Swarms of Unmanned Aerial Vehicles (UAV) have demonstrated enormous potential in many industrial and commercial applications. However, before deploying UAVs in the real world, it is essential to ensure they can operate safely in complex environments, especially with limited communication capabilities. To address this challenge, we propose a control-aware learning-based trajectory prediction algorithm that can enable communication-efficient UAV swarm control in a cluttered environment. Specifically, our proposed algorithm can enable each UAV to predict the planned trajectories of its neighbors in scenarios with various levels of communication capabilities. The predicted planned trajectories will serve as input to a distributed model predictive control (DMPC) approach. The proposed algorithm combines (1) a trajectory compression and reconstruction model based on Variational Auto-Encoder, (2) a trajectory prediction model based on EvolveGCN, a graph convolutional network (GCN) that can handle dynamic graphs, and (3) a KKT-informed training approach that applies the Karush-Kuhn-Tucker (KKT) conditions in the training process to encode DMPC information into the trained neural network. We evaluate our proposed algorithm in a funnel-like environment. Results show that the proposed algorithm outperforms state-of-the-art benchmarks, providing close-to-optimal control performance and robustness to limited communication capabilities and measurement noises.

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