Impulsive Feedback Control to Establish Specific Mean Orbit Elements of Spacecraft Formations

Abstract

An impulsive feedback control is developed to establish speci c relative orbits for spacecraft formation ying. The relative orbit tracking errors are expressed in terms of mean orbit elements. The feedback control, based on Gauss's variational equations of motion, allows speci c orbit elements or orbit element sets to be controlled with minimal impact on the remaining osculating orbit elements. This is advantageous when J 2 -invariant orbits are to be controlled, where only the argument of perigee and mean anomaly will drift apart at equal and opposite rates. The advantage of this impulsive feedback control, compared to optimal control solutions, is that it can operate with little computational effort and in a near-optimal manner, while requiring only a marginal penalty in fuel cost. When applied to the spacecraft formation ying problem, this control could also be used to perform general orbit corrections. Formulas are developed providing accurate estimates of the sensitivities of the mean semimajor axis and mean eccentricity with respect to the osculating inclination angle. With these sensitivities, the tracking error in semimajor axis, eccentricity, and inclination angle can be canceled within one orbit.

Autonomous Guidance & Control of Earth-Orbiting Formation Flying Spacecraft

“…Reconfiguration maneuvers are most likely to be made over one or two orbits [43]. If the J 2 perturbation is not accounted for, the formation accuracy will be limited by the drifting effect of J 2 during the number of orbits required to fully perform the maneuvers.…”

“…Impulsive Feedback Controller (IFC) uses instead thrust impulses at specific moments of the orbit to maintain or reconfigure a formation [46,43]. This controller was designed in order to perform any small orbit element correction From looking at GVEs (Eq.…”

Analytic Solution to Optimal Reconfigurations of Satellite Formation Flying in Circular Orbit under $J_2$ Perturbation

“…Schaub and Alfriend [21] discuss the effect of applying impulsive control on the orbital elements, perturbed by the J 2 effect. In [22], two approaches-impulsive control and continuous control-are developed and compared.…”

Autonomous Low-Earth-Orbit Station-Keeping with Electric Propulsion

“…From equations (52)- (53), it is evident that the efficiency of an impulsive cross-track maneuver for i and Ω adjustments is maximized when the spacecraft passes through the equatorial (u = kπ) and polar (u = kπ + π/2) regions, respectively [39]. The proposed approach consists in applying a sequence of impulsive burns at u = π orû = 3 2 π whenever the tracking errors δī or δΩ exceed a predefined control window.…”