A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuvers

Abstract

a b s t r a c tAir-conflict resolution is a bottleneck of air traffic management that will soon require powerful decisionaid systems to avoid the proliferation of delays. Since reactivity is critical for this application, we develop a mixed-integer linear model based on space discretization so that complex situations can be solved in near real-time. The discretization allows us to model the problem with finite and potentially small sets of variables and constraints by focusing on important points of the planned trajectories, including the points where trajectories intersect. A major goal of this work is to use space discretization while allowing velocity and heading maneuvers. Realistic trajectories are also ensured by considering speed vectors that are continuous with respect to time, and limits on the velocity, acceleration, and yaw rate. A classical indicator of economic efficiency is then optimized by minimizing a weighted sum of fuel consumption and delay. The experimental tests confirm that the model can solve complex situations within a few seconds without incurring more than a few kilograms of extra fuel consumption per aircraft.

Complex number formulation and convex relaxations for aircraft conflict resolution

“…State-of-the-art computational results for the horizontal aircraft conflict resolution problem can be found in [5], [8], [11], [13], [24]. Some of these approaches [5], [13] consider heading and speed control separately or maneuver-discretised formulations [24] which can lead to suboptimal solutions.…”

An Approach to Dynamical Distance Geometry

“…In character animation, for example, motions are generally simulated by modifying pre-recorded motions [13], and an attempt to perform this modification through distance constraints was already proposed in [9]. In air-traffic control, the positions of a set of flying airplanes needs to be predicted so that some distance constraints are satisfied, which are defined for guaranteeing collision avoidance (see for example the recent work in [15]). Similarly, in crowd simulations, one is interested in simulating a crowd motion in different situations, where distances between pairs of pedestrians can be estimated and exploited for the simulations [4].…”

Three-Dimensional Aircraft Conflict Resolution Based on Smoothing Methods

“…According to these authors, fuel-optimal conflict resolution maneuvers could be obtained nearly in real time. A similar work by Omer [10] presented the conflict resolution problem as a mixed-integer linear model based on space discretization that focused on the important points, aside from the intersection points, of planned trajectories. All of these previous works formulated the conflict resolution problem as a mixed-integer linear or nonlinear programming problem based on a simplified model and geometric construction of conflict avoidance constraints.…”