Modeling of Sheepdog Control

Abstract

This paper develops a mathematical model of a sheepdog control strategy, in order to clarify a principle for controlling autonomously (and randomly) moving multiple agents. First, by observing real behaviors of a sheepfold and a sheepdog, we extract their essential properties as a multi-agent system. Based on this, difference equations are constructed for the sheep and sheepdog. It is verified by numerical simulations that the proposed model captures their qualitative behaviors.