  In this paper, we consider the problem of protecting a high-value area from
being breached by sheep agents by crafting motions for dog robots. We use
control barrier functions to pose constraints on the dogs' velocities that
induce repulsion in the sheep relative to the high-value area. This paper
extends the results developed in our prior work on the same topic in three
ways. Firstly, we implement and validate our previously developed centralized
herding algorithm on many robots. We show herding of up to five sheep agents
using three dog robots. Secondly, as an extension to the centralized approach,
we develop two distributed herding algorithms, one favoring feasibility while
the other favoring optimality. In the first algorithm, we allocate a unique
sheep to a unique dog, making that dog responsible for herding its allocated
sheep away from the protected zone. We provide feasibility proof for this
approach, along with numerical simulations. In the second algorithm, we develop
an iterative distributed reformulation of the centralized algorithm, which
inherits the optimality (i.e. budget efficiency) from the centralized approach.
Lastly, we conduct real-world experiments of these distributed algorithms and
demonstrate herding of up to five sheep agents using five dog robots.
