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We model the dynamics of self-organized robot aggregation inspired by a study on aggregation of gregarious arthropods. In swarms of German cockroaches, aggregation into clusters emerges solely from local interactions between the individuals, whereas the probabilities to join or leave a cluster are a function of the cluster size. Rather than explicitly modeling the spatial distribution of robots in the environment, we propose a population dynamics model that keeps track of the number of robots in clusters of specific size. The model is able to quantitatively and qualitatively predict the dynamics observed in extensive realistic simulation. In particular, we show both by modeling and simulation that the emergence of a giant component requires a minimal communication distance between individuals, whereas the robots remain scattered in the environment otherwise.