Multiple Spacecraft Formation Flying Control around Artificial Equilibrium Point Using Propellantless Approach

This paper demonstrates a detailed analysis of the feasibility for compact formation system around an L2-type artificial equilibrium point by means of continuous low-thrust propulsion in the hybrid form of solar sail and Coulomb force propulsion. Firstly, in view of non-ideal solar sail, the position of L2-type artificial equilibrium point and numerical periodic orbits around L2 utilized as leader's nominal trajectory are given. Secondly, considering the external disturbances in the deep space environment, the nonlinear dynamic model of the spacecraft formation system based on the circular restricted three-body problem (CRTBP) is derived, under the assumption that the leader covers the nominal trajectory and each follower adjusts its propulsive acceleration vector (that is, both its sail attitude and electrostatic charge) in order to track a desired relative trajectory. Thirdly, based on a new double power combination function reaching law, a fast integral terminal sliding mode control methodology (MFITSM) is ameliorated to achieve orbital tracking rapidly, which has better robustness against external disturbances and the buffeting effect during spacecraft propulsion simultaneously. To properly allocate control inputs, a novel optimal allocation scheme is designed to calculate the charge product of the spacecrafts and sail attitude angles, which can make the magnitude of the acceleration required from the Coulomb propulsion system minimum and avoid formation geometry instabilities by balancing electrostatic interaction between adjacent spacecraft. Finally, several numerical examples are conducted to validate the superiority of the proposed control algorithm.