Considerations in the application of dynamic programming to optimal aircraft trajectory generation

The application of dynamic programming to optimal trajectory generation is reported with reference to the problems that arise in the selection of the size of the solution space, including the size of the grid spacing. Recommendations are given on the choice of the grid size and the size of the solution space boundaries to obtain the global optima. The effects of the control representation and interpolation procedures used within the algorithm on the solution are also reviewed. Results of an investigation into reducing the size of the solution space where the trajectory is to be generated are reported. Aspects of the mathematical formulation of the optimization criteria are considered. Imposing constraints, such as path curvature, results in the rejection of certain controls before the dynamic programming technique has chosen the optimal control. How the use of higher-order constraints may result in the choice of a trajectory that is not the global optimum is discussed. A modification of the mathematical procedure implemented to overcome this difficulty is discussed