A stochastic reachability analysis approach to aircraft conflict detection and resolution

This paper addresses aircraft conflict detection and resolution from a stochastic reachability analysis perspective. A characterization of the uncertainty on the aircraft future positions due to the presence of wind is obtained in terms of probabilistic reach sets. This involves formulating a chance-constrained optimization problem and solving it approximately via simulation, according to the so-called scenario approach. Conflict prediction can then be performed by verifying if reach sets of different aircraft get closer than some minimum safety distance. When a conflict is detected, then, the aircraft flight plans are modified so as to minimize the traveled distance while maintaining reach sets at some appropriate distance. A numerical example shows the efficacy of the proposed approach.