Constant-Speed Trajectory Processes for Uniform Coverage in UAV Networks

Unmanned Aerial Vehicles (UAVs) play a pivotal role in applications requiring uniform area coverage, such as disaster response, precision agriculture, urban monitoring, and Internet of Things (IoT) networks. Ensuring consistent spatial and temporal coverage is essential for optimizing tasks such as data collection, communication reliability, and surveillance effectiveness. This paper proposes a novel framework for constant-speed trajectory processes designed to achieve near-perfect uniform coverage within annular regions. The proposed method guarantees spatial and temporal uniformity while maintaining strict speed consistency, overcoming limitations in existing approaches that often compromise coverage quality or operational efficiency.The framework ensures that UAV positions $\left\{ {{{\mathbf{X}}_n}(t)} \right\}_{n = 1}^N$ at sufficiently large times conform to a Binomial Point Process (BPP) distribution, providing independent, identically distributed, and uniform spatial coverage. The trajectory design combines deterministic radial and angular motion with randomized initial parameters, effectively avoiding synchronization and ensuring robust spatiotemporal coverage. Analytical conditions are derived to enforce constant-speed, minimize energy consumption, and enhance communication reliability. The results highlight the following key features of the proposed algorithm: 1) Speed stability: Deviations below 0.1% from the designed constant value, 2) Uniform angular coverage: Deviations less than 1% across all angular sectors, and 3) Statistical validation: A chi-square test confirms uniformity with a p-value greater than 0.95.