  We address the aircraft conflict resolution problem under trajectory
prediction uncertainty. We consider that aircraft velocity vectors may be
perturbed due to weather effects, such as wind, or measurement errors. Such
perturbations may affect aircraft trajectory prediction which plays a key role
in ensuring flight safety in air traffic control. Our goal is to solve the
aircraft conflict resolution problem in the presence of such perturbations and
guarantee that aircraft are separated for any realization of the uncertain
data. We propose an uncertainty model wherein aircraft velocities are
represented as random variables and the uncertainty set is assumed to be
polyhedral. We consider a robust optimization approach and embed the proposed
uncertainty model within state-of-the-art mathematical programming formulations
for aircraft conflict resolution. We then adopt the approach of Bertsimas and
Sim (2004) to formulate the robust counterpart. We use the complex number
reformulation and the constraint generation algorithm proposed by Dias et al.
(2020a) to solve the resulting nonconvex optimization problem on benchmarking
instances of the literature. Our numerical experiments reveal that
perturbations of the order of $\pm 5\%$ on aircraft velocities can be accounted
for without significantly impacting the objective function compared to the
deterministic case. Our tests also show that for greater levels of uncertainty,
several instances fail to admit conflict-free solutions, thus highlighting
existing risk factors in aircraft conflict resolution. We attempt to explain
this behavior by further analyzing pre- and post-optimization aircraft
trajectories. Our findings show that most infeasible instances have both a
relatively low total aircraft pairwise minimal distance and a high number of
conflicts.
