  The shepherding problem refers to guiding a group of agents (called sheep) to
a specific destination using an external agent with repulsive forces (called
shepherd). Although various movement algorithms for the shepherd have been
explored in the literature, there is a scarcity of methodologies for selective
guidance, which is a key technology for precise swarm control. Therefore, this
study investigates the problem of guiding a single target sheep within a swarm
to a given destination using a shepherd. We first present our model of the
dynamics of sheep agents and the interaction between sheep and shepherd agents.
The model is shown to be well-defined with no collision if the interaction
magnitude between sheep and shepherd is reasonably limited. Based on the
analysis with Lyapunov stability principles, we design a shepherd control law
to guide the target sheep to the origin while avoiding collisions among sheep
agents. Experimental results demonstrate the effectiveness of the proposed
method in guiding the target sheep in both small and large scale swarms.
