Multi-Stage Trajectory Optimization for Multiple Aircraft Approaching an Airport

In the paper, a multi-stage approach for numerical trajectory optimization of multiple aircraft in the vicinity of an airport is presented. The method for solving the problem consists of 5 stages where the first four solve the problem of ordering, fixing the final times and hierarchical distance separation, and the solution of the hierarchical formulation is then used as the initial guess for the combined problem with pairwise distance constraints. The approach proved to be very efficient in terms of computation speed resulting in computation time of less than 3 minutes for all stages of solving the trajectory optimization problem for 5 aircraft. The numerical experiments were carried out with MUSCOD-II optimization software.