Abstract Autonomous underwater vehicles (AUVs) operate in the three-dimensional and time-dependent marine environment with strong and dynamic currents. Our goal is to predict the time history of the optimal three-dimensional headings of these vehicles such that they reach the given destination location in the least amount of time, starting from a known initial position. We employ the exact differential equations for time-optimal path planning and develop theory and numerical schemes to accurately predict three-dimensional optimal paths for several classes of marine vehicles, respecting their specific propulsion constraints. We further show that the three-dimensional path planning problem can be reduced to a two-dimensional one if the motion of the vehicle is partially known, e.g. if the vertical component of the motion is forced. This reduces the computational cost. We then apply the developed theory in three-dimensional analytically known flow fields to verify the schemes, benchmark the accuracy, and demonstrate capabilities. Finally, we showcase time-optimal path planning in realistic data-assimilative ocean simulations for the Middle Atlantic Bight region, integrating the primitive-equation of the Multidisciplinary Simulation Estimation and Assimilation System (MSEAS) with the three-dimensional path planning equations for three common marine vehicles, namely propelled AUVs (with unrestricted motion), floats (that only propel vertically), and gliders (that often perform sinusoidal yo-yo motions in vertical planes). These results highlight the effects of dynamic three-dimensional multiscale ocean currents on the optimal paths, including the Gulf Stream, shelfbreak front jet, upper-layer jets, eddies, and wind-driven and tidal currents. They also showcase the need to utilize data-assimilative ocean forecasts for planning efficient autonomous missions, from optimal deployment and pick-up, to monitoring and adaptive data collection.

中文翻译：

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海洋中三维时间最优路径规划

摘要 自主水下航行器（AUV）在具有强大和动态水流的三维和时间相关的海洋环境中运行。我们的目标是预测这些车辆的最佳三维航向的时间历史，以便它们从已知的初始位置开始，在最短的时间内到达给定的目的地位置。我们采用精确的微分方程进行时间最优路径规划，并开发理论和数值方案来准确预测几类船舶的三维最优路径，尊重其特定的推进约束。我们进一步表明，如果车辆的运动是部分已知的，例如，如果运动的垂直分量是被迫的，那么三维路径规划问题可以简化为二维路径规划问题。这降低了计算成本。然后，我们将开发的理论应用于三维分析已知的流场，以验证方案、对准确性进行基准测试并展示能力。最后，我们展示了大西洋中部海湾地区真实数据同化海洋模拟中的时间最优路径规划，将多学科模拟估计和同化系统 (MSEAS) 的原始方程与三个常见的三维路径规划方程相结合。海洋车辆，即推进式 AUV（运动不受限制）、漂浮物（仅垂直推进）和滑翔机（通常在垂直平面上执行正弦溜溜球运动）。这些结果突出了动态三维多尺度洋流对最佳路径的影响，包括墨西哥湾流、断层前沿急流、上层急流、涡流、风驱动和潮汐流。他们还展示了利用数据同化海洋预测来规划高效自主任务的必要性，从最佳部署和接收，到监测和自适应数据收集。