Intervening a group of mobile agents in three dimension

How we intervene the multi-agent systems (MAS) without changing the local interactions such that the system exhibits the expected collective behavior is an interesting and important topic. In this paper, we will investigate the intervention of a class of MAS, where all agents move in three dimensional Euclidean space. To guide all agents to move with the same expected direction, we put some information agents (also called leaders) into the system. Different from [11], the heading of each agent is determined by two coupled angle sequences, which makes the theoretical analysis quite hard. By estimating some characteristics concerning the initial states and applying the mathematical induction, we will provide a quantitative result on the proportion of leaders needed to guarantee the expected consensus.