotation speed, anything further away than 50cm or so blurs to be indistinguishable. It is easy to understand, however, that this is not so much a limitation of a 30fps camera but rather a property of rotation itself. At just one revolution per second, objects even a meter away are already flying through the picture frame at 6.28 m/s. Even a 120fps camera won’t help here.

Size of the Ball in Pixels

OK, next question. How large is the ball at different distances? To answer that, we made a number of shots with the ball at different distances from the camera and measured the size of the ball in pixels. The results are the following:

Distance to ball (mm) 100 200 300 400 500 600 700 800 900 1000
Ball diameter in pixels (px) 190 105 70 55 45 37 33 29 26 22
Distance vs Pixel size
Distance vs Pixel size

This data can be described fairly well using the following equation (the reasons for this are a topic of a later post):

PixelSize = 23400/(21.5 + DistanceMm)

Two observations are in order here. Firstly, a ball at distance 5m will have a pixel size of about 4.65 pixels, which not too bad. Note that it would be bad, though, if we were to use a resolution of 320×240, as then it would be just 2 pixels. Add some blur or shadows and the ball becomes especially hard to detect. Secondly, and more importantly, if we decide to use such an equation to determine the distance to the ball from its pixel size, we have to expect fairly large errors for balls that are further away than a couple of meters.

So that’s it. Now we’ve got a feel of the camera and ready for actual image processing.

Physics 101 – Measuring ball movement

In order to plan the robot (e.g. choose the motors and plan the strength of the coilgun) as well as to implement the simulator, we needed to know the movement dynamics of the golf balls on the field. There is nothing special about their movement – we can safely assume that balls roll with a constant deceleration. The problem is, however, that no one seemed to be able to tell us, even approximately, what this deceleration was exactly.

So we went on and made a crude measurement using the camera, which, in retrospect, is fun to think about. Here’s how it was done.

Measuring ball movement
Measuring ball movement

First, set up a straight path for the ball, marking the 0cm, 50cm, 100cm and 150cm points. We would then roll the ball along this path, measure the time when it passed the four points, and use the obtained numbers to fit the parameters of the equation:

s = v0 + v(t-t0) + 0.5a(t-t0)2

There are three unknowns here (v0, v, a) – that’s why we need three marks plus the starting mark (t0) for each measurement (i.e. for each ball run).

Next, we use a camera to film a number of such “ball runs” from the side. Finally, we manually examine the resulting video frames, writing out the time points at which the ball passed each of the marks.

As a side note, if anyone of you, dear readers, for some reason plans on doing something similar at some point of their life, here’s what you should do to find out the timestamps of the frames in a video:

  • Install the ffdshow codec. In FFDshow configuration switch on “OSD” (on-screen display) and on the corresponding settings screen put a checkmark near “Frame timestamps”.
  • Install Media player classic. In its configuration, switch off all “Internal Filters” and add as “External Filter” the ffdshow Video Decoder. After that, just play the video using this player. You will see frame timestamps and will be able to move frame-by-frame back and forth using the Ctrl+left/right keys.
A video frame of a moving ball
A video frame of a moving ball

Obviously, this type of measurement is very crude, however for our purposes it is enough. After having manually “parsed” a video recording of five runs we obtain the following data table:

      T0     T1     T2     T3
1 15.244 15.840 16.598 17.804
2 26.327 26.651 27.100 27.566
3 35.219 35.570 36.020 36.500
4 43.604 44.080 44.638 45.260
5 51.963 52.500 53.182 54.047

The rows here correspond to different runs and the columns – to the four marked points. The values in the cells are timestamps (in seconds from the start of the video).

At last, we fit the movement equation for each row to estimate the “a” parameter. We can do it using R, for example, as follows:

data = data.frame(T0 = c(15.244, 26.327, 35.219, 43.604, 51.963),
                  T1 = c(15.840, 26.651, 35.570, 44.080, 52.500),
                  T2 = c(16.598, 27.100, 36.020, 44.638, 53.182),
                  T3 = c(17.804, 27.566, 36.500, 45.260, 54.047));
for (i in 2:4) data[,i] = data[,i] - data[,1]
data$T0 = NULL
a = c()
for (i in 1:nrow(data)) {
  y = c(0.5, 1.0, 1.5)
  x = t(data[i,])
  x2 = t(data[i,]^2)/2
  m = lm(y~x + x2)
  a = c(a, m$coeff[3])

# Median and max a

From that we get that the median deceleration of the five runs is  -0.15 m/sand the smallest estimated value was  -0.25 m/s2.

Now we may use this value in the simulator and consider it when choosing the motors.