Distributed MPC for Directional UAV Networks: Co-design of Motion and Hybrid Beam Alignment

Abstract

This paper addresses the coupled control and communication problem in UAV networks operating at millimeter-wave (mmWave) frequencies. While hybrid mechanical-electronic steering enables high-gain directional connectivity, the narrow Field of View (FoV) of phased arrays introduces a strong coupling between agent kinematics and link quality, rendering traditional velocity-aligned guidance strategies insufficient. We propose a Distributed Model Predictive Control (MPC) framework that jointly optimizes the translational trajectory and mechanical heading to maximize network capacity while ensuring safety. The key technical challenge lies in the non-convex, piecewise-smooth structure of the hybrid beamforming gain, which exhibits vanishing gradients outside the electronic FoV. We construct a smooth surrogate objective via a differentiable Gaussian envelope of the array factor and a log-barrier relaxation of the FoV boundary, establish a closed-form sufficiency condition for the linear convergence of the sequential best-response dynamics, and prove recursive feasibility of the distributed scheme under the warm-start initialization. Extensive numerical simulations demonstrate that the proposed joint formulation reduces link outage probability by approximately 96% compared to velocity-aligned heuristics, effectively bridging the gap between physical-layer constraints and autonomous guidance.