Phase transitions are where a small change in a parameter causes a qualitative change in the behaviour or state of a system. We can apply this concept to determining the connectivity of a population of mobile robots. Consider a population of mobile robots which can pass messages to other nearby robots. When the number of robots is small, or their working environment is large, robots will only be able to pass a message to a small number of others. However there is a point where if we increase the population by a small number, increase the communication range slightly, or reduce the working area by a small amount, the connectivity of the population increases suddenly to a point where almost all robots are communicating with each other. The consequences of this for multi-robot learning are discussed
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