Application of Direct Transcription to Commercial Aircraft Trajectory Optimization

One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method. This approach combines a nonlinear programming algorithm with a discretization of the trajectory dynamics. When the resulting mathematical programming problem is solved using a sparse sequential quadratic programming algorithm, the technique produces solutions very rapidly and has demonstrated considerable robustness when applied to atmospheric and orbital trajectories. This paper describes the application of the direct transcription technique to the optimal design of a commercial aircraft trajectory, subject to realistic constraints on the aircraft flight path. A primary result of the paper is to demonstrate that the transcription formulation leads to a very natural treatment of realistic Federal Aviation Administration (FAA) imposed path constraints within a high fidelity simulation. A second important result is to demonstrate that modeling tabular data using smooth approximations significantly improves the speed of convergence.