A continuification-based control solution for large-scale shepherding

In this paper, we address the large-scale shepherding control problem using a density control strategy based on continuification. We consider a scenario in which a large group of follower agents (targets) must be confined within a designated goal region through indirect interactions with a controllable set of leader agents (herders). Our approach transforms the microscopic agent-based dynamics into a macroscopic continuum model. This formulation enables efficient, scalable control design for the herders’ behavior, with guarantees of global convergence. The approach is validated through comprehensive numerical simulations and novel mixed-reality experiments integrating physical and virtual agents, demonstrating both its effectiveness and practical applicability.