Modulation of Force Vectors for Effective Shepherding of a Swarm: A Bi-Objective Approach

In the shepherding problem, an external agent (the shepherd) attempts to influence the behavior of a swarm of agents (the sheep) by steering them towards a goal that is known to the shepherd but not the sheep. The problem offers a level of abstraction for Human-Swarm Interaction, where the human is able to shepherd the swarm towards a goal. Similarly, a smart robot could act as a shepherd to replace biological shepherds with ground or air vehicles. In both cases, it is important to preserve the energy of the shepherd by modulating the shepherd's influence vector on the sheep. Therefore, in this paper, we design a force modulation function for the shepherd agent to optimize the energy used by the agent and systematically study the effect of modulating the force of the influence vector on task success and energy used. The problem is further investigated using a bi-objective optimization formulation, where the energy used by the shepherd as well as the time of completion of the task are minimized, subject to a threshold of success rate. The findings demonstrate the coupling between contextual information used by the shepherd to modulate its influence vector and the effectiveness and efficiency of shepherd to complete the task.