# Formation Control Algorithm of Multi-UAV-Based Network Infrastructure
## 1 Introduction
Optimizing the formation of the UAVs according to the network requirement in a certain area is challengeable since the terrestrial devices are mobile, and tracking all of their exact location is generously hard. Figure 1: Multi-UAV-based network infrastructure. UAV: Unmanned Air Vehicles. Our approach is a real-time feedback control where the UAVs exchange the information of the network (both access network and the ad hoc network) and location status with the neighbors and determine the proper direction to move. To determine the direction, the UAV should consider several aspects: the ad hoc connectivity with nearby UAVs, the extension of the network coverage area, and the traffic management of the ground. We model each concern as a _force_ and each UAV determines a single direction from the sum of the forces. For example, if an UAV establishes excessively many connections with terrestrial devices, the UAV's network status is reported to the neighbors and the formation is changed to disperse the traffic load of the UAV. However, since the UAV should not lose the ad hoc connection, so the UAV cannot move too far from the others. All of the behaviors are defined as the forces, derived from the information UAVs exchange. To find the optimal direction of each UAV, we should consider the benefit of the overall network performance on the movement. We firstly analyze the dynamics of the multi-UAV-based network infrastructure on the side of the end-to-end communication between the terrestrial mobile devices and the backbone network. We model the generic phenomenon of the medium access of wireless network and propose the estimation equation of the aggregated throughput among the mobile devices. We verified our model by comparing the analytic result and the simulation result conducted by ns-3, and achieved above 98% accuracy with the simulation. Based on the analytic model, we propose a novel formation control algorithm that consistently enhances the overall network throughput of the multi-UAV-based network infrastructure. Due to the large-scale and extremely high cost feature of the practical experiment, we thoroughly simulated our algorithm and the network environment via ns-3 and shows approximately 41% increase in network throughput. The contribution of the paper is listed as follows. * We designed a network analysis model of the multi-UAV-based network infrastructure. During the derivation of the equations, we suggested a generic mathematical form of the multiple access behavior on the wireless access network. We proved that the generic form fits to the simulated behavior of the wireless access network, and applied the analysis results to the design of the algorithm. * We proposed a multi-UAV control algorithm for the multi-UAV-based network infrastructure. The algorithm continuously transforms the formation of a fleet of UAV, while optimizing the network throughput of the infrastructure. Also, we proved that the result of the algorithm is a Nash equilibrium. * We implemented a design of the multi-UAV-based network infrastructure, using ns-3. With the simulation tool, we evaluated our algorithm and proved that the algorithm outperforms the regular, static formation of the UAVs. This paper is organized as follows. Section 2 investigates the former studies in UAV-based network-providing domain, and compares with our study to seize the motivation of this paper. Section 3 addresses the network analysis model of multi-UAV-based network infrastructure and Section 4 proposes a formation control algorithm of the UAVs. Then, we introduce the simulation environment and the evaluation of the model and the algorithm in Section 5. Finally, Section 6 concludes the paper.