Enhanced Lyapunov Guidance for Low-Thrust Maneuvers with Orbital Perturbations

This study introduces an enhanced Lyapunov-based guidance method for low-thrust maneuvers under orbital perturbations. We redesign the guidance parameters that describe orbital deviations within the framework of inertial system dynamics, thereby streamlining the complex expressions inherent in traditional Q-Law models. The proposed method extends to the derivation of analytical expressions for the maximum change rate in these guidance parameters when subjected to perturbative accelerations, effectively addressing the challenges posed by such accelerations in conventional Q-Law formulations. To impose critical orbital parameter constraints during maneuvers, we devise a novel penalty function that incorporates upper and lower bounds for these parameters. This function is particularly effective in managing semi-major axis constraints during orbital plane maneuvers, leading to a notable reduction in fuel expenditure. Additionally, the thrust switch mechanism is improved by refining the characterization of overall efficiency into specific local variables. For rendezvous missions with stringent terminal phase constraints, we propose a three-phase rendezvous strategy designed to mitigate convergence oscillations associated with significant phase deviations. Numerical simulations on three typical examples of orbital maneuvers validate the significant advantages and effectiveness of the proposed method. This work enhances Q-Law guidance considering orbital perturbations for the first time, offering substantial practical value for long-duration, wide-range low-thrust orbit maneuvers.