Study on stability of formation for gravity field exploration subjected to disturbance based on prescribed performance control

Double satellite formation for gravity field exploration is a complex space virtual instrument system with high-precision, whose normal manner is threatened by the space debris environment. The normal manner of the formation based on control with prescribed performance is studied. Based on the random impact of space debris, nonlinear dynamical equations with 20 variables are established considering the relative attitude of the double satellite. The interferential characteristics and expected stability under certain disturbance conditions by the space debris in low Earth orbit are analyzed. To simplify the relative motion of the formation and the motion of the test mass (TM) relative to the cage, a prescribed performance function is introduced to constrain the relative attitude errors of transient and steady states. An adaptive attitude control design method based on a prescribed performance function is proposed. Finally, the analysis is carried out. The results show that the probability of normal manner of the formation is about 78.45% in the first year and about 45.59% in the first three years. The normal manner of the double satellite formation for gravity field exploration can be effectively simulated and analyzed based on the prescribed performance control methods.