A Cooperative Path Planning Method for Multiple Autonomous Underwater Vehicles in Complex Dynamic Marine Environments

Autonomous underwater vehicles (AUVs) face significant challenges in complex dynamic marine environments, where ocean currents, uncertain obstacles, and in-ter-vehicle interactions increase collision and mission failure risks. This study proposes a risk-aware cooperative path planning framework for multiple AUVs that integrates conditional Bayesian networks (CBN) for probabilistic environmental risk assessment directly into a receding horizon optimization scheme. The approach models AUV kinematics under time-varying ocean currents, incorporates collision avoidance, en-ergy consumption, path smoothness, and dynamic risk constraints derived from CBN-inferred probabilities. Risk levels are mapped nonlinearly to enable gradi-ent-based optimization while maintaining continuous sensitivity. The framework is evaluated through Monte Carlo simulations in a realistic South China Sea canyon en-vironment using HYCOM reanalysis current data, with comparisons against baseline methods. Results demonstrate substantial improvements: mission success rate increas-es by up to 35%, energy consumption decreases by 12–18%, path smoothness improves, and risk exposure is significantly reduced across various current intensities and obsta-cle densities. This method enhances operational safety and efficiency for cooperative AUV missions in uncertain dynamic oceans, offering a promising engineering solution for real-world underwater applications. This work presents an engineering-oriented framework that embeds a CBN-derived probabilistic risk index into cooperative re-ceding-horizon trajectory optimization for multi-AUV systems operating under realis-tic, time-varying ocean current fields. The main contributions of this work are summarized as follows: (1) A risk-aware cooperative path planning framework is developed for mul-ti-AUV systems, in which a probabilistic environmental risk model based on a Conditional Bayesian Network (CBN) is directly embedded into a reced-ing-horizon optimization process, rather than used as a post hoc evaluation or external safety filter. (2) Unlike existing deterministic or purely reactive approaches, the proposed CBN-based risk inference mechanism enables the planner to explicitly reason about coupled terrain–current–uncertainty effects, providing a continuous risk gradient that cannot be obtained from binary obstacle representations. (3) The proposed receding-horizon cooperative optimization embeds probabilis-tic risk directly into the planning objective, allowing multi-AUV systems to proactively trade off efficiency and safety in a mathematically tractable manner, rather than relying on post hoc risk filtering. (4) The effectiveness and practical applicability of the proposed method are demonstrated through extensive Monte Carlo simulations in a realistic sub-marine canyon environment using reanalysis-based ocean current data, showing statistically consistent improvements in mission success rate, energy efficiency, trajectory smoothness, and reduction of high-risk exposure com-pared with a baseline cooperative planning strategy. The proposed framework provides a practical and scalable solution for real-world multi-AUV missions, with potential applications in marine environmental monitoring, seabed surveying, underwater inspection, and ocean engineering operations.