NextGen Air Transportation Systems

Several Next Generation Air Transportation Systems concepts require aircraft to be able to safely fly routes on the same airspace in a timely fashion. Therefore it is necessary that aircraft are able to comply with 4D trajectories, that is, routes with spatial and temporal constraints.

Required Navigation Performance Tube

The aircraft is flying on the reference trajectory with spatial constraints, represented by the surrounding tube, and temporal constraints, represented by the window, in which the aircraft must be at a required time of arrival.

Here at the GRITS Lab, we propose an optimal control approach at solving the problem. A number of benefits are obtained by phrasing the problem as an optimal control one. We are able to generate nominal trajectories which can provide:

  1. feasible trajectories for the aircraft to follow, in a dynamical sense,
  2. fuel-efficient maneuvers through the length of the flight, and
  3. compliance with the spatial and temporal constraints required of the aircraft.

With the proposed formulation, we are also able to solve for the first order necessary conditions for optimality. This reduces the need for intense, off-line computations to obtain the nominal trajectory, thus providing

  1. computationally-efficient results.

In order to compensate for the inevitable presence of model uncertainty and external disturbances, the robustness of the solution can be improved by: (a) recomputing future trajectory segments to compensate for errors and delays, and (b) the introduction of a feedback control term in the control law. These result in

  1. improved robustness to disturbances and modeling errors,

in the sense that requirements on navigation performance can be met with a certain statistical confidence level.

Simulation results are used to verify the computational feasibility and efficacy of the proposed approach.

Tube Trajectory Rotating

Nominal, Open-Loop and Closed-Loop Generated Trajectories. Even in the presence of disturbances, the closed-loop trajectory is able to remain close to the nominal trajectory.






  • Diaz-Mercado, Y.; Lee, S.G.; Egerstedt, M.; Young, S., “Optimal Trajectory Generation for Next Generation Air Transportation Systems,” Digital Avionics Systems Conference (DASC), 2013 IEEE/AIAA 32nd , Oct. 2013.



Rockwell Collins, Inc.

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