Space Efficient Airspace Geofence Volume Sizing

This paper will present methodologies to construct space-efficient airspace geofence volumes around Unmanned Aircraft Systems (UAS) for two specific cases: longitudinal climbing/descending flight paths, and cooperatively controlled swarms for which a provable containment boundary can be defined. Airspace geofencing defines polygon or polyhedron boundaries that partition the airspace into available fly zones (keep-in boundaries) and no-fly zones (keep-out boundaries) to assure aircraft separation and obstacle/terrain avoidance. Geofencing is a key enabler for safe Unmanned Aircraft System (UAS) Traffic Management (UTM). In densely populated low-altitude airspace, UTM must safely and efficiently manage the airspace geofence volumes around different UAS missions. Particularly, UAS operations often include complex flight paths with several climb/descent phases for missions such as package delivery and search and rescue. Constructing spatially efficient geofences around climb/descent paths becomes increasingly important in densely populated airspace to maximize usable airspace for other UAS. For the case of swarm flight/containment control, a single geofence volume can be used to wrap the entire team for air traffic control treatment as a flight-of-n" vehicles, assuming the controller and connected network are robust. In both cases of climb/descent and swarm flight/containment control, the geofencing problem is to construct spatially efficient airspace volumes wrapping the UAS or swarm throughout its flight trajectory. This paper will extend our previous work \cite{kim2021volumization} in three-dimensional climb/descent geofence by generating parallelepiped airspace geofence volumes with variable ceilings and floors. This paper's parallelepiped geofencing for climb/descent trajectories complements previous work defining efficient airspace geofence volumes for optimal cruise trajectories \cite{kim2022airspace_2}. This paper extends previous work in single-vehicle geofencing to multi-agent teams following containment control by wrapping this team with a three-dimensional convex hull \cite{preparata1977convex}. Algorithms, case studies, and benchmark comparisons of geofence volume sizings will be presented in the full paper.