Optimal Trajectory and Control Generation for Landing of Multiple Aircraft in the Presence of Obstacles

Due to the large increase in the density of aircraft arrivals at airports in recent years, it has become important to optimize the scheduling of aircraft landings in order to reduce wait time, improve airport efficiency, and minimize fuel consumption while maintaining safety. As the density of aircraft arrivals increases, however, so too does the complexity of trajectory planning and generation. A key aspect of landing multiple aircraft on a single runway is conflict detection and resolution. In the context aircraft landing, a conflict is defined as the situation of loss of minimum safe separation between two aircraft Ref. 1. The conflict detection and resolution process consists of predicting, communicating to the pilot, and resolving the conflict. Typically, evaluating the likelihood of a conflict is based on the current position and velocity of an aircraft. The conflict is then resolved by determining a maneuver required by one or more aircraft to avoid the predicted conflict. The required information is then provided to the air traffic controller who communicates with the pilot to resolve the conflict. A great deal of research has been done on the problem of multiple-aircraft conflict detection and resolution and landing of multiple aircraft. Ref. 2 considers the problem of managing landing sequences for an arbitrary number of aircraft moving in the vicinity of a controlled aerodome. Ref. 3 considers how different airport landing sequencing algorithms affect both the arrival sequence of aircraft and air traffic control. Ref. 4 develops an approach for determining optimal trajectories to bring an unmanned aerial vehicle from a loitering state to a planted landing. Ref. 5 develops a queueing algorithm for routing aircraft on two airport runways. Ref. 6 considers a three-dimensional trajectory optimization algorithm is developed by to obtain a conflict-free flight path using a nonlinear point mass model with realistic operational constraints on individual aircraft. Ref. 7 considers the problem of optimal cooperative three-dimensional conflict resolution involving multiple aircraft, where the the initial and final locations of the aircraft are specified along with detailed point-mass aircraft dynamic models. The infinite-dimensional optimal control problem is then converted into a finite dimensional nonlinear program (NLP) using collocation on finite elements. Finally, Ref. 8