Controllability and Reachability for Micro-Aerial-Vehicle Trajectory Planning in Winds

CD0 = zero-lift drag coefficient CL, CD = lift and drag coefficients D = aerodynamic drag Emax = maximum lift-to-drag ratio or aerodynamic efficiency g = gravitational acceleration I = performance index K = induced drag factor L = aerodynamic lift m = aircraft mass N = number of nodes in the discretization of time interval n = load factor S = vehicle reference area T = engine thrust t = time V = airspeed VI = inertial speed Vm = maximum airspeed trajectory constraint Vmax = maximum permitted airspeed for vehicle Wm = wind magnitude Wx,Wy = east and north wind components x, y = east and north positions = bank angle m = maximum bank angle trajectory constraint = direction angle measured clockwise from the North = air density = normalized time = heading angle measured clockwise from the North I = inertial heading angle measured clockwise from the North w = wind direction angle measured clockwise from the North 0 = derivative with respect to normalized time