本文为美国麻省理工学院（作者：Sri Venkata Tapovan Lolla）的硕士论文，共177页。
滑翔器（Glider）等自主水下航行器因其在多个海洋应用领域的日益广泛应用而成为有价值的科学平台，它能够在特定地点从安全、水声监测和军事侦察等方面收集海洋数据，用于海洋预测、监视和动力学研究。滑翔器具有高度的自主性，是执行远程任务的理想选择。随着滑翔器的性能变得更加可靠且成本可负担，多机协调和数据采集任务有望在不久的将来变得非常普遍。然而，滑翔器的这种续航能力是以对典型的沿海洋流敏感为代价的。由于水下航行器的物理局限性和沿海海洋的高度动态性，制定出安全、快速的航行路线是其成功运行的关键。因此，本论文的目的在于开发一种计算效率高且严谨的方法，以预测水下航行器在连续、强烈动态流场中的时间最优路径。其目的是预测一系列运行方向，以便航行器能够最好地利用或避免流动的洋流，从而最大限度地缩短行驶时间。
本文首先回顾了现有的路径规划方法，讨论了它们的优缺点。然后，讨论了水平集方法的理论及其在解决前向跟踪问题中的应用。然后，我们提出了一种基于水平集方法的严格（偏微分方程）方法，它可以计算水下航行器群的时间最优路径，不需要任何基于启发式控制的方法。我们陈述并证明了一个定理以及多个推论，构成了该路径规划方法的基础。我们证明了我们的算法在计算上是有效的——计算代价随航行器数量线性增长，随空间方向呈现几何增长。我们通过一些实际应用来说明我们的路径规划算法内容及功能。
首先，我们通过简单的基准应用程序验证我们的方法，然后将我们的方法应用于更复杂、真实和数值模拟的流场，包括涡流、射流、障碍物和禁区。最后，对强动力流场中多航行器协调运动问题进行了推广。这里，协调是指多部航行器保持特定的几何形状。我们推导的基于水平集的控制方案为局部控制方法提供了实质性的优势。具体来说，我们的研究表明，所产生的航行器协调运动能够在具有强动力、复杂空间梯度的动态流场中保持特定的模式。
Autonomous underwater vehicles such asgliders have emerged as valuable scientific platforms due to their increasinguses in several oceanic applications, ranging from security, acousticsurveillance and military reconnaissance to collection of ocean data at specificlocations for ocean prediction, monitoring and dynamics investigation. Glidersexhibit high levels of autonomy and are ideal for long range missions. As thesegliders become more reliable and affordable, multi-vehicle coordination andsampling missions are expected to become very common in the near future. Thisendurance of gliders however, comes at an expense of being susceptible totypical coastal ocean currents. Due to the physical limitations of underwatervehicles and the highly dynamic nature of the coastal ocean, path planning togenerate safe and fast vehicle trajectories becomes crucial for theirsuccessful operation. As a result, our motivation in this thesis is to developa computationally efficient and rigorous methodology that can predict thetime-optimal paths of underwater vehicles navigating in continuous, strong anddynamic flow-fields. The goal is to predict a sequence of steering directions sothat vehicles can best utilize or avoid flow currents to minimize their traveltime. In this thesis, we first review existing path planning methods anddiscuss their advantages and drawbacks. Then, we discuss the theory of levelset methods and their utility in solving front tracking problems. Then, wepresent a rigorous (partial differential equation based) methodology based onthe level set method, which can compute time-optimal paths of swarms ofunderwater vehicles, obviating the need for any heuristic control basedapproaches. We state and prove a theorem, along with several corollaries, thatforms the foundation of our approach for path planning. We show that ouralgorithm is computationally efficient - the computational cost grows linearlywith the number of vehicles and geometrically with spatial directions. We illustratethe working and capabilities of our path planning algorithm by means of anumber of applications. First, we validate our approach through simplebenchmark applications, and later apply our methodology to more complex,realistic and numerically simulated flow-fields, which include eddies, jets,obstacles and forbidden regions. Finally, we extend our methodology to solveproblems of coordinated motion of multiple vehicles in strong dynamicflow-fields. Here, coordination refers to maintenance of specific geometricpatterns by the vehicles. The level-set based control scheme that we derive isshown to provide substantial advantages to a local control approach.Specifically, the illustrations show that the resulting coordinated vehiclemotions can maintain specific patterns in dynamic flow fields with strong and complexspatial gradients.
1 引言与研究动机
2 问题描述
3 文献回顾
4 水平集方法
5 基于水平集方法的路径规划
6 算法实现与讨论
7 具体应用
8 协作路径规划
9 结论与未来工作展望
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