一种参数全解析的改进小推力李雅普诺夫制导方法

Low-thrust maneuvers, characterized by their high specific impulse, have become the preferred mode for low-fuel consumption orbital maneuvers. The optimization of low-thrust maneuver strategies, however, presents a significant challenge due to strong nonlinear dynamics and initial value sensitivity, marking a core issue in the application and development of low-thrust technologies. This study introduces an improved Lyapunov guidance (Q-Law) method for large-scale, long-duration low-thrust maneuvers. Addressing the singularity issue in orbital elements inherent in traditional Q-Law algorithms, we propose a novel set of orbital descriptors based on orbital orientation vectors, ensuring no singularity in the solution space during orbital transfers. Additionally, we fully analytically derive the maximum rates of change for orbital elements, overcoming the difficulty in analytically determining these rates in traditional Q-Law, which often requires iterative solutions, thereby significantly enhancing the efficiency of Q-Law open-loop guidance calculations. Finally, an analytical expression for the optimal thrust direction is derived based on the maximum rates of change of orbital elements. Numerical simulations, involving classic line-of-apsides rotation and inclination transfer, as well as the GTO to GEO rendezvous problem, validate the effectiveness and scenario adaptability of the proposed method.