Distributed numerical optimal control of unmanned aerial vehicle (UAV) networks

无人机轨迹规划问题已经从许多不同的角度进行了探讨，然而，目前的文献和工业公司未能提供一个可靠的分布式解决方案来控制无人机群。系统中具有大量不确定性的复杂动力学问题通常被近似或简化，以适应当前可用的数值优化求解器。该项目的目的是构建动态代理，可以解决给定的任务，在一个最佳的分布式方式，并将这些代理集成到一个不确定的，动态的环境。这是相关的，因为以集中的方式解决大规模问题不适合于需要连续更新控制动作的固有不稳定应用。尽管现有的方法，拟议的框架将有多个目标：最大限度地减少能源消耗，最大限度地减少时间来完成使命以及最大限度地提高可靠性。基于用户需求，这些目标可以相应地优先化，而不是解决单个问题，我们将能够解决由不同的相对优先级给定的多个问题。为了给出可以应用所提出的分布式数控算法的相关示例问题，考虑第五代（5G）无人机通信固定节点可能无法满足需求，并且需要使用多个UAV来增强连接性。为了确保足够的覆盖范围，无人机需要根据用户的移动来重新定位自己。多目标优化功能是非常相关的，因为不同的用户可能有相互冲突的要求，例如，前往犯罪现场的警察团队将更加强调可靠的连接，使他们能够在途中收集信息，而主流用户将更有兴趣获得更低的价格（这与能源消耗和网络规模直接相关）。另一个潜在的用例可以通过为自主港口操作或任何现场检查任务提供空中支持和视频监控来表示。一般方法包括将三种类型的动力学放在一起，即无人机动力学，用户/目标运动预测和通信动力学，在仿真环境中包括所有这些不同的控制方程作为约束。虽然这些控制方程并不是新的，但它们还没有被放在同一个分布式优化问题中，它们之间的相互作用也没有被深入研究，因为许多人假设用户位置固定，或者传输功率分布固定。在设计了一个代表性模型之后，下一步将是设计一个能够实时在线有效解决问题的数值算法。我们的方法将与现有的集中式算法进行比较，这些算法需要对环境有充分的了解。我们的方法可能会执行得更好（在运行时方面），因为数据收集和代理之间的通信是耗时的。通过求解多个低维并行问题，可以在无人机的机载嵌入式处理器上进行计算拆分，从而解决轨迹规划问题。我们还旨在回答与系统弹性相关的问题，例如：如果一个或多个无人机发生故障会发生什么，其余的无人机应该如何适应这种情况，或者当无人机的数据存储/传输容量达到上限时应该如何处理？该项目将主要是计算性的，开发新的数学，其中新开发的数值算法的鲁棒性保证将需要正式证明。该项目的输出将通过实际用例的数值模拟来表示，以证明我们方法的有效性和适用性。最终在嵌入式平台上的物理实现是可能的，这取决于可用的基础设施

The problem of UAV trajectory planning has been approached from many different perspectives, however current literature and industrial companies fail to provide a reliable distributed solution for controlling UAV swarms. Complex dynamical problems with a significant amount of uncertainty in the system are often approximated or simplified in order to fit the current numerical optimization solvers available. The aim of this project is to construct dynamical agents that can solve given tasks in an optimally distributed manner and integrate these agents into an uncertain, dynamic environment. This is relevant because solving a large-scale problem in a centralized way is not suited for inherently unstable applications where a continuous update of the control action is needed. Despite existing approaches, the proposed framework will have multiple objectives in mind: minimise energy consumption, minimise time to complete the mission as well as maximise reliability. Based on user needs, these objectives can be prioritised accordingly and, instead of solving a single problem, we would be able to solve multiple problems given by different relative prioritisations.To give a relevant example problem where the presented distributed numerical control algorithms can be applied, consider UAV communications in fifth generation(5G) networks.Stationary nodes may not be able to meet the demand and multiple UAVs will need to be used to enhance the connectivity. In order to ensure sufficient coverage, UAVs need to reposition themselves based on user movement. The multi-objective optimization feature is extremely relevant since different users may have conflicting requirements, for example a police team travelling to a crime scene will put more emphasis on reliable connection that will enable them to gather information on the way, while a mainstream user will be more interested in getting lower price (which is directly linked to energy consumption and network size). Another potential use case can be represented by providing aerial support and video monitoring for autonomous port operations or any site-inspection task.The general methodology involves putting together three types of dynamics, namely UAV dynamics, user/target movement prediction and communication dynamics, in a simulation environment that includes all these different governing equations as constraints. While these governing equations are not new, they have not yet been put together in the same distributed optimization problem and the interaction between them has not been studied in-depth, since many people assume either fixed user positions, or fixed transmission power profiles.After designing a representative model, the next step would be to design a numerical algorithm that is able to efficiently solve the problem online in real-time. Our method will be compared against existing centralized algorithms that require full knowledge about the environment. Our method is likely to perform better (in terms of runtime), since data gathering and communications between agents is time consuming. By solving multiple lower-dimensional parallel problems, we can split the computation and solve the trajectory planning problem on the UAVs' on-board embedded processors. We also aim to answer questions related to the system's resilience, such as: what happens if one or more UAVs fail, how should the remaining ones adapt to this, or how should one deal with situations when the data storage/transmission capacity of a drone hits the upper limit? The project will mainly be computational, with novel mathematics to be developed where the robustness guarantees of the newly developed numerical algorithm will need to be formally proven.The output of the project will be represented by numerical simulations of practical use cases in order to prove the effectiveness and applicability of our approach. Eventual physical implementation on embedded platforms is possible, depending on the infrastructure available