Computer Simulation Based Robustness Comparison Regarding Agents' Moving-Speeds in Two- and Three-Dimensional Herding Algorithms

The shepherding problem is to control and guide the flock of multiple autonomous agents by means of one or more external controllable agents. By solving this problem, it can be expected to develop such as a robot for herding livestock and a robot for guiding people who need evacuation. D. Strömbom et al. modeled the shepherd's behavior mathematically, in which a single shepherd can herd a flock of agents to a target. In this study, we have demonstrated that the shepherd succeeds to herd the agents moving in the multidimensional space according to the rules of sheep's moving just by increasing the dimensional-numbers of the shepherd's and agents' coordinates without changing the rules of their interaction. Then, we have simulated herding algorithm (HA) proposed by D. Strömbom and the dimension-extended algorithm for three-dimensional (3D) space in the cases of various differences between the shepherd's and agents' moving-speeds, and have analyzed the robustness of this algorithm regarding agents' moving-speeds. The experimental results have shown that the herding success is mostly guaranteed when all the agents' moving-speeds in the flock are slower than the shepherd's moving-speed. Also, the results have shown that the herding succeeds even if the flock consists of agents having various moving-speeds. From these results, we have clarified that the conventional HA (2D-HA) and 3D-HA with a single shepherd are mostly robust regarding agents' moving-speeds.