Optimal shepherding and transport of a flock

We investigate how a shepherd should move in order to effectively herd and guide a flock of agents towards a target. Using a detailed agent-based model (ABM) for the members of the flock, we pose and solve an optimization problem for the shepherd that has to simultaneously work to keep the flock cohesive while coercing it towards a prescribed project. We find that three distinct strategies emerge as potential solutions as a function of just two parameters: the ratio of herd size to shepherd repulsion length and the ratio of herd speed to shepherd speed. We term these as: (i) mustering, in which the shepherd circles the herd to ensure compactness, (ii) droving, in which the shepherd chases the herd in a desired direction, and (iii) driving, a hitherto unreported strategy where the flock surrounds a shepherd that drives it from within. A minimal dynamical model for the size, shape and position of the herd captures the effective behavior of the ABM, and further allows us to characterize the different herding strategies in terms of the behavior of the shepherd that librates (mustering), oscillates (droving) or moves steadily (driving). All together, our study yields a simple and intuitive classification of herding strategies that ought to be of general interest in the context of controlling the collective behavior of active matter.