The optimization of communication topology of persistent formation is to minimize the communication energy consumption between agents on the basis of ensuring that the multi-agents use the persistent formation control method to maintain formation. The existing methods can minimize the total communication energy consumption of agents, but do not consider balancing communication energy consumption between agents, which will lead to early withdrawal of some agents from the formation. To solve this problem and maximize the formation keeping time, a communication topology generation method of 3D optimally persistent formation considering energy consumption balance is proposed. First, an offline optimization mechanism of communication topology is designed, including selecting a suitable cycle, calculating the communication topology of each cycle before formation movement, and adjusting the communication topology periodically during the formation keeping process, so as to avoid additional communication energy consumption caused by online calculating and publishing communication topology. When calculating the communication topology of each cycle off-line, the remaining communication energy of each agent at the beginning of each cycle is estimated, the weight of each communication link in the network topology is updated accordingly, and then a 3D optimally persistent graph is generated from the updated network topology as the communication topology in this cycle. Second, for the problem of 3D optimally persistent graph generation in each cycle, it is difficult to apply the existing algorithms due to the asymmetric link weights in the updated network topology. Therefore, an approximate algorithm is proposed based on the rigid matrix and arc adding operation. The time complexity of the algorithm is analyzed and its effectiveness is proved theoretically. Finally, the simulation results show that the proposed method can effectively reduce and balance the communication energy consumption of each agent. Compared with the average level of all the comparison methods, the formation keeping time increases by 29.5%, 59.4% and 72.01% when there are 5, 10 and 15 nodes, respectively.
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