Dynamic modeling and simulation of a post-capture spacecraft with X-shape isolation system

The dynamic model of a post-capture spacecraft with X-shape isolation system is established considering the coupling of attitude changes, orbit motion and structural vibration. The post-capture spacecraft consists of a flexible servicing spacecraft, a target object (i.e., the debris), and an X-shape isolator. Based on hybrid coordinate method the kinetic energy, potential energy, and virtual work of the system are expressed, and the governing equations of the system are derived using Lagrange’s equations. To validate the model, the natural frequencies and mode shapes of the post-capture spacecraft are calculated and compared with the results from FEM (finite element method) software. Besides, comparisons between X-shape isolator and SMD (spring-mass-damper) isolator are conducted to prove the advantages of X-shape isolator. Furthermore, the effects of structural parameters and initial velocity of the target object on the dynamic responses of the post-capture spacecraft with X-shape isolation system are shown in detail. At last, an effective controller is designed for the attitude and orbital motion of the post-capture spacecraft by using the LQR (linear quadratic regulator) control strategy.