Revisiting the shepherding problem: An exercise in agent-based modelling

Revisiting the herd control problem, we propose a minimalistic protocol for controlling and guiding animal flocks towards a stationary target in a predator-prey framework. Our model considers stochastic activation of the herd (prey) from an initially static (grazing) state to motion on exposure to a predator. The information about the predator's presence propagates across the herd, leading to activation and, eventually, collective motion in a direction dictated by inter-prey alignment interactions and repulsive interaction with the predator. However, the herd moves intermittently, i.e., in a stop-and-go fashion often observed in livestock. The direction of movement of the herd is found to be highly correlated to the direction of the first activated agent relative to the predator. We determine the probability of a prey agent being activated first in the herd as a function of its position relative to the predator and surmise the predator's optimal path to drive the herd towards the target location. The analytical expression for the probability conforms to the results obtained from the agent-based simulations and can provide insights into a simple approach to herd control.