Multi-UAV-Assisted Cooperative Localization of Underground Sensor Nodes Using Multiobjective Reinforcement Learning

Rapid, accurate, and energy-efficient localization of underground sensor nodes remains a key challenge in wireless underground sensor networks (WUSNs) due to severe signal attenuation and complex subterranean conditions. In the meantime, Unmanned Aerial Vehicles (UAVs) can overcome accessibility constraints by enabling flexible coverage across diverse environments, including Urban, Suburban, Farm, and Rural scenarios. This paper presents a multi-objective reinforcement learning framework that combines a UAV-based MADDPG algorithm with the Prioritized Experience Replay (PER) method, leveraging multimodal localization of hard-to-reach underground sensor nodes. With coordinated UAV navigation, the framework further adopts a relative localization paradigm, where potential collisions of UAVs are resolved through a vertical-prioritized collision avoidance strategy. By fusing multimodal signals and benchmarking against the Cramér–Rao Lower Bound, the combination of the Received Signal Strength Indicator and the Time-Of-Arrival is identified as a practical trade-off. Building on this scheme, extensive simulations demonstrate that the proposed MADDPG+PER algorithm reduces the 90% CDF of the aggregated 3D Relative Positioning Error (3D-RPE) by 1.8%–22.8% relative to the MADDPG baseline, and by at least 6.8% when compared with non-learning heuristic baselines, across all investigated environments. Meanwhile, as the UAV team size increases from two to twenty, the mean flight distance drops by 85.4%–86.1% and the energy consumption drops by 84.3%–84.4% across all environments, whereas the 90% CDF of aggregated 3D-RPE decreases by 44.4%–47.5%. The results also show that the vertical-prioritized collision avoidance scheme not only improves the flight efficiency, but also reduces the energy consumption by avoiding unnecessary horizontal detours. Finally, sensitivity analyses indicate that the volumetric water content of soils exerts the strongest impact on the localization and energy performance, the burial depth introduces a moderate but consistent effect, and the clay fraction causes only minor but measurable degradation. These findings indicate the practicality of the proposed framework for efficient and robust localization in diverse WUSNs.