Gnomonic Projection Application in Solving the Problems of Flight Route Optimization and Processing the Terrain Elevation Matrix in the Flying Vehicle On-Board Computers

Abstract

The paper proposes an approach that allows accounting for the Earth sphericity in solving the problems of optimizing the flight route of an aerial vehicle and processing the terrain elevation matrix using the initial information presentation in the gnomonic projection. The use of the gnomonic projection main property, i.e., representation of the orthodromies in the form of straight lines, makes it possible to apply the generally accepted algorithms and approaches in route optimization and solve these problems with limited computation capabilities of the aerial vehicle onboard computers. For example, the graph theory methods widely used in solving the similar problems on a plane could be applied. The need to take into account the Earth sphericity in the route optimization algorithms is caused primarily by features of the aerial vehicle trajectory control (namely, flight along the orthodromy) between the route turning points. The paper presents algorithms and dependencies that allow processing the initial information (including the terrain elevation matrix) on the gnomonic projection. They include formulas to solving the direct and inverse geodetic problem, simplified (from the point of view of computation resources) dependency to determine the distance between two points in the projection, and solutions to select cells belonging to the given polygon or circle. To demonstrate the use of the obtained dependencies in solving a practical problem of determining the shortest path between two points on the Earth’s surface with bypassing the forbidden zones (formed by analyzing the terrain elevation matrix in the area under consideration), an example of its solution using the graph theory methods (Dijkstra’s algorithm) is considered

Please cite this article in English as:

Puchkov L.D., Zerkalenkov D.A. Gnomonic projection application in solving the problems of flight route optimization and processing the terrain elevation matrix in the flying vehicle on-board computers. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2025, no. 2 (151), pp. 102--121 (in Russ.). EDN: TPXVEA

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