本文为英国南安普顿大学（作者：Walton Pereira Coutinho）的博士论文，共132页。

近年来，利用无人机（UAV）进行数据采集和测量得到了广泛的应用。通常，无人机的使用可以降低成本并改进其他性能标准。学术界已经认识到公司和组织对在其运营中采用无人机的兴趣。然而，由于无人机飞行动力学的限制常常被忽略。在无人机的航路问题中，寻找可行的航路是一项复杂的任务，但必须保证航路的可行性。

本文介绍了无人机航迹优化问题（UAVRTOP），即受飞行动力学约束的无人机编队航迹优化问题。出于灾害评估应用的动机，我们提出了UAVRTOP的一种变体，其中要求一组自主飞行滑翔机在灾难发生后拍摄一组感兴趣的点。这个问题被称为滑翔机路径和轨迹优化问题（GRTOP）。在这项工作中，我们提出了一个单相混合整数非线性规划（MINLP）的GRTOP公式。当滑翔机的飞行动力学被建模为常微分方程时，我们的公式同时优化了这些航线上的航线和飞行轨迹。我们通过线性化滑翔机运动方程（EOMs），将提出的MINLP问题简化为一个混合整数二阶锥规划（MISOCP）问题，避免了对非凸动力约束的处理。这项工作的另一个贡献是为GRTOP的修改版本提出了一个多阶段MINLP公式。我们不试图直接求解这个公式，而是提出了一种混合启发式方法，它由两个主要组成部分组成：

（i）顺序轨迹优化（STO）启发式，设计用于解决为给定路线寻找可行（可飞行）轨迹的挑战性任务；

（ii）路由数学，能够生成可由STO评估的路由。

我们根据英国城市洪水风险图和大量随机生成的实例，对现实生活中的实例进行了计算实验。

In recent years, employing Unmanned AerialVehicles (UAV) to collect data and making measurements has gained popularity.Often, the use of UAVs allows for a reduction in costs and improvements ofother performance criteria. The academic routing community has acknowledged theinterest of companies and organisations in adopting UAVs in their operations.However, constraints due to the flight dynamics of UAVs have often beenneglected. Finding feasible trajectories for UAVs in a routing problem is acomplex task, but it is necessary to ensure the feasibility of the routes. Inthis thesis we introduce the Unmanned Aerial Vehicle Routing and TrajectoryOptimisation Problem (UAVRTOP), the problem of optimising the routes andtrajectories of a fleet of UAVs subject to flight dynamics constraints.Motivated by a disaster assessment application, we propose a variant of theUAVRTOP, in which a fleet of autonomous aerial gliders is required tophotograph a set of points of interest in the aftermath of a disaster. Thisproblem is referred to as the Glider Routing and Trajectory OptimisationProblem (GRTOP). In this work, we propose a single-phase Mixed-IntegerNon-linear Programming (MINLP) formulation for the GRTOP. Our formulationsimultaneously optimises routes and the flight trajectories along these routeswhile the flight dynamics of the gliders are modelled as ordinary differentialequations. We avoid dealing with non-convex dynamical constraints bylinearising the gliders’ Equations of Motion (EOMs), reducing the proposedMINLP into a Mixed-Integer Second-Order Cone Programming (MISOCP) problem.Another contribution of this work consists of proposing a multi-phase MINLPformulation for a modified version of the GRTOP. We do not attempt to solvethis formulation directly, instead we propose a hybrid heuristic method that iscomposed of two main building blocks: (i) a Sequential Trajectory Optimisation(STO) heuristic, designed to cope with the challenging task of finding feasible(flyable) trajectories for a given route; and (ii) a routing matheuristic,capable of generating routes that can be evaluated by STO. We performcomputational experiments with real-life instances based on flood risk maps ofcities in the UK as well as in a large number of randomly generated instances.

1. 引言

2. 文献回顾

3. 滑翔机动力学

4. 滑翔机路径与轨迹优化问题

5. 基于数学的GRTOP轨迹优化

6. 结论与未来工作展望

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