Control >> Aggregation >> Chains with LEGO Mindtorm©

Chain formation experiments with LEGO Mindstorm©

preview of the movie
Movie 1. Example of an aggregation experiment with LEGO robots.
This film shows an experiment in collective robotics, performed with Mindstorm© Invention System made by LEGO. Our goal is to determine simple rules at the level of the robots, in order to organise and regulate group behaviour. In this case we have considered chain formation, a particular type of aggregation behaviour. In the chain formation process, first a robot is stopping, allowing another one to stop just behind it and so on, like in polymerising process. Here the robots only stop when they "see" a black surface like the back of other robots or the two aggregation sites (white boxes with a black face). The presence of two aggregation sites is convenient to highlight the presence of collective choices (aggregation asymmetry). Although real s-bots will be able to detect other robots in a better way and to grip to each other forming a physical chain, here, we only focus on the way the robots aggregate related to their individual behaviours. That is, we are interested in the dynamics of pattern formation.

Figure 1 shows the configuration of the robots used in our experiments (a) and of the arena were they were performed (b). The two boxes are the aggregation sites were the robots nucleate they chains. These chains may take different forms like in the following pictures (c and d).

experimental setup
Figure 1. Setup of the robot (a) and of the arena (b), and some examples of final configurations.

The signature of collective choice is an asymmetrical distribution of robots on both sites, as shown in Fig. 2. The empirical distribution is compared with the the theoretical distribution if the two sites were equally probable (which is a Gaussian). In this system, the selection of one site (i.e. asymmetry) grows with the group size, as shown in the distributions of the robots on both sites for all the experiments, for 2, 4 and 8 robots.

Comparison of the theoretical and empirical distribution of robots on the two sites
Figure 2. Empirical and theoretical distributions of the number of robots
on the two sites for groups of 2, 4 and 8 robots.

At the end of each experiments different patterns of aggregation were observed. Some of them are shown in Fig. 3. The patterns can be describes in terms of the connections between robots. When a robot is connected to the back of another, the connection is labelled C1; when two robots are connected at the same point, it is labelled C2; C3 in case of three connections and C0 if the back of a robot remains without connections (Fig. 4). We found that whatever the experimental parameters are (group size, time of the experiment or number of sites) the proportion of C0, C1 and C2 remained constant: respectively 40%, 45% and 15% (C3 are negligible).

preview image 1 preview image 3 preview image 4 preview image 5
Figure 3. Some examples of final patterns of aggregation.

Classification of aggregation patterns
Figure 4. Classification of aggregation patterns.

Control >> Aggregation >> Chains with LEGO Mindtorm©

Swarm-bots project started
on October 1,2001
The project terminated
on March 31, 2005.
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