Game-theoretic Resolution of Stochastic Multi-aircraft Near Midair Collisions

This paper presents a multi-aircraft Markov decision process congestion game to resolve multi-aircraft near midair collisions (NMACs) for small unmanned aerial vehicles (sUAVs). Two key features of this framework are: 1) it leverages the concept of strategic equilibria from game theory to define optimality in multi-aircraft near midair encounters and 2) it extends the existing NMAC metrics to stochastic formulations via the occupancy measure of a Markov decision process. This game-theoretic approach decomposes the classically centralized air traffic control objective to multiple objectives that correspond to each aircraft within the NMAC, and as result, provides an aircraft-centric notion of optimality and safety that is well-suited for distributed conflict resolutions in multi-aircraft NMACs. In addition to modeling multi-aircraft as a game, stochastic metrics that extend the deterministic notions of NMACs are explored. The safety and optimality of the Nash equilibrium multi-aircraft trajectory under a joint NMAC threat is analyzed under different NMAC thresholds and evaluation metrics. Results are simulated numerically for a representative sUAV NMAC geometry.