Energy-Efficient Trajectories of Unmanned Aerial Vehicles Flying through Thermals

Abstract

This study presents optimal energy-efficient flight trajectories of a generic unmanned aerial vehicle (UAV) flying through a vertical moving thermal cell. A two-dimensional point-mass model of a jet-engined UAV in the vertical plane is used. UAV equations of motion and the thermal wind expression are normalized for numerical efficiency and four fundamental parameters are identified. UAV flights through a thermal cell are formulated as nonlinear optimal control problems that minimize the average thrust per unit time, subject to UAV performance constraints and periodic flight boundary conditions. These problems are converted into parameter optimizations and solved numerically. Fuel efficiencies of these optimal trajectories are compared with those of reference optimal flights in the lack of thermal winds. Both constant thrust and variable thrust solutions are obtained. Two patterns of optimal flights through thermals are identified, and their characteristics are analyzed. Both patterns of optimal flights are also explained from an energy maximization point of view. Effects of the fundamental parameters on optimal UAV flights are examined. Results suggest that significant improvements in UAV fuel consumption are possible by taking advantage of thermal energies.