Linear Feedback Guidance for Low-Thrust Many-Revolution Earth-Orbit Transfers

Abstract

TO GUIDE a low-thrust spacecraft to a target orbit, the most commonly used strategy is to frequently uplink control commands to correct orbital deviations. However, this guidance scheme requires a large amount of offline optimal control computations and data communications between the ground and the spacecraft, especially for low-thrust many-revolution Earth-orbit transfer missions (whichmay last several months). For the purpose of reducing ground operational loads, autonomous guidance has to be placed onboard. Kluever developed an inverse dynamics approach [1] and an empirical control law [2] to track reference trajectories, based on the concept of predictive control. These two methods require onboard iterative algorithms to find appropriate control-related parameters. In engineering practice, the implementation of the predictive control guidance usually depends on accurate calibration of thrust magnitude and direction as well as predictive horizon. Another strategy of low-thrust autonomous guidance is based on Lyapunov control laws [3–6] (which, however, usually do not provide optimal solutions). The question of how to select feedback gains of the Lyapunov control laws to achieve optimal or near-optimal performance is still unresolved. In this study, a new linear feedback guidance scheme is proposed for low-thrust Earth-orbit transfers involving large numbers of orbital revolutions. The key concept of this guidance scheme is that the spacecraft tracks the nominal trajectory, which is expressed by mean orbital elements without involving short periodic osculating motion. First, optimal trajectory and control are obtained via a direct optimization method with the consideration of both J2 perturbations and shadowing conditions. Along the optimal trajectory and control, a set of linearized equations of spacecraft motion expressed by mean orbital elements is then developed. At last, the trajectory tracking problem is formulated as a standard time-varying linear control problem, and linear control theory can be readily used for designing the guidance control law. An example transfer from a geostationary transfer orbit (GTO) to a geostationary orbit (GEO) was simulated to verify the guidance performance.