The technique for approximation of three-dimensional surfaces in order to synthesize algorithms for preventing aircraft collisions with obstacles

Abstract

The work marks the beginning of the practical application of algorithms for making the aircraft recovery maneuver from three-dimensional constraint surfaces, which are a combination of terrain and artificial obstacles. An analysis of events leading to aviation accidents was carried out, and a comparison of on-board systems for preliminary notification of aircraft crews about collisions with natural or artificial obstacles was made. It is shown that such systems are insufficient due to their passive-recommendatory nature of issuing warnings. A question has been raised about the need to implement an active automatic collision avoidance system with spatial obstacles. In order to apply existing algorithms for the aircraft recovery maneuver from spatial constraint surfaces, a technique has been developed for approximating three-dimensional surfaces (obstacles) specified on a digital terrain map in the form of discrete height readings with a certain step on a coordinate grid. A paraboloid of revolution was chosen as a continuous 2nd order surface approximating the obstacle, and its characteristic parameters were determined. To determine the characteristic parameters of the paraboloid, an algorithm for determining the intersection of a three-dimensional surface and a plane, based on the principle of determining the intersection of triangles in space, as well as a method for selecting the inflection point of the terrain, based on determining the value of the terrain height gradient, are proposed for use. The construction of an approximating paraboloid using the example of a natural obstacle in the form of a mountain range is given. When synthesizing algorithms for preventing collisions of aircraft with obstacles, the need to take into account not only the parameters of the constraint surfaces and dynamic characteristics of aircraft, but also the accuracy characteristics of data sources about their position is noted. Promising application areas of the developed methodology are shown.