Physical Sciences and Mathematics Commons^™

We examine the theoretical foundations for the dynamics of puck clustering systems. Key in this investigation is the development of methods of controlling variance in cluster size, an important precursor to swarm-mediated clustering. We derive conditions under which clustering can take place in a general framework, and demonstrate two different behavioral regimes for clustering systems.

We investigate the use of swarm clustering algorithms in the design of simple robots capable of carrying out swarm-mediated construction. Methods for generating multiple clusters of predetermined size are developed. Relative cluster motion algorithms are also developed and explored. All robotic algorithms are predicated on the use of only robots utilizing no processing, gps, or explicit communication. Simple stigmergic communication and minimal sensing capabilities are used exclusively. We demonstrate swarms of minimal agents building equilateral triangles, squares, and pentagons. Future use of these methods in the design of more sophisticated construction techniques is discussed.

Puck clustering involves the physical relocation of small objects known as ‘pucks’ from random positions to a central location, which need not be specified a priori. The evolution of systems of clusters of pucks under the action of robots capable of moving pucks from several locations is considered. A general set of conditions by which a puck collection system may be seen to evolve to a one-cluster system is developed. General conditions leading to clustering behavior in the presence and absence of non-embodied agents are derived. Conditions leading to more efficient algorithms are also derived. Several examples are given to …