On statistical analysis for shepherd guidance system

Abstract

This paper is concerned with group navigation which utilizes strong interaction between two types of mobile agents, what we call sheepdog agent (dog agent) and sheep agent. Natural sheepdog system exhibits that one or a small number of sheepdog guides large population of sheep, up to a thousand, to a pre-determined goal position thanks to the characteristics of the sheep; they live in a flock and they hate a dog. From the viewpoint of multi-robots navigation, the sheepdog system will help us to grasp some key tricks for control strategies; sufficient and minimum number of controllers will manipulate many degree of freedoms. After deriving mathematical models of sheep flocks and a shepherd dog, we propose to conduct a statistical approach for understanding the navigation mechanism; we mainly focus on the interaction factor, flocking effect, and the dog performance. Firstly, we dare to run repeated simulations by adding statistical errors in the interaction vector between sheep flocks and the dog. Secondly, we examine the navigation performance by changing the flock characteristics: the size of individual attraction/alignment zone. Finally, we analyze the relation between the speed of dog and the sheepdog-like navigation performance.