Morozova G. Geometric modeling of movement trajectory of shape on a plane among obstacles using R-functions

Dissertation is devoted to development of the calculation method of curve shape on the plane, which is the shor path connecting two given points of the plane and passes between the obstacles - rectangles, described by equations in implicit form for the coordinates of nodal points; method is based on the potential use of virtual functions and R-functions. The aim of study is the development of an algorithm for calculating the movement trajectories on the plane among obstacles for the mobile robot accounting its overall dimensions circle. It is developed the ways of construing the potential virtual functions and search of passing points of iteration in the process of focus point movement till minimum, and defining the lanes between obstacles gone by the mobile robot with the given overall circle. The method based on this is elaborated for construing the potential virtual function which allows to define the lanes between obstacles gone by the mobile robot accounting its overall circle. Results of research are presented for introduction at Prilutsk factory of fire and special engineering when designing robotic systems trace in emergency and in the system of computer-aided placement of containers in the company "Feodosia sea trade port", in teaching process of the National University of Civil Defense of Ukraine.