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Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization

  • Flight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods. Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories. Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators.

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Author:Ralf BorndörferORCiD, Fabian DaneckerORCiD, Martin WeiserORCiD
Document Type:Article
Parent Title (English):Journal of Optimization Theory and Applications
First Page:830
Last Page:856
Year of first publication:2023
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