Aena

We formulate fuel-optimal conflict-free aircraft trajectory planning as a hybrid optimal control problem. The discrete modes of the hybrid system capture the air traffic procedures for conflict resolution, e.g., speed and turn advisories. To solve problems of realistic dimensions arising from air traffic sector planning, we formulate a numerically tractable approach to solve the hybrid optimal control problem. The approach is based on introducing binary functions for each mode, relaxing the binary functions and including a penalty term on the relaxation. The transformed and discretized problem is a nonlinear program. We use the approach on a realistic case study with seven aircraft within an air traffic control sector, in which we find minimum-fuel conflict-free trajectories.

This paper presents a method to segment airplane radar tracks in high density terminal areas where the air traffic follows trajectories with several changes in heading, speed and altitude. The radar tracks are modelled with different types of segments, straight lines, cubic spline function and shape preserving cubic function. The longitudinal, lateral and vertical deviations are calculated for terminal manoeuvring area scenarios. The most promising model of the radar tracks resulted from a mixed interpolation using straight lines for linear segments and spline cubic functions for curved segments. A sensitivity analysis is used to optimise the size of the window for the segmentation process.