Numerical Techniques for Minimum-Time Routing on Sphere with Realistic Winds

A new method for computing globally the minimum-time function of the Zermelo navigation problem on a sphere, was proposed in the presence of a spatially varying wind field. One of the distinctive features of the method is the ability to handle discontinuities in the minimum-time function and singularities of the optimal synthesis. The proposed algorithm exploits the structure of the solution to the optimal control problem and uses a systematic method to filter out suboptimal solutions. This allows for the computation of the minimum-time function using a discretized mesh of points that are assigned minimum time values specific to their respective positions. the use of a mesh may lead to slow computational times if the mesh size is very large. However, the mesh size depends on the desired application, which in this case does not require an extremely fine resolution. Furthermore, with the minimum-time function already generated, minimum-time trajectories can be obtained with minimal computational effort.