Autonomous Lunar Orbit Rendezvous Guidance Based on J_2-Perturbed State Transition Matrix

摘要

An optimal, multi-impulsive rendezvous control strategy based on the SGA-STM has been developed for a lunar lander rendezvous problem. This model accounts for the J_2 perturbation. It allows for a systematic design process and refinement of the number of thrust impulses, their application times, and the mission duration. The predicted relative states provided by the SGA-STM are accurate when compared with the numerically integrated data obtained from a high-fidelity model, absolute position e'rrors being less than 1.5 km over a 25 h period. The SGA-STM-based optimal targeting method performs remarkably well within a high-fidelity rendezvous simulation. The relative position and velocity differences between the SGA-STM and the numerically integrated solutions are very small, less than 5 km and 1.0 m/s, respectively. These residual state differences can be eliminated in less than 10 iterations by a simple gradient algorithm. The impulsive-thrust assumption is validated by a finite-burn thruster model simulation in the STK-9 environment. The impulsive-thrust solutions obtained from the SGA-STM model are reasonably accurate and feasible finite-burn solutions can be obtained with a few iterations of a differential correction procedure. This optimization method for impulsive-thrust assumption is well-suited for the determination and refinement of onboard guidance strategies for lunar missions.