On Cyclic and Nearly Cyclic Multiagent Interactions in the Plane

TL;DR

This paper explores cyclic and nearly cyclic multi-agent interactions in the plane, analyzing how symmetry-breaking interactions lead to unique geometric formations and different matrix structures.

Contribution

It introduces nearly cyclic interactions that break symmetry, resulting in factor circulant matrices, expanding understanding beyond traditional cyclic pursuit models.

Findings

Analysis of nearly cyclic interactions and their geometric formations

Identification of factor circulant matrices in asymmetric interactions

Extension of multi-agent gathering models to nearly cyclic cases

Abstract

We discuss certain types of cyclic and nearly cyclic interactions among N "point"-agents in the plane, leading to formations of interesting limiting geometric configurations. Cyclic pursuit and local averaging interactions have been analyzed in the context of multi-agent gathering. In this paper, we consider some nearly cyclic interactions that break symmetry leading to factor circulants rather than circulant interaction matrices.