Collision-Free Shepherding Control of a Single Target within a Swarm

Abstract: 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.