针对智能体间的通信拓扑优化问题，结合图论知识研究了三维空间中最优持久图的生成算法。首先，利用刚度矩阵生成最优刚性图；然后，根据顶点连通度数的不同分别采取有向化操作方法，通过逐层缩小最优刚性图范围的方式把刚性图持久化，生成了最优持久图；最后，对三维空间中随机分布的智能体进行仿真实验，其结果验证了该算法的可行性和有效性，此算法能降低编队拓扑的通信复杂度，减少通信能量消耗。%Aiming at the problem of network communication topology optimization in agents, the algorithm of generating optimally persistent graph is combined with the knowledge of graph theories in the 3D space. First, an optimally rigid graph is generated by the rigidity matrix, then in the light of the difference of vertex connectivity, different oriented operation of adding directions to each edge are performed. By narrowing the scope of the optimally rigid graph one by one, the rigid graph is made persistent. As a result the optimal persistent graph is presented. At last, simulation experiments on random multi-agents in 3D space show the effectiveness and the feasibility of the proposed approach. This algorithm can lower the complexity of communication formation topology and reduce the energy consumption.
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