Simplex Methods for Optimal Control of Unmanned Aircraft Flight Trajectories

The feasibility of using a constrained Delaunay triangulation method for determining optimal flight trajectories of unmanned air vehicles in a constrained environment is explored. Current methods for developing optimal flight trajectories have yet to achieve computational times that allow for real-time implementation. The proposed method alleviates the dependency of problem specific parameters while eliminating constraints on the Non-Linear Program. Given an input of obstacles with n vertices, a constrained Delaunay triangulation is performed on the space. Converting the vertices of the triangulation to barycentric coordinates on a phased approach defines the state bounds and max time for each phase. With two-dimensional aircraft dynamics, direct orthogonal collocation methods are performed to compute the optimal flight trajectory. Results illustrate computational times and feasibility of Small Unmanned Aircraft System flight trajectories through polygon constraints.