Robot Spatial Distribution and Boundary Effects Matter in Puck Clustering

Puck Clustering, a particularly widely studied problem domain for self-organized multi-robot systems, involves gathering spatially distributed objects, called pucks, into piles within a planar workspace. Structures in the environment (partially formed clusters) encode information about where clusters should be formed, and their positions are involved in the mechanics of subsequent cluster formation. In this paper, we consider questions regarding the spatial distribution of robots and clusters, and their relation to the boundaries of the workspace. Prior theoretical analysis has assumed a uniform distribution of robots for gathering all objects into a single pile. Yet, in some instances, a disproportionate amount of time may be spent by robots on the boundary. Also, others have documented that the boundary can cause cluster growth itself. This paper considers the problem of clustering square boxes in the center of the workspace. The flat edges of these objects appear to exacerbate the affinity for cluster growth near boundaries. However, by exploiting the shape of our objects, we show that novel "Twisting" and "Digging" operations overcome this effect and enhance production of central clusters. We analyze the dynamics of boundary versus central puck clusters, and investigate how the spatial distribution of the robots changes along with the clustering process: showing stark differences between the standard mode of clustering and the mode we introduce here.