空间多智能体编队控制集群运动的动力学建模及分析

Dynamic Modeling and Analysis of Formation Control for Spatial Multi-Agent System

摘要: 本文基于对自组织系统集群运动的研究，结合图实现理论、微分方程动力学，为多智能体系统构建了做编队控制集群运动的三维动力学模型。首先，基于图实现理论以及智能体间的相互作用关系及期望距离，为智能体构造局部控制率。然后，为系统构造Lyapunov函数，并用Lyapunov稳定性理论证明随机产生智能体的初始位置和初始速度，系统总会以期望编队构型达到集群运动的稳定，即运动速度相同，方向一致。最后，分别给出三个不同构型的期望编队并进行模拟仿真，以此来验证理论结果。

Abstract: Based on the study of flocking of self-organizing system, combining graphs realization, differential equation dynamics and stability theory, this paper constructs a dynamic model of multi-agent system formation control flocking in three-dimensional space. First, based on the graph realization theory, the interaction relationship between the agents and the expected distance, the local control law is constructed for the agents. Then, the lyapunov function for the system is constructed. When the initial position and initial velocity of the agent are randomly generated, we prove that the system will always be formed in the desired formation. The system eventually achieves the stability of the swarming motility with desired formation, that is, the movement speed is the same, the direction is the same. The stability analysis is proved by the Lyapunov’s second method. Finally, three expected formations of different configurations are given and simulated to verify the theoretical proof.