Optimal Coordinated Maneuvers for Three-Dimensional Aircraft Conflict Resolution

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.