Multi-aircraft Conflict Detection and Resolution Based on Probabilistic Reach Sets

In this brief, a novel scheme to multi-aircraft conflict detection and resolution is introduced. A key feature of the proposed scheme is that uncertainty affecting the aircraft future positions along some look-ahead prediction horizon is accounted for via a probabilistic reachability analysis approach. In particular, ellipsoidal probabilistic reach sets are determined by formulating a chance-constrained optimization problem and solving it via a simulation-based method called scenario approach. Conflict detection is then performed by verifying if the ellipsoidal reach sets of different aircraft intersect. If a conflict is detected, then the aircraft flight plans are redesigned by solving a second-order cone program resting on the approximation of the ellipsoidal reach sets with spheres with constant radius along the look-ahead horizon. A bisection procedure allows one to determine the minimum radius such that the ellipsoidal reach sets of different aircraft along the corresponding new flight plans do not intersect. Some numerical examples are presented to show the efficacy of the proposed scheme.