Four-Dimensional Multi-Objective Trajectory Optimization using High-Fidelity Aircraft Models and a Projected Parameterization

Improving the sustainability of modern air traffic has been one of the urgent topics in the effort of reducing aviation's contribution to global climate change until today. One building block of this task is the prediction and simulation of aircraft operation and its optimization with respect to the effect on the environment. So far, modeling and simulation approaches with reduced coverage of aircraft dynamics (e.g. neglect of dynamic transient flight phases) are most frequently employed for this purpose. With the goal of increasing modeling fidelity and, in consequence, optimization result quality, this work presents a new approach towards a more detailed and realistic treatment of passenger aircraft trajectory optimization problems. Improvements are achieved by establishing a novel four-dimensional trajectory description (in position and time) in projected coordinates yielding shortest-path routes by definition. Further, a dedicated B-Spline based trajectory parameterization method with degree elevation allows to define higher continuity control inputs. In combination with a 4-D trajectory following flight control system, this allows a higher precision in tracking the optimized trajectory as well as improved computational execution due to less discontinuities in controls and derivatives. A pseudo-control-hedging controller ensures the flyability/validity of trajectories specified by the optimization algorithm. Aircraft models of varying level of detail are developed in the language Modelica, which incurs a high modularity and also promotes physics-based modeling of environment models depicting the dynamics of the most relevant influences (pollutant and noise emissions, contrail formation and fuel combustion) of air traffic on the environment. These are treated in a multi-objective problem formulation. In summary, the proposed contributions allow to devise more realistic optimization scenarios and to obtain more accurate and representative results when investigating the potential gains in environmental and operational effects of optimized trajectories