Energy-Optimal Path Planning for Solar-Powered Aircraft in Level Flight

[Abstract] Motivated by long-endurance requirements in surveillance, reconnaissance and exploration, this paper considers level flight path planning for unmanned aerial vehicles (UAVs) equipped with solar cells on the upper surface of the wings. These solar cells collect energy that is stored in a battery and used to drive a propeller. The mission of the UAV is to travel from a given initial position to a given final position, in less than an allowed duration, using energy from the battery. The subsequent problem of energy-optimal path planning features the interaction between the aircraft kinematics, the energy collection model, and the energy loss model. All three models are coupled by the bank angle of the UAV. Within this framework, the problem is formulated as an optimal path planning problem, with the aircraft bank angle and speed serving as control inputs. Necessary conditions for optimality are given, whose solution yields extremal paths. These necessary conditions are utilized to study analytically the properties of extremal paths. An efficient numerical procedure is also given. It is shown that optimal paths belong to one of two regimes: solar or drag. The Power Ratio, a non-dimensional number that can be computed before flight, is identified. It is shown that this ratio predicts the regime of the optimal path, which facilitates the solution. Implications of the power ratio for UAV design are discussed. Several illustrations are given.