Kinematic projection in modern technologies
Authors: Svidrak I. G. , Aftanaziv I. S. , Strogan O. I. , Shevchuk A. O. 
Published: December 2021

The trajectories and coordinates of unmanned aircrafts spatial location determination is researched with the help of kinematic projection means. The methodology offered below considers the formation of two mobile and independent kinematic projection centers raised into the air by drones. The electromagnetic radio waves emitted by them, penetrating an unknown aircraft object, form two independent projecting rays intersecting at the searched aircraft location point. In this case, the searched object spatial location instantaneous (at a certain point in time) point will be placed on an imaginary “picture plane” on a line connecting the points projections generated by drones interceptors projecting rays. As far as all of the projection objects in this case are movable, all the moving trajectory projection of the searched aircraft will be displayed on the monitor. The introduction of another “picture plane”, perpendicular to the main one, will help to build an axonometric mapping not only for projections, but also for the aircraft spatial movement trajectory itself. Each point of this trajectory gives an information about the “instantaneous” coordinates of the aircraft spatial location. The method of application of kinematic projection for display of a trajectory of movement and search of coordinates of moving objects is described. In kinematic projection, all its key components, namely the object, the center of projection, the image plane and the projecting rays, are in continuous motion with certain speeds and accelerations. Kinematic projection deepens the field of practical application of descriptive geometry. This is confirmed by the example of practical application of kinematic projection presented in the article for improvement of remote control of tillage equipment in automated land treatment complexes. The main technical support for the practical application of kinematic projection are stationary radio towers or unmanned aerial vehicles (BPLA), such as drones. They are equipped with video cameras and electromagnetic radiation devices. This equipment serves as a center of kinematic projection. The projecting rays generated by the projection center will be received by a stationary command post (center). It is equipped with a radar system (radar) and modern computer equipment with appropriate software. This equipment, in this case, performs the function of a “picture plane”, which will reflect the trajectory of agricultural machinery. Actuators and controls of the movement of tillage equipment are equipped with receivers of control radio waves and means of automated control. The use of kinematic projection helps to improve the quality of tillage. This is ensured by the fact that its use is carried out automatically and eliminates possible errors of operators. Kinematic projection can also be used in military affairs to detect enemy drones in the airspace. In this case, use a kind of kinematic projection with its two centers of generation of projecting rays. This is an example of the solution of the so-called “inverse problem” of kinematic projection, which provides the ability to search for the coordinates of the motion of the projected object at a known trajectory of its motion. The main advantage of kinematic projection is the ability to identify and display an object on a computer screen not only in a flat view, but also taking into account its spatial coordinates.