| A major objective of next generation reusable launch vehicle (RLV) programs includes significant improvements in vehicle safety, reliability, and operational costs. We first discuss trajectory generation on approach and landing (A&L) for RLVs using motion primitives (MPs) and neighboring optimal control (NOC). The proposed approach is based on an MP scheme that consists of trims and maneuvers. From an initial point to a given touchdown point, all feasible trajectories that satisfy certain constraints are generated and stored in a trajectory database. An optimal trajectory can then be found off-line by using Dijkstra's algorithm. If a vehicle failure occurs, perturbations are imposed on the initial states of the off-line optimal trajectory, and it is reshaped into a neighboring feasible trajectory by using NOC approach. If the perturbations are small enough, a neighboring feasible trajectory existence theorem (NFTET) is then investigated. The approach given in the NFTET shows that the vehicle with stuck effectors can be recovered from failures in real time. However, when the perturbations become large, for example, in severe failure scenarios, the NFTET is no longer applicable. A new method is now used to deal with this situation. The NFTET is then extended to trajectory robustness theorem (TRT). According to the TRT, a robustifying term is introduced to compensate for the effects of the linear approximation in the NFTET. The upper bounds with respect to input deviation are adaptively adjusted to eliminate their uncertainty. In order to obtain best performance, sigma-modification is employed. The simulation results verify the excellent robust performance of this method. Until now, the atmosphere has been assumed to be at rest. Since this is the exceptional rather than the usual case, it is necessary to investigate the wind effects on the behavior of RLVs, where the atmosphere has nonuniform and unsteady motion. When wind effect is included, two corollaries will be easily inferred from the NFTET and TRT. A wind effect theorem (WET) is investigated based on these two corollaries. Modified NOC and robustification approaches are used to recover vehicles in winds from failures in real time. Finally, some future research works are discussed. |
