  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.
