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On a Hamilton-Jacobi-Bellman approach for coordinated optimal aircraft trajectories planning

Abstract : In the context of future air trfic management (ATM), an increasing importance is given to environmental considerations and especially fuel consumption. It is thus advisable to make an optimal use of external conditions knowledge, like wind or temperature, to reduce the total fuel needed to complete a flight. On the other hand,safety must be guaranteed all over the trajectory: encounters below the regulatory separation minima, termed as conflicts, must never occur. In this paper, we consider the problem of optimally planning conflict free aircraft trajectories, based on a minimal time criterion and taking into account an ambient wind field. Aircraft motions are restricted to the horizontal plane only in order to reduce the dimension of the problem and to avoid costly changes of flight level. Since global optimality for the whole set of aircraft is sought after, the admissible space is modeled after a Cartesian product of the individual, two-dimensional state spaces with forbidden configurations removed. An Hamilton-Jacobi-Bellman approach in the so-called configuration space obtained that way is then applied to get a coordinated, conflict-free optimal planning. One of the main advantages of this method is the insurance of getting a global optimum without having to rely on an complex initialization procedure. However, as the size of the instances increases with the power of the number of aircraft considered, a dedicated numerical algorithm must be designed. In this work, the Ultra-Bee scheme is adapted to configuration spaces and solved in a four dimensional plus time setting.
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Céline Parzani, Stéphane Puechmorel. On a Hamilton-Jacobi-Bellman approach for coordinated optimal aircraft trajectories planning. Optimal Control Applications and Methods, Wiley, 2017, Special Issue : Global and robust optimization of dynamic systems, 39 (2), pp.933-948. ⟨10.1002/oca.2389⟩. ⟨hal-01340565⟩

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