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A study was conducted to develop an approach that is capable of computing optimal aircraft trajectories near terrain in real-time. A suitable analytic representation of three-dimensional terrain was developed, using polynomial bases and Kronecker factorization. A three-dimensional point-mass aircraft model was used to obtain the outer-loop optimal, trajectories, using a Legendre pseusppectral method. A method for converting these trajectories into inner-loop commands, implemented through a diminishing horizon strategy, based on Gauss-Lobatto quadrature was also developed for computing aircraft trajectories near terrain in real-time. The aerodynamic data were taken from the six-degree-of-freedom aircraft model and the lift and drag coefficients were found to be dependent on the angle of attack.
Paul Williams (Wed,) studied this question.