On Cyclic and Nearly Cyclic Multiagent Interactions in the Plane

Cyclic pursuit and local averaging interactions have been extensively analyzed in the context of multiagent gathering, in the field of distributed robotics. This paper reviews some results on cyclically structured dynamical systems, and discusses their application to nearly cyclic interactions among N point-agents in the plane, leading to formations of interesting limiting geometric configurations. In particular, we consider evolutions that can be modeled by a Toeplitz operator, and explain how they can be decoupled into independent evolving modes, focusing on nearly cyclic interactions that break symmetry leading to factor circulants rather than circulant interaction matrices.

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