  We study the shepherding control problem where a group of "herders" need to
orchestrate their collective behaviour in order to steer the dynamics of a
group of "target" agents towards a desired goal. We relax the strong
assumptions of targets showing cohesive collective behavior in the absence of
the herders, and herders owning global sensing capabilities. We find scaling
laws linking the number of targets and minimum herders needed, and we unveil
the existence of a critical threshold of the density of the targets, below
which the number of herders needed for success significantly increases. We
explain the existence of such a threshold in terms of the percolation of a
suitably defined herdability graph and support our numerical evidence by
deriving and analysing a PDE describing the herders dynamics in a simplified
one-dimensional setting. Extensive numerical experiments validate our
methodology.
