Ascent Trajectory Optimization and Neighboring Optimal Guidance of Multistage Launch Vehicles

Multistage launch vehicles are employed to place spacecraft and satellites in their operational orbits. If the rocket aerodynamics and propulsion are modeled appropriately, optimization of their ascent trajectory consists in determining the coast duration and the thrust time history that maximize the final mass at injection. This research derives all the necessary conditions for ascent path optimization of a multistage launch vehicle. With reference to an existing rocket, the indirect heuristic method is then applied, for the numerical determination of the overall ascent trajectory. An effective approach is used with the intent of satisfying the path constraint related to the maximum dynamical pressure in the atmospheric phase. Then, the recently introduced, implicit-type variable-time-domain neighboring optimal guidance is applied to the upper stage powered arc, for the purpose of obtaining the corrective control actions in the presence of nonnominal flight conditions. The guidance approach at hand, based on the second-order analytical conditions for optimality, proves to be rather effective (in terms of propellant budget), and guarantees very accurate orbit injection in spite of perturbations.