Resilient Time Synchronisation for Aerial Swarms by Distributed Graph Neural Networks

Aerial swarms consisting of multiple Unmanned Aerial Vehicles (UAVs) have been applied across various domains. Time synchronisation is important for swarm wireless networks. However, most studies assume that UAV clocks are synchronised, without addressing how synchronisation is achieved. Moreover, existing control techniques are typically designed in a centralised manner with a known topology, limiting their applicability to large swarms or those with dynamic wireless networks caused by high mobility or communication link failures resulting from jamming attacks. These limitations may lead to the instability of the controllers, or even the downtime of the entire swarm system, particularly under the communication link failures. Therefore, in this work, we propose leveraging Graph Neural Networks (GNNs) to achieve resilient clock synchronisation among UAVs. First, we integrate the heat kernel into the graph neural network, allowing it to retain low-frequency graph signals while attenuating high-frequency components. This is consistent with the aim of time synchronisation, which is to ensure that the states of all the clocks are the same, corresponding to low-frequency graph signals. Meanwhile, we introduce a distributed GNN architecture with low communication overhead, in contrast to existing decentralised GNNs that rely on fully-connected networks. Through adversarial imitation learning, our GNN-based control policies achieve similar synchronisation performance without requiring re-training when scaled to large swarms, as compared to the centralised controller using fully-connected wireless networks. Once trained, the proposed GNN-based control policies are also resilient to varying wireless networks, including temporary or permanent communication link failures, and can maintain synchronisation even when the swarm is split into two disconnected parts.