A Nonlinear Model for Vertical Free-Flight Trajectory Planning

The traditional approach of flight trajectory planning for commercial airplanes aligns the routes to a finite air travel network (ATN) graph. A new alternative is the free-flight trajectory planning, where routes can use the entire 4D space (3D+time) for more fuel-efficient trajectories that minimize the travel costs. In this work, we focus on the vertical optimization part of such trajectories for a fixed horizontal trajectory, computed or manually derived beforehand. The idea is to assign to each of the trajectory’s segments an optimal altitude and speed for the cruise phase of the flight. We formulate this problem as a nonlinear programming (NLP) problem. As for the input of the model, information about the airplane’s fuel consumption is provided for discrete levels of speed and weight values. Thus a continuous formulation of this input data is required, to meet the NLP requirements. We implement different interpolation and approximation techniques for this. Using AMPL as modeling language, along with nonlinear commercial solvers such as SNOPT, CONOPT, KNITRO, and MINOS, we present numerical results on test instances for real-world instance data and compare the resulting trajectories in terms of the fuel consumption and the computation times.