Envelopes and Waves: Safe Multivehicle Collision Avoidance for Horizontal Non-deterministic Turns

We present an approach to analyzing the safety of asynchronous, independent, non-deterministic, turn-to-bearing horizontal maneuvers for two vehicles. Future turn rates, final bearings, and continuously varying ground speeds throughout the encounter are unknown but restricted to known ranges. We develop a library of formal proofs about turning kinematics, and apply the library to create a formally verified timing computation. Additionally, we create a technique that evaluates future collision possibilities that is based on waves of position possibilities and relies on the timing computation. The result either determines that the encounter will be collision-free, or computes a safe overapproximation for when and where collisions may occur.