Reachability calculations for automated aerial refueling

This paper describes Hamilton-Jacobi (HJ) reachability calculations for a hybrid systems formalism governing unmanned aerial vehicles (UAVs) interacting with another vehicle in a safety-critical situation. We use this problem to lay the foundations toward the goal of refining or designing protocols for multi-UAV and/or manned vehicle interaction. We describe here what mathematical foundations are necessary to formulate verification problems on reachability and safety of flight maneuvers. We finally show how this formalism can be used in the chosen application to inform UAV decisions on avoiding unsafe scenarios while achieving mission objectives.