Cross-entropy based flight trajectory generation

What is it about?

In this article, our objective is to provide a theoretically sound and practically efficient framework for solving tactical 4D-trajectory management problems. The proposed method involves a sophisticated aircraft performance model (APM) based on Base of AircraftData (BADA) 4 and recent algorithmic advances in stochastic approaches to motion planning. Such probabilistic algorithms embed stochastic behavior, which is inherent in air traffic. The proposed method also utilizes operational cost objectives in the calculation of cost-efficient trajectory segments through the structured flight-template automaton. These flight templates employ their own approximate trajectory optimization and involve lower level maneuver mode automatons that effectively utilize advanced performance definitions in BADA 4. Moreover, multi-modal maneuver-modeling framework significantly reduces complexity by reducing the dimension of the problem and relaxing parameter optimization by designing specific optimization procedures for each mode. The sampling-based trajectory planner algorithm utilized here spatially explores the airspace and provides proper separation with local trajectory segments. The algorithm guarantees asymptotic opti-mality under certain conditions. Moreover, we have developed an efficient sampling strategy based-on cross-entropy method with sampling discrepancy control, which transforms sampling problems into stochastic optimization problems and provides rapid convergence to the optimal solution. By taking into account the operational reality, the initialization of the problem exploits the last-available flight plan that was compromised (subject to potential conflict) due to uncertainties such as wind speed change. The idea behind importance sampling with cross-entropy is that the new plan is most likely to be spatially nearby to the original flight plan. This practice is inherent to tactical flight planning, where the strategic flight plan (i.e. Reference Business Trajectory) already reflects many objectives of the stakeholders (e.g. airlines, air traffic flow managers) subject to comprehensive optimization that is run in-ground systems. In the hypothetical worst-case scenario, where the new flight plan is far from the previous optimum, our sampling strategy based-on cross entropy with discrepancy control iteratively converges on a low-discrepancy sampling, which is purely quasi-random sampling. Otherwise, and mostly, the elite sampling sets rapidly converge on a delta function, in the other words, the minimum cost trajectory.

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Why is it important?

The integration of the proposed strategies lets us solve challenging, real-time in-tactical 4D-trajectory planning problems within the current and the envisioned future realm of air traffic managementsystems