Flight Mechanics and Control: Optimal Trajectories for Hypersonic Vehicles with Predefined Levels of Inherent Safety

Three-dimensional optimal flight trajectories including singular subarcs are computed for a single-stage, suborbital hypersonic demonstrator system. An optimal primary trajectory is only permissible if it offers a prescribed level of safety along the total flight path. As an example, the problem of mission abort is considered. The flight vehicle has to reach an emergency landing site from every point of the primary trajectory after a total failure of the aircraft engine. The mathematical model describing the motion of the rocket-powered vehicle is based on the three-dimensional equations of motion of a point mass with reference to the spherical rotating Earth. The safety condition is fulfilled pointwise; secondary optimal control problems describing mission abort are connected to an adaptively refined subset of points along the primary trajectory. The resulting problem is reformulated as a joint optimal control problem and transformed into a series of boundary value problems for systems of highly nonlinear differential equations. The numerical solution is by the advanced multiple shooting method JANUS. The demand for full safety in case of mission abort leads to significant deformations of the unperturbed primary trajectory, whereas the value of the objective function for the modified trajectory is only slightly reduced.