Optimal path planning in a constant wind with a bounded turning rate

In this paper, we explore the problem of generating the optimal time path from an initial position and orientation to a final position and orientation in the two-dimensional plane for an aircraft with a bounded turning radius in the presence of a constant wind. Following the work of Boissonnat, we show using the Minimum Principle that the optimal path consists of periods of maximum turn rate or straight lines. We demonstrate, however, that unlike the no wind case, the optimal path can consist of three arcs where the length of the second arc is less than π. A method for generating the optimal path is also presented which iteratively solves the no wind case to intercept a moving virtual target.