Robust UAV Array Formation for Distributed Beamforming Under Position Uncertainty

Abstract

We address the design of a three-dimensional unmanned aerial vehicle (UAV) formation for distributed beamforming toward a remote target area when each UAV’s position deviates from its nominal value during flight. We cast the design as a stochastic optimization problem whose objectives are the expected directivity and side-lobe level under the position-perturbation distribution, subject to spacing and beam-width constraints. Since the objective is black-box and non-separable and a single deployable formation is sought, we solve it with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) using Monte-Carlo fitness averaging. Across a range of uncertainty levels and array sizes, the comparison confirms this choice: CMA-ES attains the highest scalarized objective among the compared multi-objective, swarm, differential-evolution, and noise-adaptive optimizers. With the solver fixed, we then show that the robust design keeps its expected beam width within the constraint under perturbation, whereas a formation optimized without regard to uncertainty violates it.