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214    S. Pr¨uter et al.
                                                      wireless
                             microcontroller on the robot  communication  PC outside the field
                                FFN         Output                 Error      Backpropagation
                                                    FFN Output
                                Input     set weights             weights        FFN Copy
                                                       weights
                           Fig. 18. Separation of the actual feed-forward network (indicated by FFN in the
                           figure) and the back-propagation training algorithm



                           hardware, the numbers of nodes and connections that the robot can store on
                           its hardware is limited. From a hardware point of view, the memory available
                           on the robot itself is the major constraint. In addition to the actual learn-
                           ing problem, this section is also faced with the challenge of finding a good
                           compromise between the network’s complexity and its processing accuracy.
                              A second constraint to be taken into account concerns the update mecha-
                           nism of the learning algorithm. It is known that, back-propagation temporarily
                           stores the calculated error counts as well as all the weight changes ∆w ij [4].
                           This leads to a doubling of the memory requirements, which would exhaust
                           the robot’s onboard memory size even for moderately sized networks. As a
                           solution for the problem, this section stores those values on the central control
                           PC and communicates the weight changes by means of the wireless commu-
                           nication facility. This separation is illustrated in Fig. 18. Thereby, the neural
                           network can be trained on a PC using the current outputs of the FFN on
                           the robot. A further benefit of the method is that the training can be done
                           during the soccer game, provided that the communication channel has enough
                           capacity for game-control and FFN data. The FFN sends its output values to
                           the PC, which then compares them with the camera data after the latency
                           time t. The PC uses the comparison results to train its network weights with-
                           out interfering with the robot control. When training is completed and the
                           results are better than the currently used configuration, the new weights are
                           sent to the robot, which start computing the next cycle with these weights.


                           4.3 Methods

                           Since the coding of the present problem is not trivial, this section provides a
                           detailed description. In order to avoid a combinatorial explosion, the robot is
                           set at the origin of the coordinate system for every iteration. All other values,
                           such as target position and orientation, are relative to that point. The relative
                           values mentioned above are scaled to be within the range −40 to 40. All angles
                           are directly coded between 0 and 359 degrees. With all these values, the input
                           layer has to have seven nodes.
                              Fig. 19 illustrates an example configuration. This configuration considers
                           three robot positions labeled “global”, “offset”, and “target”. The first robot
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