{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T18:23:34Z","timestamp":1770834214332,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T00:00:00Z","timestamp":1770768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In underwater reconnaissance and patrol, AUV has to sense and judge traversability in cluttered areas that include reefs, cliffs, and seabed infrastructure. A narrow sonar field of view, occlusion, and current-driven disturbances leave the vehicle with local, time-varying information, so decisions are made with incomplete and uncertain observations. A path-planning framework is built around two coupled components: spatiotemporal graph neural network prediction and conditional normalizing flow (CNF)-based probabilistic environment reconstruction. Forward-looking sonar and inertial navigation system (INS) measurements are fused online to form a local environment graph with temporal encoding. Cross-temporal message passing captures how occupancy and maneuver patterns evolve, which supports path prediction under dynamic reachability and collision-avoidance constraints. For regions that remain unobserved, CNF performs conditional generation from the available local observations, producing probabilistic completion and an explicit uncertainty output. Conformal calibration then maps model confidence to credible intervals with controlled miscoverage, giving a consistent probabilistic interface for risk budgeting. To keep pace with ocean currents and moving targets, edge weights and graph connectivity are updated online as new observations arrive. Compared with Informed Random Tree star (RRT*), D* Lite, Soft Actor-Critic (SAC), and Graph Neural Network-Probabilistic Roadmap (GNN-PRM), the proposed method achieves a near 100% success rate at 20% occlusion and maintains about an 80% success rate even under 70% occlusion. In dynamic obstacle scenarios, it yields about a 4% collision rate at low speeds and keeps the collision rate below 20% when obstacle speed increases to 3 m\/s. Ablation studies further demonstrate that temporal modeling improves success rate by about 7.1%, CNF-based probabilistic completion boosts success rate by about 13.2% and reduces collisions by about 17%, while conformal calibration reduces coverage error by about 6.6%, confirming robust planning under heavy occlusion and time-varying uncertainty.<\/jats:p>","DOI":"10.3390\/a19020147","type":"journal-article","created":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T17:45:36Z","timestamp":1770831936000},"page":"147","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive Path Planning for Autonomous Underwater Vehicle (AUV) Based on Spatio-Temporal Graph Neural Networks and Conditional Normalizing Flow Probabilistic Reconstruction"],"prefix":"10.3390","volume":"19","author":[{"given":"Guoshuai","family":"Li","sequence":"first","affiliation":[{"name":"Aviation University of Air Force, Changchun 130022, China"},{"name":"Jilin Provincial Key Laboratory of Unmanned Aerial Vehicle Intelligent Application, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinghua","family":"Wang","sequence":"additional","affiliation":[{"name":"Aviation University of Air Force, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jichuan","family":"Dai","sequence":"additional","affiliation":[{"name":"Shandong Jiaotong University, Jinan 250357, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tian","family":"Zhao","sequence":"additional","affiliation":[{"name":"Aviation University of Air Force, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Danqiang","family":"Chen","sequence":"additional","affiliation":[{"name":"Aviation University of Air Force, Changchun 130022, China"},{"name":"Jilin Provincial Key Laboratory of Unmanned Aerial Vehicle Intelligent Application, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cui","family":"Chen","sequence":"additional","affiliation":[{"name":"Aviation University of Air Force, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Song, Y.S., and Arshad, M.R. 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