Near-Optimal Very Low-Thrust Earth-Orbit Transfers and Guidance Schemes

Abstract

A novel direct approach is developed for computing near-optimal very low-thrust Earth-orbit transfers and constructing feasible onboard guidance schemes for the spacecraft propelled by low-thrust acceleration with thrust-to-weight ratio on the order of 10 -5 . Both minimum-time and minimum-fuel orbital transfers with a mechanism for coasting are solved. The direct approach employs three types of control laws-the perigee-centered tangential steering, apogee-centered inertial steering, and piecewise constant yaw steering, over different orbital arcs within each transfer revolution to simultaneously change semimajor axis, eccentricity, and inclination, respectively. An analytic orbital averaging technique is developed to efficiently propagate the long-duration, many-revolution trajectories by computing analytic incremental changes in classical orbital elements for each transfer revolution involving thrusting, and Earth J 2 and shadow effects. The optimal orbital transfer problems are converted to parameter optimization problems that are in turn solved by nonlinear programming, and only a small number of parameters related to the control laws are optimized. The onboard guidance schemes that guide the spacecraft in an open-loop fashion are developed based on optimal parameters obtained by trajectory optimization results. Finally, numerical results of Earth-orbit transfers and performances of guidance schemes are presented.