On-line approach/landing trajectory generation with input deviation bound uncertainty for reusable launch vehicles

For next generation reusable launch vehicle (RLV) programs, a main objective is significant improvements in vehicle safety, reliability, and operational costs. Novel approaches are required in order to deliver a RLV to its landing site safely and reliably, recover the vehicle from some failures, and avoid mission abort as much as possible. One of such approaches was trajectory generation on approach and landing (A&L) for RLVs using motion primitives (MPs) and neighboring optimal control (NOC). The approach showed that a vehicle with stuck effectors could be recovered from failures in real time. In this paper, further discussion on robustness issues of the above approach is given. Based on neighboring feasible trajectory existence theorem (NFTET), a trajectory robustness theorem (TRT) is investigated and its proof is provided as well. According to TRT, a robustifying term is introduced to compensate for the effects of the linear approximation in 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 demonstrated excellent robust performance of this method.