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Evolutionary Design of a Control Architecture for Soccer-Playing Robots 213
units yield sufficient good results, larger networks do not decrease the net-
work’s error.
Since the time delay equals seven camera images the network has to make
its prediction for seven time steps in the future.
Fig. 16 plots the networks accuracy when predicting more than one
timestamp. It can be seen that the accuracy drastically degrades beyond
eleven time steps.

4 Local Position Correction

Another approach to solve the latency problem is to do the compensation
on the robot itself. The main advantage of this approach is that the robot’s
wheel encoders can be used to obtain additional information about the robot’s
actual behavior. However, since the wheel encoders measure only the wheel
rotations, they cannot sense any slip or friction effects directly.

4.1 Increased Position Accuracy by Local Sensors
In the ideal case of slip-free motion, the robot can extrapolate its current
position by combining the position delivered by the image processing system,
the duration of the entire time delay, and the traveled distance as reported
by the wheel encoders. In other words: When slip does not occur, the robot
can compensate for all the delays by storing previous and current wheel tick
counts. This calculation is illustrated in Fig. 17.
Since the soccer robots are real-world entities, they also have to account
for slip and friction, which are among other things, nonlinear and stochastic
by nature. The following subsection employs back-propagation networks to
account for those effects.

4.2 Embedded Back-Propagation Networks

This section uses the same neural network architectures as have already been
discussed in Subsection 3.3. Due to the resource limitations of the robot

latency corrected robot
= 5 position
x offset ∑ hx i
i =1 4
3
latency y
= ∑ offset
y offset hy i 2 camera
i =1 1 position
x
offset
Fig. 17. Extrapolation of the robot’s position using the image processing system
and the robot’s previous tick count