Enhanced Lyapunov Guidance for Low-Thrust Maneuvers With Orbital Perturbations

As a low-thrust guidance approach, the Q-Law method demonstrates high applicability in multiturn orbit transfer problems. This article introduces an Lyapunov-based guidance law to address the existing limitations of Q-Law and improve its overall performance. First, the guidance parameters describing orbital deviation are redefined, thereby reducing the intrinsic guidance dimensionality of the traditional Q-Law model. On this basis, the maximum rate of change of the guidance parameters under perturbation was rigorously analyzed and rederived. This approach effectively addresses the challenges posed by J2 perturbations in the traditional Q-Law formula. Furthermore, to impose constraints on critical orbital parameters during maneuvering, the constraint mode and additional penalty functions were systematically redesigned. These improvements are especially effective in controlling orbital height during orbital plane maneuvers. Furthermore, the thrust switching mechanism is refined by decomposing the overall efficiency characterization into specific local variables. Finally, for rendezvous tasks with stringent terminal phase constraints, this article innovatively proposes a three-phase rendezvous strategy aimed at mitigating convergent oscillations caused by phase deviations. This resolves the limitations of existing methods in handling rendezvous problems involving large phase differences in elliptical orbits. Through numerical simulations of three representative orbital maneuvering scenarios, the superiority of the proposed method is demonstrated. Enhanced Q-Law guidance, which accounts for orbital disturbances, can offer substantial practical value in long-duration, large-scale, and low-thrust orbital maneuvers.