Energy-Optimal Trajectory Planning of Hybrid Ultra-Long Endurance UAV in Time-Varying Energy Fields

The paper addresses the problem of calculating energy optimal trajectory for a novel class of hybrid unmanned aircraft equipped with hydrogen fuel cell and solar photovoltaic energy production technologies. The goal of the design is to minimize the energy (fuel) used in flight by optimally using the finite energy stored in the hydrogen fuel cell and routing the aircraft through the dynamic energy fields of solar irradiance and wind. The optimization task is formulated as a two-point boundary value problem for an aircraft traveling in time-varying atmospheric fields with an objective of finding the minimum energy route and the associated controls. The task is solved by applying the Pontryagin maximum principle to the resulting $2D$ kinematics of a UAV along with the associated energy models that characterize its energy efficiency. Utilizing the necessary conditions of optimality allows synthesizing the optimal control laws of the bank angle and airspeed. The problem of initial guess is solved by designing a continuation algorithm that is based on scaling the wind magnitude. As a result, the initial guess becomes precisely known as the arc of a great circle that is well-defined by its states and the costates. Not only it initializes the next step of the continuation algorithm, but it also serves as a reference for the comparison of energy expenditures along with the energy optimal and the shortest routes.