The Virtual Filament Model

Abstract

In the present work, a framework is proposed for studying autonomous agents which interact locally yet effect a globally coherent behavior. This problem of locally induced organization is ubiquitous in decentralized multi-robot environments and various micro- and macroscopic biological contexts (e.g., cellular chemotaxis, avian flocking). In analogy with the local equations of motion which arise in various elastic rod and vorticity theories, we pursue this question in a continuum setting where agents are uniquely associated with material points of a virtual filament. The governing dynamics for this filament are chosen so that an established set of control objectives is achieved. The appropriate configuration space of continua is shown to be an infinite dimensional Hilbert Lie group admitting a separable topology. A class of filament models is studied in a Lagrangian formalism on this manifold, leading to a natural curvature feedback law.