Flight Path Optimization for Competition Sailplanes through State Variables Parameterization

Abstract

This paper presents a numerical process for determining optimal flight paths for competition soaring.  The goal is reduction of flight time required to fly towards an ascending thermal and climb to a given altitude.  The optimization procedure applies a direct method to obtain sub-optimal solutions through parameterization of state variables, unlike a previous study by the same authors which was based on control parameterization.  A mathematical programming procedure is used to determine the sub-optimal values for the parameterized state variables.  The optimal control law, which is necessary for the generation of the sub-optimal state, is obtained through a step-by-step penalty technique.  The results demonstrate that the optimization of transitory phases is important for the minimization of total flight time.