Optimal Coordinated Maneuvers for Three-Dimensional Aircraft Conflict Resolution

Abstract

In this paper, we study the problem of designing optimal coordinated maneuvers for multiple aircraft conflict resolution. We propose an energy function to select among all the conflict-free maneuvers the optimal one. The introduced cost function incorporates a priority mechanism that favors those maneuvers where aircraft with lower priority assume more responsibility in resolving the predicted conflicts. The energy-minimizing resolution maneuvers may involve changes of heading and speed, as well as of altitude. However, vertical maneuvers are penalized with respect to horizontal ones for the sake of passenger comfort. A geometric construction and a numerical algorithm for computing the optimal resolution maneuvers are given in the two aircraft case. As for the multiaircraft case, an approximation scheme is proposed to compute a suboptimal two-legged solution. Extensive examples are presented to illustrate the effectiveness of the proposed algorithms.

Joint Metering and Conflict Resolution in Air Traffic Control

“…; N. Let p i x i;0 ; y i;0 denote the initial position of aircraft i. Following much of the previous work on conflict resolution [6,13,14,16], aircraft are represented by a kinematic model and can hence change their heading and speed instantaneously. Any two aircraft must always maintain a mandatory separation distance, denoted d, between themselves.…”

“…With the headings fixed, all the separation constraints (2), (3), (6), and (7) are constraints on the speed variables of the form of Eq. (16).…”

“…Bilimoria [19] describes a geometric optimization method that resolves conflicts between pairs of aircraft in real time but cannot guarantee safety for multipleaircraft conflicts. Hu et al [16] consider the problem of designing three-dimensional conflict-free maneuvers minimizing a certain energy cost function and allow for a richer set of trajectories than the previously mentioned work: in particular, optimization over two-leg trajectories. Hwang et al [10] propose a protocol based conflict resolution scheme where maneuvers consist of two straight paths of equal length.…”

“…Note, however, that except in case of imminent conflict, altitude changes are typically avoided for conflict resolution, in order to minimize passenger discomfort and maintain compatibility with the vertically layered structure of the airspace ( [1], chapter 3). Second, aircraft are represented by kinematic models, as in, e.g., [6,13,14,16], with speed and heading changes assumed to occur instantaneously. More detailed dynamic models have been used in some previous work, at the expense of more complex computations [17,18].…”

Decentralized Cooperative Trajectory Planning of Multiple Aircraft with Hard Safety Guarantees

“…Several methods with hard anti-collision constraints have been proposed, including approaches based on semidefinite programming, 5 nonlinear programming, 6 mixed integer linear programming, 7-9 mixed integer nonlinear programming, 10 and variational analysis. 11 However, since the number of inter-vehicle combinations in the planning problem increases polynomially as n(n − 1)/2 with the number of aircraft n involved in the conflict, the computation times of these methods typically scale exponentially.…”