We develop a library of proofs to support rigorous mathematical reasoning about horizontal aircraft turning maneuvers, and apply it to formally verify a timing computation for use during mixed horizontal and vertical aircraft collision avoidance maneuvers. We consider turns that follow non-deterministic circular turn-to-bearing horizontal motion, formalizing path-length and timing properties. These kinematics are the building blocks for Dubins trajectories, and can be used to formalize a variety of techniques, including those that contain non-determinism. The timing computation establishes, for intersecting trajectories, the exact bounds of time intervals when the horizontal position of the aircraft might coincide, and during which they must be at different altitudes to avoid collision.
For AI-controlled mobile platforms, avoiding collisions with walls and boundaries is an important safety requirement. This is a problem especially for fast-moving aerial vehicles, such as fixed-wing aircraft, that cannot be brought to a stop in an emergency. To enable geographic confinement of such AI-controlled vehicles, we present a formally verified algorithm for predicting geofence violations and selecting a safe maneuver that will keep the vehicle within the designated operations area. The algorithm is based on a higher-order dynamics model that generalizes circular turns using linearly changing centripetal acceleration and allows handling of uncertainty in model parameters. The proposed algorithm was implemented along with extensions to handle non-determinism, and flight-tested on an autonomous aircraft.1 For our purposes, we will focus on geofencing for keep-in regions only.Defense Nuclear Facilities Safety Board-The views expressed herein are solely those of the authors, and no official support or endorsement by the Defense Nuclear Facilities Safety Board or the U.S. Government is intended or should be inferred.
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