Holistic Approach for Aircraft Trajectory Optimization Using Optimal Control

Abstract

This paper deals with an optimal control approach for commercial aircraft trajectory planning, focusing on the vertical path and the minimization of the fuel burned. The main contribution is the optimization of the whole trajectory, also called the mission, without prior separation into different flight phases (climb, cruise, and descent), contrary to traditional approaches that consider the flight phases sequentially. The proposed optimal control problem (OCP) is formulated and then solved using a direct collocation method. Initial results yield optimal trajectories with a gradual climb during the cruise (climb cruise), which correspond to theoretical trajectories that minimize fuel consumption. Furthermore, a penalization is introduced to ensure vertical profiles featuring horizontal cruise levels on so-called flight levels, compliant with current air traffic management regulations. The use of direct methods to address this OCP induces large nonlinear optimization problems that are solved using an interior point method. This methodology is likely to lead to poor local optima, but a simple multistart heuristic shows that the solutions found for standard problems appear to be globally optimal. Such an approach does not need to impose a priori the cruise flight levels and is suitable for commercial aircraft flight planning purposes. It leads to fuel saving and subsequently to important improvements against environmental impact by reducing [Formula: see text] emissions.