On-line robust trajectory generation on approach and landing for reusable launch vehicles

Abstract

A major objective of next generation reusable launch vehicle (RLV) programs includes significant improvements in vehicle safety, reliability, and operational costs. In this paper, novel approaches that can deliver an RLV to its landing site safely and reliably are proposed. Trajectory generation on approach/landing (A&L) for RLVs using motion primitives (MPs) and neighboring optimal control (NOC) is first discussed. In this stage, the proposed trajectory generation 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 saved into 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 on-line by using an NOC approach. If the perturbations are small enough, a neighboring feasible trajectory existence theorem (NFTET) is then investigated and its proof is provided as well. The approach given in the NFTET shows that a 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 However, when the perturbations become large, for example, in severe failure scenarios, the NFTET is no longer applicable and often the vehicle cannot be recovered from such failures. A new method is then used to deal with this situation. The NFTET is now extended to the trajectory robustness theorem (TRT). According to the TRT and its proof, 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, σ -modification is employed. The simulation results verify the excellent robust performance of this method.