In this paper, we consider the problem of protecting a high-value area from being breached by sheep agents by crafting motions for dog robots. We use control barrier functions to pose constraints on the dogs' velocities that induce repulsion in the sheep relative to the high-value area. This paper extends the results developed in our prior work on the same topic in three ways. Firstly, we implement and validate our previously developed centralized herding algorithm on many robots. We show herding of up to five sheep agents using three dog robots. Secondly, as an extension to the centralized approach, we develop two distributed herding algorithms, one favoring feasibility while the other favoring optimality. In the first algorithm, we allocate a unique sheep to a unique dog, making that dog responsible for herding its allocated sheep away from the protected zone. We provide feasibility proof for this approach, along with numerical simulations. In the second algorithm, we develop an iterative distributed reformulation of the centralized algorithm, which inherits the optimality (i.e. budget efficiency) from the centralized approach. Lastly, we conduct real-world experiments of these distributed algorithms and demonstrate herding of up to five sheep agents using five dog robots.

翻译：本文研究通过设计牧羊犬机器人的运动轨迹，保护高价值区域免受羊群智能体入侵的问题。我们采用控制障碍函数对牧羊犬机器人的速度施加约束，促使羊群产生远离高价值区域的排斥运动。本研究在以下三个方面拓展了前期同类研究成果：首先，实现了先前开发的集中式牧羊算法在多机器人系统上的验证，成功使用三台牧羊犬机器人围堵五只羊群智能体；其次，作为集中式方法的扩展，提出两种分布式牧羊算法——其中一种侧重可行性，另一种侧重最优性。第一种算法通过为每只牧羊犬分配专属羊群目标，使其负责将指定羊群驱离保护区，我们给出了该方法的可行性证明及数值仿真结果。第二种算法将集中式算法重构为迭代分布式形式，继承了集中式方法的最优性（即预算效率）；最后，通过真实世界实验验证了这些分布式算法的有效性，成功使用五台牧羊犬机器人围堵五只羊群智能体。