Chance-constrained UAM traffic flow optimization with fast disruption recovery under uncertain waypoint occupancy time

Trajectory-based operations offer a promising solution for effective urban air mobility (UAM) traffic management with conflict-free four-dimensional trajectories. However, these trajectories generated in strategic phases by existing methods could be significantly disrupted due to uncertainties such as flight delays and trajectory deviations. This paper develops a chance-constrained UAM traffic flow management (UTFM) optimization model with fast disruption recovery to solve observed disrupted trajectories and improve their resilience. Our model introduces a novel concept of waypoint occupancy time to cope with the probabilistic separation constraints induced by variables, notably urban wind field. We then convert the probabilistic constraint into a deterministic one, incorporating risk-bounded separation guarantees derived from flight experiment data. Furthermore, we develop a hierarchical stochastic search algorithm for solving the redefined deterministic optimization problem. Our comprehensive numerical studies demonstrate the model's effectiveness in restoring disrupted flights and resolving conflicts within seconds. Additionally, our reliability testing showcases the resilience of the model in managing disruptions, even at levels as high as 50%, and its adaptability in addressing varying levels of uncertainty risk. We further demonstrate the ability of the UTFM model to capture tail risks across Gaussian and non-Gaussian uncertainty distributions. Lastly, our scalability analysis highlights the potential capacity of the model to support up to 3,000 flights per hour in Singapore's urban airspace below 400 ft. This study introduces an adaptable framework to facilitate the modelling of robust traffic flow management and performance-based separation for a variety of eVTOL types under uncertainties.