Nonlinear Feedback Control of a Spinning Two-Spacecraft Coulomb Virtual Structure

This paper studies a spinning two-spacecraft Coulomb virtual structure control scenario in an orbital environment. Only Coulomb forces are utilized to control the two-spacecraft formation shape while flying in a geostationary orbit. After deriving the separation distance equation of motion which determines the two-vehicle formation shape, a feed-forward nominal control charge is developed by assuming a purely two-spacecraft configuration. An asymptotically stable full-state feedback control law is developed. It requires the inertial and relative position vectors which are difficult to measure accurately. A partial-state feedback control law is proven to be stable assuming a fast spinning rate in comparison with the orbit rate. The boundaries of the orbital motion contributions are proven to be negligible for a relatively tight and fast-spinning formation in a geostationary orbit. An integral feedback term is utilized to compensate for the error in estimating the feed-forward nominal charge product. Numerical simulations illustrate the performance of the controllers.