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

Abstract

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.Nomenclature a = azimuth of the sun, degof the aircraft, N E R = energy ratio E T = total energy, J E in = energy collected, J E out = energy lost, J e = elevation of the sun, deg g = gravitational acceleration, m=s 2 H = Hamiltonian, W H VV = @ 2 H=@V 2 H V = @ 2 H=@@V H = @ 2 H=@ 2 i = incidence angle of sun rays, deg j = dummy summation index K = amount whereby the induced drag exceeds that of an elliptical lift distribution m = mass, kg P R = power ratio P in = power collected, W P out = power lost, W P sd = power spectral density of the sun, W=m 2 S = surface area of the wing, m 2 T = thrust of the aircraft, N T M = mission time, s t f = final time, s t o = initial time, s V = speed, m=s V energy min = speed at minimum energy out, m=s V power min = speed at minimum power out, m=s x = X position, m W = weight of the aircraft, N y = Y position, m = Oswald efficiency factor prop = efficiency of the propeller sol = efficiency of the solar cells = incidence angle of sunlight upon the aircraft, deg x = x costate, N y = y costate, N = costate, J = air density, kg=m 2 w = mass per unit area of the wing, kg=m 2 = bank angle, deg = heading, deg

Reviews of methods to extract and store energy for solar-powered aircraft

“…For the case they studied, the optimization reduces the mass of the aircraft and increases the cruise speed simultaneously. Klesh and Kabamba [133,134] also prove that level flight trajectory planning for solar-powered aircraft has a great impact on their energy consumption. Spangelo and Gilbert [6] formulate a new optimization problem about flight trajectories for solar-powered aircraft with specified closed ground tracks.…”

“…Many designers have realized that the energy is the crucial constraint for the success flights of solar-powered aircrafts [10,14,114], so, the tracking accuracy and energy tracking factor are important for the MPPT applied in solar-powered aircraft. For example, the Zephyr had been equipped with an advanced power management system to ensure the photovoltaic cells operate at or near their peak power point whether the cells are working in propulsion or energy storage mode [108].…”

“…Additionally, by using an autopilot system to the aircraft, it is possible to work anywhere in the world [4]. Thus, the solar-powered aircrafts can be employed as an ideal communication platform and are especially suitable for the high-altitude, longendurance (HALE) missions, such as border surveillance [5], forest fire fighting, ground tracking [6], precision agriculture [7] and even the future exploration of Venus [8,9] and Mars [10,11].…”

Meteorological path planning using dynamic programming for a solar-powered UAV

“…As a fuel-powered UAV is considered, environmental impediments and solar radiation are not taken into account. [7] and [8] address the maximization of solar power generation in theoretical situations without any consideration of meteorological data. [9] and [10] investigate path optimization with respect to military threats or restricted areas.…”

Faster, Higher, and Greener: Vehicular Optimal Control

“…Energy-optimal trajectories for UAVs equipped with solar cells are considered in [3]. These vehicles may be used to travel between given positions within an allowed time or for loitering indefinitely in a target neighborhood.…”