Minimum fuel powered dynamic soaring of unmanned aerial vehicles utilizing wind gradients

This paper studies optimal powered dynamic soaring flights of unmanned aerial vehicles (UAVs) that utilize low-altitude wind gradients for reducing fuel consumptions. Three-dimensional point-mass UAV equations of motion are used, and linear wind gradients are assumed. Fundamental UAV performance parameters are identified through the normalization of the equations of motion. In particular, a single wind condition parameter is defined that represents the combined effect of air density, UAV wing loading, and wind gradient slope on UAV flight. An optimal control problem is first used to determine bounds on wind conditions over which optimal powered dynamic soaring is meaningful. Then, powered UAV dynamic soaring flights through wind gradients are formulated as non-linear optimal control problems. For a jet-engined UAV, performance indices are selected to minimize the average thrust required per cycle of powered dynamic soaring that employs either variable or constant thrust. For a propeller-driven UAV, in comparison, performance indices are selected to minimize the average power required per cycle of powered dynamic soaring with either variable or constant power. All problem formulations are subject to UAV equations of motion, UAV operational constraints, proper initial conditions, and terminal conditions that enforce a periodic flight. These optimal control problems are converted into parameter optimization with a collocation method and solved numerically using the parameter optimization software NPSOL. Analytical gradient expressions are derived for the numerical solution process. Extensive numerical solutions are obtained for a wide range of wind conditions and UAV performance parameters. Results reveal basic features of powered dynamic soaring flights through linear wind gradients.