Low-thrust nonlinear guidance by tracking mean orbital elements

A low-thrust nonlinear guidance for long-duration, many-revolution transfer trajectories is constructed by tracking mean orbital elements based on the concept of semi-analytic satellite theory. Three simple control laws are applied over appropriate orbital arc segments within each transfer revolution to simultaneously change semimajor axis, eccentricity, and inclination. The analytic time rates of mean classical orbital elements using the proposed control strategy are computed by an orbital averaging method. Along the mean elements of nominal transfer trajectories, a tracking guidance scheme is developed using the concept of nonlinear model predictive control over finite time horizons, in which simple constrained optimization problems are formed to minimize mean orbital elements errors between the actual and nominal trajectories. Rosenbrock's optimization method, which does not calculate derivatives, guarantees robustness for optimum searching with a small number of parameters. The approach for removing deviations from the nominal trajectories is based on the changeable powered are lengths of different steering programs and the mechanism of variable specific impulse modulation. Furthermore, the Earth's oblateness and shadow effects are taken into consideration in the guidance scheme.