Solar-Powered Aircraft: Energy-Optimal Path Planning and Perpetual Endurance

This paper considers energy-optimal path planning and perpetual endurance for unmanned aerial vehicles equipped with solar cells on the wings, which collect energy used to drive a propeller. Perpetual endurance is the ability to collect more energy than is lost during a day. This paper considers two unmanned aerial vehicle missions: 1) to travel between given positions within an allowed duration while maximizing the final value of energy and 2) to loiter perpetually from a given position, which requires perpetual endurance. For the first mission, the subsequent problem of energy-optimal path planning features the coupling of the aircraft kinematics and energetics models through the bank angle. The problem is then formulated as an optimal control problem, with the bank angle and speed as inputs. Necessary conditions for optimality are formulated and used to study the optimal paths. The power ratio, a nondimensional number, is shown to predict the qualitative features of the optimal paths. This ratio also quantifies a design requirement for the second mission. Specifically, perpetual endurance is possible if and only if the power ratio exceeds a certain threshold. Comparisons are made of this threshold between Earth and Mars. Implications of the power ratio for unmanned aerial vehicle design are also discussed. Several illustrations are given.