A Macroscopic Model for Probabilistic Aggregation in Swarm Robotic Systems

We study the self-organized aggregation of a swarm of robots in a closed arena. We assume that the perceptual range of the robots are smaller than the size of the arena and the robots do not have information on the size of the swarm of the size of the arena. Using a probabilistic generic aggregation behavior model inspired from studies of social insects, we propose a macroscopic model for predicting the final distribution of aggregates parameterized by the parameters of the swarm system including the parameters of the aggregation behavior, the arena size and the sensing characteristics of the robots. Specifically, we use the partition concept, developed in number theory, and its related results to build a discrete-time, non-spatial model of the aggregation in swarm robotic systems under a number of simplifying assumptions. We provide simplistic simulations of self-organized aggregation in swarm robotic systems using the aggregation behavior with different parameters and arena sizes. The results show that, despite the fact that the simulations did not explicitly enforce to satisfy the assumptions put forward by the macroscopic model, the final aggregate distributions predicted by the macroscopic model and obtained from simulations match under different behavioral parameters and arena sizes. Finally, the differences between predictions and results are discussed together with some possible future extensions of the model.