Droving, Driving, and Mustering: Phases of Optimal Herding

While flocking behavior---of cells, animals, robots etc. ---is an area of growing interest, little is understood about how a few shepherds are able to control large groups of swarms, flocks, or herds. Here, we investigate how a shepherd (such as dogs, humans, or robots) should move in order to effectively herd and guide a flock towards a target. Using agent-based, ODE, and PDE models, we find that three distinct phases of control algorithms emerge as potential solutions---despite no specific control algorithm being prescribed---as a result of optimizing herd cohesion, distance to a target, and line of sight. Transitions between the phases are dependent on just two parameters: the scaled herd size and the scaled herd speed. Two of these phases---mustering and droving---show agreement with the behavior of sheepdogs in nature. The third, driving, is a novel phase that suggests an efficient control algorithm for the transport of a very large group of animals by a single agent. Several potential applications of driving can be seen in swarm robots.