Linearizing assumptions and control design for spacecraft formation flying maneuvers

In this paper the validity of neglecting the relative effect of the gravitational force of the Earth on a formation of spacecraft is studied. This relative effect is treated as an unknown disturbance acting on the system and all control laws are designed using a linear model that neglects this effect. A previously designed simple linear feedback controller is tested under different conditions using the linear model and the full nonlinear model that includes the gravitational force. All tests are carried out in the presence of saturation limits. The results show that the linear controller exhibits oscillations in the transient response and poor robustness under certain conditions. It also exhibits a high saturation tendency, thereby leading to increased fuel consumption. This controller also causes a high rise in the velocity errors at ordinary values of the gains. Based on the behavior of this controller, new controllers are proposed that overcome these drawbacks without any need for modifying the gains. The controllers, when tested under saturation limits exhibit high robustness characteristics due to their low saturation tendency and nearly eliminate oscillations in the transient response. Since these controllers operate under low control forces for a greater duration of the maneuver, they reduce the fuel required for the process. Simulation results are provided to show the effectiveness of these new controllers.