Macroscopic modeling of aggregation experiments using embodied agents in teams of constant and time-varying sizes

In this paper, we present discrete-time, nonspatial, macroscopic models able to capture the dynamics of collective aggregation experiments using groups of embodied agents endowed with reactive controllers. The strength of the proposed models is that they have been built up incrementally, with matching between models and embodied simulations verified at each step as new complexity was added. Precise heuristic criteria based on geometrical considerations and systematic tests with one or two embodied agents prevent the introduction of free parameters into the models. The collective aggregation experiments presented in this paper are concerned with the gathering and clustering of small objects initially scattered in an enclosed arena. Experiments were carried out with teams consisting of one to ten individuals, using groups of both constant and time-varying sizes. In the latter case, the number of active workers was controlled by a simple, fully distributed, threshold-based algorithm whose aim was to allocate an appropriate number of individuals to a time-evolving aggregation demand. To this purpose, agents exclusively used their local perception to estimate the availability of work. Results show that models can deliver both qualitatively and quantitatively correct predictions and they represent a useful tool for generalizing the dynamics of these highly stochastic, asynchronous, nonlinear systems, often outperforming intuitive reasoning. Finally, in addition to discussions of small prediction discrepancies and difficulties in generating quantitatively correct macroscopic models, we conclude the paper by reviewing the intrinsic limitations of the current modeling methodology and by proposing a few suggestions for future work.