Optimal Coordinated Maneuvers for Three Dimensional Aircraft Conflict Resolution

for Three Dimensional Aircraft Conflict Resolution Jianghai Hu∗ University of California, Berkeley, CA 94720 Maria Prandini† University of Brescia, 25123 Brescia, Italy Shankar Sastry‡ University of California, Berkeley, CA 94720 Abstract In this paper, the problem of designing optimal conflict-free maneuvers for multiple aircraft encounters is studied. The candidate maneuvers may involve not only changes of heading and speed, but also of altitude. The goal is to determine among all the conflict-free maneuvers the one that minimizes a certain energy cost function. A priority mechanism is incorporated into the energy function so that optimal resolution maneuvers are such that aircraft with lower priorities assume more responsibility in resolving the conflicts. Moreover, 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 multi-aircraft case, an approximation scheme is proposed to compute a suboptimal two-legged solution. Extensive simulation results are presented to illustrate the effectiveness of the proposed algorithms.