In the paper at hand, the simultaneous computation of fuel-minimal approach trajectories for multiple aircraft present in the vicinity of an airport at a certain point in time is treated. The trajectory optimization task includes the determination of the optimal aircraft queuing sequence on the ILS glide path, minimizing the total fuel consumption of all aircraft involved. The trajectory optimization is based on aircraft point-mass simulation models with the aircraft characteristics taken from the BADA database of EUROCONTROL. Specifically tailored path constraints are introduced that define the permitted airspace and that enforce the aircraft to follow the ILS glide path once they have passed the final approach fix. Furthermore, path constraints are implemented that guarantee certain separation distances between the involved aircraft throughout the approach flights. An algorithmic procedure is set up which is aimed at producing a good initial guess for the multi-aircraft trajectory optimization task. The proposed framework is applied to a generic scenario where a fuel-efficient approach scheduling for four civil passenger aircraft has to be determined.
An algorithm for solving aircraft trajectory optimization problems using scalable high fidelity simulation models and pseudospectral discretization methods is presented. The resulting parameter optimization problem is solved with an SQP algorithm. One of the problems that arise when using complex simulation models in combination with gradient based optimization algorithms is the generation of an appropriate initial guess. To address this issue two different simulation models are implemented: a mere point-mass simulation model with three degrees of freedom (DoF) and a full nonlinear six degree of freedom dynamic model of the same aircraft. In contrast to the 6-DoF model, the generation of an initial guess for the point-mass model can be performed by a geometric approach that can easily be handled by the user. The optimal solution of the point-mass model will be used as an initial guess for the high fidelity optimization problem. To enable this, an iterated extended Kalman Filter is implemented to adapt the optimal solution of the point-mass model such that it can be used as an initial guess for the 6-DoF optimization. This way, the convergence rate of the overall trajectory optimization problem can be significantly improved. The benefits of the method are illustrated by an air race example involving two dynamic models of an aerobatic aircraft. NomenclatureFrames / References = Aerodynamic Frame / Motion / Force = Body-Fixed Frame = Earth-Centered Earth-Fixed Frame = Kinematic Flight Path Frame / Motion = Navigation Frame = North-East-Down Frame (NED) = Center of Gravity / Gravitational Force = Commanded (as index) = Reference (as index) = Propulsive Force (as index) = Total Force (as index) = Transformation matrix Aircraft Controls = Aileron deflection = Elevator deflection = Rudder deflection = Thrust lever position State Space Modeling = State vector = Control vector Kinematics = Kinematic velocity ⃑ ⃑ = Kinematic velocity vector = Northward position = Eastward position = Downward position = Flight-path course angle = Flight-path climb angle = Flight-path bank angle = Angle of attack = Angle of sideslip ⃑⃑⃑ = Angular velocity vector = Roll rate = Pitch rate = Yaw rate 2 Aircraft parameters = Aircraft mass = Aerodynamic coefficient = Aerodynamic derivative = Zero-lift drag coefficient = Reference area ̅ = Dynamic pressure = Gravitational constant = Inertia tensor = Half wing span ̅ = Length of aerodynamic chord = Air density Forces and Moments = Force vector ⃑⃑⃑ = Moment vector = Thrust = Lift = Drag = Aerodynamic side force Optimal control problem formulation = Bolza cost function = Mayer cost function = Lagrange cost function = Initial / Final boundary conditions = Interior point conditions = Equality / Inequality constraints Collocation Method = Lagrange polynomial = State approximation over time = Control approximation over time = Derivatives of Lagrange polynomials = Gauss weights = Time = Normalized time Kalman Filter = Process noise = Measurement noise = Covariance matrix of process noise = Covariance matr...
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