STOCHASTIC TRAJECTORY PROCESSES AND GRAPH NEURAL NETWORK LEARNING FOR ADAPTIVE COVERAGE IN UAV NETWORKS

Abstract

This dissertation develops a framework for UAV trajectory design that bridges theoretical coverage guarantees and practical implementation constraints. The research introduces stochastic trajectory processes as a unifying paradigm, departing from deterministic optimization approaches that require precise user locations and extensive computation. The first contribution establishes constant-speed trajectory processes achieving provably uniform spatial coverage through Binomial Point Process distributions. By combining deterministic radial and angular motion with randomized initial conditions, the framework ensures UAV positions become independent and identically distributed across the operational region after a transient period. The second contribution extends the framework to non-uniform coverage through a distribution-centric design methodology. A time-warping mechanism modulates UAV velocity to match arbitrary spatial demand distributions using only aggregate statistical information, eliminating the need for real-time user tracking. Theoretical guarantees establish that time-averaged coverage converges to any prescribed spatial distribution. Validation on the Telecom Italia Milano dataset demonstrates 4.7×fairness improvement over deep reinforcement learning baselines and up to 65% outage reduction. The third contribution applies the time-warping framework to buffer-constrained IoT data harvesting, where sensor overflow causes permanent data loss. An interval-based angular evolution with modular arithmetic eliminates angular-boundary truncation, and minimum enclosing circle embedding extends the framework to arbitrary convex regions. Simulations on the Intel Berkeley Research Lab dataset (52 sensors, 1.8 M readings) and four synthetic fields achieve 94–97% collection efficiency with near-perfect proportional service and 12.2% total energy reduction. The fourth contribution introduces a polar-grid Graph Neural Network with UAV cross-attention that replaces random angle sampling with learned, globally informed angle selection for finite-horizon missions. The GNN predicts the per-interval starting angle while preserving the ergodic trajectory executor. Simulations on convex service regions demonstrate consistent outage reductions over random sampling, reinforcement learning, and optimal transport baselines. The dissertation concludes with future directions including multi-UAV coordination, temporal attention, and Large Language Model integration for mission specification.