Theoretical Analysis of Mobile Control Method for Group Agents Motivated by Sheepdog Shepherding

In this paper, we deal with the control problem to manipulate autonomous multiple agents (a flock of sheep) escaping from an agent (a sheepdog) according to nonlinear interaction. This work was motivated by so-called sheepdog system inspired by sheepdog shepherding: a flock of several thousands of sheep are controlled by only a few sheepdogs in the real world. It is an interesting control system because one or more sheepdogs, who act as a small number of controllers, can control many sheep that cannot be directly controlled, taking advantage of their own maneuverability. For this reason, there have been many studies about this system; however, these studies have been limited to building numerical models or performing simulation analyses. Therefore, we aim to clarify the control principle theoretically. For this purpose, we conduct theoretical analysis for a sheepdog-type navigation system which we design based on a flock control model proposed by Vaughan et.al. in the case that one sheep is controlled by a sheepdog. Moreover, we also demonstrate the results by using simulations to confirm the validity of the analysis.