Real-Time Computation of Optimal Three-Dimensional Aircraft Trajectories Including Terrain-Following

Aircraft trajectories must often be computed in rapid time, particularly if trajectories close to terrain are to be flown without radar detection. Furthermore, collision avoidance strategies for complex three-dimensional terrain must be computed quickly if the aircraft is to safely maneuver past the obstacle. In this paper, an approach for computing such trajectories near arbitrary three-dimensional terrain is presented. The approach relies on the application of the Legendre pseudospectral method with analytic derivatives for the aircraft performance parameters and terrain. A nonlinear point mass aircraft model is used to generate optimal trajectories using a weighted cost that combines minimum altitude with minimum flight-path/heading angle rates, and minimum aircraft acceleration. To simulate the optimal trajectories, a six-degree-of-freedom aircraft model is used. The outer-loop trajectories are transformed into appropriate inner-loop trajectories and actuator inputs. The inner-loop is tracked via a linear receding horizon strategy using state feedback with terminal state constraints.