Geometric Verification of Vector Fields for Autonomous Aircraft Navigation

New generations of small advanced aircraft may soon transform how people and freight are transported. Thus, ensuring safe and reliable operation of these systems, in all plausible scenarios, is of utmost priority. In this paper, we address this problem by proposing a method to verify the safety of an autonomous aircraft controller following a navigational policy. The policy is encoded using discrete vector fields that are meant to drive the vehicle to a goal state and away from obstacles or restricted airspace. The solution presented in this paper provides the ability to verify the policy, catching unsafe scenarios which may be missed by random Monte Carlo methods or general reachability analysis. After illustrating the main theoretical principles, a possible practical implementation is described and compared with analysis based on Monte Carlo simulations. The comparison shows an insightful example where Monte Carlo simulations fail to detect several corner cases that are uncovered by the proposed method. In the conclusion of the paper, we provide insights about possible future research to implement the proposed solution obtaining higher accuracy and efficiency.