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Advanced Air Mobility (AAM) using electrical vertical take-off and landing (eVTOL) aircraft is an emerging way of air transportation within metropolitan areas. A key challenge for the success of AAM is how to manage large-scale flight operations with safety guarantees in high-density, dynamic, and uncertain airspace environments in real time. To address these challenges, we introduce the concept of a data-driven probabilistic geofence, which can guarantee that the probability of potential conflicts between eVTOL aircraft is bounded under data-driven uncertainties. To evaluate the probabilistic geofences online, Kernel Density Estimation (KDE) based on Fast Fourier Transform (FFT) is customized to model data-driven uncertainties. Based on the FFT-KDE values from data-driven uncertainties, we introduce an optimization framework of Integer Linear Programming (ILP) to find a parallelogram box to approximate the data-driven probabilistic geofence. To overcome the computational burden of ILP, an efficient heuristic algorithm is further developed. Numerical results demonstrate the feasibility and efficiency of the proposed algorithms. 

Urban air mobility (UAM) using unmanned aerial vehicles (UAV) is an emerging way of air transportation within metropolitan areas. For the sake of the successful operations of UAM in dynamic and uncertain airspace environments, it is important to provide safe path planning for UAVs. To achieve the path planning with safety assurance, the first step is to detect collisions. Due to uncertainty, especially data-driven uncertainty, it’s impossible to decide deterministically whether a collision occurs between a pair of UAVs. Instead, we are going to evaluate the probability of collision online in this paper for any general data-driven distribution. A sampling method based on kernel density estimator (KDE) is introduced to approximate the data-driven distribution of the uncertainty, and then the probability of collision can be converted to the Riemann sum of KDE values over the domain of the combined safety range. Comprehensive numerical simulations demonstrate the feasibility and eciency of the online evaluation of probabilistic collision for UAM using the proposed algorithm of collision detection.