The Limits of Reactive Shepherding Approaches for Swarm Guidance

Sheepdogs smartly herd a flock of sheep and guide them towards a goal. A single dog can herd a few hundred sheep in easy to navigate environments. Understanding the interaction space between the sheepdogs, sheep and the environment is important due to the possibility of transferring this knowledge to solve practical swarm robotics problems. This interaction space is a complex mesh of influencing factors. We scrutinize this interaction space to identify areas where the complexity of the herding problem changes from low (easy to solve) to high (harder to solve or becoming unsolvable) complexity. In particular, we study reactive models for shepherding, whereby agents respond directly to stimuli in the environments by fusing the set of force vectors influencing their behaviour. We present an enhanced shepherding model with higher success rate than its predecessor. We investigate four key factors that influence the complexity of the problem: the relative speed between the sheepdog and sheep, the spatial configuration of the sheep at the start of the task, the number of sheepdogs, and the density of obstacles in the environment. We discovered a phase transition in shepherding resulting from the interaction between the number of sheepdogs and obstacles. The phase transition occurs as the density of obstacles range from 0.2% for a single shepherding agent to 5% for 10 shepherding agents. During this phase transition, the problem changes from being an easy problem where the flock gets collected quickly, to a hard one where the overall herding task becomes utterly not achievable using reactive approaches.