An Automatic Mesh Refinement Method for Aircraft Trajectory Optimization Problems

An automatic grid refinement algorithm for the control grid within an aircraft trajectory optimization problem is presented. In the paper at hand, a direct multiple shooting approach is used but the procedure can also be applied in combination with other discretization methods. The algorithm takes the special properties of the considered dynamic system into account. It is based on the idea of a density function which is also used in the DENMRA algorithm (Ref. 1). In contrast to DENMRA which is only considering the control histories to calculate the density function but no information about the underlying system, here, the states of the dynamic system as well as the controls are used. Hence, the resulting density function is specially tailored to aircraft dynamics but can be calculated more precisely because of the good knowledge of the state histories. The better representation of the controls and the better convergence of the overall problem is demonstrated in an example considering a simple air race scenario.