Iterative shepherding control for agents with heterogeneous responsivity

In the context of the theory of multi-agent systems, the shepherding problem refers to designing the dynamics of a herding agent, called a sheepdog, so that a given flock of agents, called sheep, is guided into a goal region. Although several effective methodologies and algorithms have been proposed in the last decade for the shepherding problem under various formulations, little research has been directed to the practically important case in which the flock contains sheep agents unresponsive to the sheepdog agent. To fill in this gap, we propose a sheepdog algorithm for guiding unresponsive sheep in this paper. In the algorithm, the sheepdog iteratively applies an existing shepherding algorithm, the farthest-agent targeting algorithm, while dynamically switching its destination. This procedure achieves the incremental growth of a controllable flock, which finally enables the sheepdog to guide the entire flock into the goal region. Furthermore, we illustrate by numerical simulations that the proposed algorithm can outperform the farthest-agent targeting algorithm.