A New Metric for the Analysis of Swarms Using Potential Fields

There are many metrics defined for the analysis of swarm coordination algorithms. These metrics are usually based upon the distances between agents, the distance between agents and a fixed point, or the resultant vectors that
potential field
effects produce. This paper examines a distance-based metric that measures a swarm’s overall structure using inter-agent distances. More importantly, it introduces a new metric that identifies a swarm’s state based upon the resultant magnitude of the vectors produced by the agent interactions that create the agent distribution within the swarm’s structure. The algorithms used to implement the swarming feature are based upon cohesion and repulsion vectors between an agent and its neighbors. In comparing and contrasting the two metrics, we find that the
cohesion/repulsion
metric offers a number of advantages over the distance metric. In particular, the
cohesion/repulsion
metric allows the identification of the essential characteristic of a swarm as “expanding,” “stable,” or “contracting.” These states cannot be identified using a distance-based metric. Practical swarming applications where the new metric can be applied advantageously include area-filling and reconnaissance.