The features of numerical solution to a 4D navigation problem are considered. When solving that problem it is necessary to find the optimal path and control minimising the fuel consumption along a flight path with the given boundary conditions (in particular with the given range and time of flight). The motion of non-manoeuvrable aircraft is considered in a vertical plane. The problem is solved by means of the maximum principle.
The paper presents a short description of two approaches to solving of the fly-around-obstacles problem. This problem consists in finding of a global optimal flying object trajectory or route for a flight over an area with obstacles of natural or artificial type. The trajectory length or fuel consumption is limited. The paper contains two parts corresponding to the combinatory and variational approaches, respectively.
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