Supporting material for the paper:

Evolution of Signalling in a Multi-Robot System:
Categorisation and Communication

by Christos Ampatzis, Elio Tuci, Vito Trianni, and Marco Dorigo
December 2006

To appear in Adaptive Behavior Journal

Table of Contents
  1. Real Robot Experiments
  2. Neuron Graphs and Lesion Analysis
  3. Offset &Delta of successful groups
  4. Statistics in Env.A

Real Robot Experiments:

Below are sample movies from the experiments performed in the arena above:

Experiments with 2 robots.
Movies are encoded in wmv format.

Experiments with 4 robots.
Movies are encoded in mpeg format.

All videos recordings from all the trials can be accessed at:

Experiments in simulation are performed with two robots and in reality with two and four robots. Movies are taken from an overhead camera and a hand camera and are encoded in .mpg or .wmv formats. Notice that when the robots emit a sound signal we light their colour turret red for visualisation purposes.

The behaviour of the group for the two robots is analysed in the paper. Concerning the four robots experiment, the results are almost perfect. In one trial though, sbot5 while performing antiphototaxis as a reaction to the sound emitted by sbot3, made a turn of 180 degrees and started moving wrongly towards the light. In all other trials though we did not observe this error and it looks to be a hardware crash. Another error which was not expected and revealed some property of our controller about which we would not have found out had we not performed the four robot test, is the fact that the robot-robot avoidance behaviour does not work while the robots perform antiphototaxis. In fact, as they leave the band after they perceive a sound signal, their sensorial input is ignored, with the consequence that in case they encounter another agent on their way, they collide against each other. A possible explanation for this is that this condition was never encountered during evolution, and therefore the mechanism shaped was confined to just leaving the band without paying attention to obstacles (other robots). Finally, by allowing more agents to interact in the target area, we discovered that the robot-robot avoidance mechanism is different once the robots are interacting there---a case not often encountered during the two robot experiments--and can be described as follows: if an agent detects others in its vicinity, it stops and spins until the other agents have moved away.

Neuron Graphs and Lesion Analysis:

Plot of the firing rate of all neurons with time for a robot of g2 (red continuous lines) and g10 (blue dashed lines)
Neurons graphs

In the case of a robot of a signalling group (e.g., g2), we have seen in the paper that the output of N13 (sound output) is integrating the information over time by rising and passing over the threshold of 0.5 when the discrimination is performed. But since this is not the case for non-signalling groups (e.g., g10), we should look elsewhere to find a neuron that performs the integration. Therefore, in the Figure above we plot the firing rates of all the neurons of the network, for one robot of groups g2 and g10, over time for both environments, during a successful trial (this we do because we are interested in discovering a mechanism that goes beyond a certain threshold in the case of Env. B---bringing forth the discrimination, while it stays below this threshold for Env. A). Notice that these values are not passed through the sigmoid function, that is why the plot for N13 is different than the one in the paper (in the paper we plot the sound output (cell potential passed through the sigmoid function). We notice that for group g2 there is N3 (that takes input from one floor sensor) whose firing rate's evolution through time has the characteristics defined above: starts rising (from 0) when the robots start circling around the band (approximately constant distance to light) and, in case the way-in zone is encountered, stops rising and starts decreasing, in case the agent is in Env. B, it passes beyond the threshold of 0.5. Immediately after we notice that the robot is leaving the band. This suggests that there is also an internal integration mechanism, apart from the one present in the activation of the sound output neuron. Concerning the behavior of the robot of group g10, the neuron that plays this role is N5 (that takes input from a combination of proximity sensors). To prove that these neurons are indeed essential for the discrimination to take place, we introduce lesions in the robot controllers which selectively damage the functionality of one neuron at a time. Specifically, we confine the value of the firing rate of a neuron to the average value observed throughout the robots lifetime and we re-evaluate the system with the new conditions. We are interested in discovering the functionality of each neuron in the network and also which neurons are indeed tied to the discrimination mechanism. The Table below gives us the results of this lesion analysis, by displaying the average final distance of the two agents over 500 evaluations in Env. A and 500 in Env. B, for g10 and g2. What we notice is that indeed N3 is the integration neuron for g2 and N5 for g10, and without them the robots are unable to trigger antiphototaxis (the average distances for Env. A suggest that they do find the way-in zone, while for Env. B that they stay on the band). Furthermore, the numbers suggest that one light sensor is enough to solve the task, since the disruption of N2 (the second light sensor) does not make the group unsuccessful. For g2, the sound input and output neurons are essential to complete the task in Env. B. What is surprising though is that if N9 (sound input neuron) is disturbed, g10's performance gets disrupted, despite the fact that as we saw this genotype does not rely on the presence of sound to trigger antiphototaxis. In detail what happens is that the disruption prevents robots from performing antiphototaxis in Env. B, while they are able to find the way-in zone in Env. A).

Lesion Analysis Table

lesion table

Offset &Delta of successful groups

Table showing Offset &Delta of successful signalling groups of Table 1 of the paper

signalling groups delta values Table showing Offset &Delta of successful non-signalling groups of Table 1 of the paper

non-signalling groups delta values

Statistics in Env.A

Table showing the statistics complementing Table 4 of the paper - statistics of post-evaluation tests in Env.A

statistics Env.A