Collocation Methods to Minimum-Fuel Trajectory Problems with Required Time of Arrival in ATM

In the future air traffic management system, the trajectory becomes the fundamental element of a new set of operating procedures collectively referred to as trajectory-based operations. Trajectory-based operations require the air traffic management to introduce profound innovations to enable the envisioned changes. Some of these include collaborative decision-making processes, better data and information management, and advanced decision support tools to aid human operators. In particular, fast and accurate computation of optimal trajectories could certainly contribute to enhance trajectory management within the future air traffic management. The trajectory optimization problem can be solved using optimal control methods. In this paper, the existing methods for solving optimal control problems focusing on direct collocation are discussed. In particular, pseudospectral collocation methods have shown to be numerically more accurate and computationally much faster than other direct methods. A very relevant problem arising in air traffic management is analyzed, that is the minimum-fuel trajectory with required time of arrival. Preliminary results illustrate the advantages of using pseudoespectral collocation methods for trajectory optimization in air traffic management; for the same order of numerical accuracy, they present computational times that are at least two orders of magnitude better than other collocation methods. For similar computational times, pseudospectral collocation methods achieve a numerical accuracy that is at least one order of magnitude better than other methods.