Optimization of communication topology for persistent formation in case of communication faults

To address the optimization problem of communication topology for persistent formation in the case of communication faults such as link interruption, transmitter failure, and receiver failure a two-stage model including fast reconstruction of communication topology and re-optimization of communication topology is constructed. Then, a fast reconstruction algorithm of communication topology for persistent formation (FRA-CT-PF), based on optimally rigid graph, arc addition operation, and path reversal operation, is proposed, which can quickly generate a feasible reconstructed communication topology after communication faults, thus ensuring the safety of the agents and maintaining the formation shape of persistent formation. Furthermore, a re-optimization algorithm of communication topology for persistent formation (ROA-CT-PF), based on agent position exchange, is proposed, which can further obtain a reoptimized communication topology to minimize the formation communication cost while still maintaining the formation shape of persistent formation. The time complexities of these two algorithms are also analyzed. Finally, the effectiveness of the above algorithms is verified by numerical experiments. Compared with existing algorithms, FRA-CT-PF can always obtain feasible reconstructed communication topology in much less time under all communication fault scenarios, and ROA-CT-PF can obtain a reoptimized communication topology to further reduce the formation communication cost in a shorter time.