Daneev A. V. Postroyeniye opornykh pryamykh k dvum neperesekayushchimsya ogra-nichennym mnozhestvam tochek na ploskosti v zadache formiro-vaniya trayektorii dvizheniya transportnykh sredstv [Construction of supporting lines to two non-intersecting limited sets of points on a plane in the problem of formation of a vehicle trajectory]. Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie [Modern Technologies. System Analysis. Modeling], 2019. Vol. 64, No. 4. Pp. 108–112. DOI: 10.26731/1813-9108.2019.4(64). 108-112
This article proposes a method for finding supporting lines to two non-intersecting, limited sets of points on the plane. For cases where the sets are convex polygons, known algorithms are based on the classification of the vertices of the polygons and the angles between the supporting lines and the sides of the polygons. A new criterion and an algorithm for finding supporting lines of two strictly convex polygons are proposed. Such problems may arise in the study of the tasks of the formation of the trajectory of movement of vehicles, including taking into account the bypass of hazardous areas along the route. Well-known mathematical statements and methodologies for solving problems whose internal content is close to the problem of forming a route either do not consider the possibility of physical implementation of the solutions obtained with their help, or use the dynamics factor in the form of equations of motion. This significantly complicates the algorithmic side of solving the problem. The geometrical approach, taking into account the dynamics factor, makes it possible, on the one hand, not to rely on the dynamics equation when synthesizing control, and on the other hand, it allows a priori asserting the feasibility property of the resulting vehicle route in terms of their allowable maneuver capabilities. The material of the article can make up a mathematical component of software and mathematical support for solving the navigation problem to determine the optimal (based on the minimum length) trajectory of vehicles and meets the requirements for RAM and speed during its software implementation on the on-board processor.
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