  In this paper, we consider the swarm-control problem of spatially separating
a specified target agent within the swarm from all the other agents, while
maintaining the connectivity among the other agents. We specifically aim to
achieve the separation by designing the movement algorithm of an external
agent, called a shepherd, which exerts repulsive forces on the agents in the
swarm. This problem has potential applications in the context of the
manipulation of the swarm of micro- and nano-particles. We first formulate the
separation problem, where the swarm agents (called sheep) are modeled by the
Boid model. We then analytically study the special case of two-sheep swarms. By
leveraging the analysis, we then propose a potential function-based movement
algorithm of the shepherd to achieve separation while maintaining the
connectivity within the remaining swarm. We demonstrate the effectiveness of
the proposed algorithm with numerical simulations.
