Formation of unmanned aircraft trajectory when flying around prohibited areas

Considered the problem of flying over restricted areas by an unmanned aerial vehicle (UAV), which have various shapes and restrictions, set on the basis of the international airspace classification system for aviation in accordance with the Chicago Convention and the recommended principles for the formation of forbidden zones, rules for creating a flight route along forbidden zones and actions in case of border violations of restricted areas. The problem of analytical synthesis of the control acceleration of an unmanned aerial vehicle (UAV) is solved during its flight along a route passing along the boundaries of the forbidden zone of a given shape, along a given trajectory, which consists of subsequent segments located at the same height relative to the earth’s surface, in a given coordinate system. The optimal control synthesis problem is solved as an analytical definition of the optimal control of a linear non-stationary system based on the quadratic quality functional. A mathematical model of UAV motion in the horizontal plane is proposed, in the form of a system of ordinary differential equations in the Cauchy form. A law for measuring the control acceleration of the UAV’s center of mass is obtained on the basis of specifying the minimized quality functional and the corresponding constraints, which is a feature of the considered method of solving the problem. The proposed quality functional takes into account the parameters of coordinates and speed of the UAV, which correspond to the given points in the airspace, which characterize the necessary trajectory for flying around the restricted area. The derived mathematical dependences make it possible to implement them on board a UAV and minimize energy costs when guiding a UAV moving through specified points in space. Computer modeling of the derived analytical results, mathematical dependencies representing the optimal trajectory of the UAV flight along the boundaries of the forbidden zone, as well as the corresponding processes of changing the control acceleration and speed of the UAV movement was carried out, which made it possible to draw conclusions about the efficiency of the proposed method and the feasibility of its further use as a basis. for the initial stage of the synthesis of the UAV control system.

Synthetic Aircraft Trajectories Generated with Multivariate Density Models

Aircraft trajectory generation is a high stakes problem with a wide scope of applications, including collision risk estimation, capacity management and airspace design. Most generation methods focus on optimizing a criterion under constraints to find an optimal path, or on predicting aircraft trajectories. Nevertheless, little in the way of contribution has been made in the field of the artificial generation of random sets of trajectories. This work proposes a new approach to model two-dimensional flows in order to build realistic artificial flight paths. The method has the advantage of being highly intuitive and explainable. Experiments were conducted on go-arounds at Zurich Airport, and the quality of the generated trajectories was evaluated with respect their shape and statistical distribution. The last part of the study explores strategies to extend the work to non-regularly shaped trajectories.

Aircraft Trajectory Clustering in Terminal Airspace Based on Deep Autoencoder and Gaussian Mixture Model

The aircraft trajectory clustering analysis in the terminal airspace is conducive to determining the representative route structure of the arrival and departure trajectory and extracting their typical patterns, which is important for air traffic management such as airspace structure optimization, trajectory planning, and trajectory prediction. However, the current clustering methods perform poorly due to the large flight traffic, high density, and complex airspace structure in the terminal airspace. In recent years, the continuous development of Deep Learning has demonstrated its powerful ability to extract internal potential features of large dataset. Therefore, this paper mainly tries a deep trajectory clustering method based on deep autoencoder (DAE). To this end, this paper proposes a trajectory clustering method based on deep autoencoder (DAE) and Gaussian mixture model (GMM) to mine the prevailing traffic flow patterns in the terminal airspace. The DAE is trained to extract feature representations from historical high-dimensional trajectory data. Subsequently, the output of DAE is input into GMM for clustering. This paper takes the terminal airspace of Guangzhou Baiyun International Airport in China as a case to verify the proposed method. Through the direct visualization and dimensionality reduction visualization of the clustering results, it is found that the traffic flow patterns identified by the clustering method in this paper are intuitive and separable.