Optimal path planning for unmanned aerial vehicles in average winds

This paper considers the optimal route planning problem for an unmanned aerial vehicle which flies in average wind field with constant altitude and airspeed between two fixed positions. According to characters of the average wind and voyage of the unmanned aerial vehicles, constant wind model and wind model varying with position are presented based on formula from meteorology and function approximation. By defining new Euler angles, kinematic model in arbitrary variable wind fields and equations expressing relation between airspeed and ground speed are derived. If the distance between origin and destination is much larger than minimum turning radius, the turn rate constraint can be neglected. Analytic expressions are developed to solve the problem by calculus of variations. This solution has small calculation quantity, and it can be used to real-time online implementation for the unmanned aerial vehicle. Simulation examples show that it is feasible and effective for optimal route planning.