Trajectory Planning in Windy Urban Environment Using Gappy Proper Orthogonal Decomposition for Wind Estimates

Abstract

A trajectory planning algorithm based on the traditional A* formulation is designed to determine the minimum-energy path from a start to a final location taking into account the prevailing wind conditions. To obtain average wind conditions in an urban environment, full-scale Reynolds-averaged Navier–Stokes simulations are first performed using OpenFoam® for various inlet wind directions on a computational model representing complex buildings on the campus of the Technical University of Berlin. The proper orthogonal decomposition (POD) modes of the full database are then calculated in an offline stage with the wind direction as a parameter. Next, the online reconstruction of the complete urban wind field is performed by Gappy POD using simulated pointwise measurements obtained by sparse sensors. Finally, the trajectory planning algorithm is applied to the reconstructed wind field and validated by comparison with the trajectory computed on the full-order computational fluid dynamics (CFD) model. The main conclusion is that the error made by calculating the energy requirements for a specific trajectory based on an inexpensive reduced-order model of the wind field instead of an expensive full-order CFD database is only a few percent in all investigated cases. Therefore, a reliable and trustworthy trajectory can be calculated from the inexpensive reduced-order model obtained with only a few velocity sensors. Furthermore, it is shown that the energy consumption along a trajectory could be reduced by up to 20% by taking the prevailing wind field into consideration instead of considering the shortest path.