A new concept for controlling formation flying satellite constellations

This paper demonstrates the use of Hill's equations to design and control relative motion orbits of satellites in a constellation. Hill's equations describe the linearized dynamics of a satellite (Deputy) with respect to another satellite (Chief) or a fictitious point, which is assumed to move in a particular orbit. Given the initial conditions of the Chief, it is easy to determine initial conditions of a Deputy, for periodic relative motion. The control acceleration or the fuel required to cancel the J2 perturbation varies for each Deputy, depending upon its orbital inclination with respect to that of the Chief. A novel, disturbance accommodating control design process is presented for minimizing the total fuel consumption of the constellation and maintain equal, average fuel consumption of each satellite, over a desired period of time. This is achieved by introducing small, periodic variations in the mean orbital elements of each Deputy. The reference relative orbit is modified to take into account the eccentricity of the Chief's orbit. Analytical results, which have been verified by numerical simulations, indicate that intelligent cancellation of the disturbance for constellation control can be achieved with an average of 12% reduction in the impulse required compared to the "brute force" approach. The maximum impulse reduction for specific Deputies is 38%.

A new concept for controlling formation flying satellite constellations Conference Paper