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

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