Advances in Highly Constrained Multi-Phase Trajectory Generation using the General Pseudospectral Optimization Software (GPOPS)

Abstract : Recent events in hypersonic glide vehicle programs have necessitated a new approach to examine possible flight test trajectories to include new constraints on optimal trajectory generation. Aircraft stability, combined thermo-structural loading, and vehicle ablation are all important considerations for hypersonic vehicle flight; optimal trajectory generation should account for these complex constraints. A collaborative effort was undertaken by the Air Force Research Laboratory Aerospace Systems Directorate and the 412th Test Wing at Edwards Air Force Base to analyze possible optimal control solutions that satisfy these constraints. A three-stage booster aerodynamic and propulsion model and a hypersonic glide vehicle aerodynamic and ablation model were implemented in the General Pseudospectral Optimization Software (GPOPS). The resulting optimal control problem models booster launch through re-entry vehicle impact and incorporates multiple complex constraints including stagnation heating, ablation, no-y zones, aircraft stability, dynamic pressure, time-rate of change of flight path angle, loads and a terminal phase target. Furthermore, the optimal control problem uses derived events as guidance mode or booster stage linkages; including range to target, range from launch site, vehicle loads, altitudes, dynamic pressure and time rate of change of altitude. The optimal control variables are specified to be the guidance variable derivatives; this allows for constraining attitude rates in a translational (point mass) problem. GPOPS is shown to be capable of analyzing highly constrained, multiple-phase optimal control problems using complex vehicle models and flexible enough to incorporate new constraints quickly allowing for exploration of new guidance methodologies.