A new model for self-organized robotic clustering: Understanding boundary induced densities and cluster compactness

For self-organized multi-robot systems, one of the widely studied task domains is object clustering, which involves gathering randomly scattered objects into a few piles. Earlier studies have pointed out that environmental boundaries influence the cluster formation process, generally causing clusters to form around the perimeter rather than centrally within the workspace. But it is usually central clusters that are desired in robotic clustering systems. In this paper, we derive general conditions that prevent the problem of boundaries causing perimeter clusters. We develop a mathematical model to explain how sets of clusters evolve into a single cluster without any boundary cluster being formed. Through analysis of the model, we show that time-averaged spatial densities of the robots play a significant role in producing conditions that ensure a single central cluster emerges. Thus, local densities of robots can be considered a system-level control parameter to achieve this task. We further investigate how the physical packing of clusters affects clustering dynamics. To do this, we introduce a measure of scaled compactness and show that the lifetime of clusters is well predicted by this descriptor.