Application of MINLP techniques to conflict resolution of multiple aircraft

An algorithm to obtain conflict-free trajectories for multiple aircraft in an en-route sector is presented. An optimal solution is sought in terms of minimizing delay and steering effort of the individual aircraft. Furthermore, the resulting control histories shall be from a discrete set to be compatible with today's air traffic management clearances. To this end, the problem is stated using a mixed integer optimal control formulation and a relaxation method is applied for solution. The considered aircraft are modeled as kinematic point masses that may enter or leave the sector at different times. To efficiently evaluate the separation between aircraft a method is introduced to switch on and off dynamics and path constraints of individual aircraft. The capabilities of the proposed algorithm are demonstrated in a numerical example involving four aircraft.