Spherical Trigonometry, a Bridge from Trajectory Waypoints to Guidance Algorithm

Conventionally flight path in airplanes and unmanned air vehicles is determined with waypoints. Waypoints are points on the surface of the earth with specific latitude and longitude. For accurate crossing the waypoints at a specific time, definition of accurate guidance error parameters is essential. Guidance algorithm based on these parameters can make appropriate commands. In this article two parameters, guidance latitude and guidance longitude, based on spherical trigonometry, are defined. Indeed these parameters show guidance error in horizontal channel and longitudinal channel respect to great circles between waypoints. These parameters can be calculated in a closed form and solution of complicated integrals, which is in geodetics on an ellipsoid, do not required. Also guidance algorithms in two channel based on these parameters are designed. In horizontal channel, a PD controller and in longitudinal channel a proportional controller on the difference between desired and real velocity, are designed as guidance algorithms. Also performance of these algorithms is shown with simulation results in comparison with plane simulation.

Keywords:

Spherical trigonometry , Guidance latitude , Guidance longitude , Waypoints , Guidance algorithm , کلید واژگان , مثلثات کروی , طول هدایتی , عرض هدایتی , نقطه­راه مسیر , الگوریتم هدایت