Optimal 4D Trajectory Planning for Multiple Aircraft in Continuous Descent Operations (original) (raw)

This paper deals with trajectory planning for multiple aircraft in continuous descent operations using logical constraints in disjunctive form which arise in modeling passage through waypoints and time-based separation constraints. In the literature, logical constraints are modelled by means of the introduction of auxiliary integer variables. Furthermore, for the passage through waypoints usually a multiphase optimal control approach is considered. In this paper, an embedding technique is employed to transform logical constraints in disjunctive form into inequality and equality constraints which involve only continuous auxiliary variables, thus avoiding the computational complexity of multi-phase mixed-integer optimal control approaches.