Analysis of trajectory deviation for spacecraft relative motion in close-range

The trajectory deviation analysis of relative motion in closed-loop control system was conducted with the concept of relative reachable domain (RRD), which is a geometric description for the collection of all the possible relative positions. Given that the state error of spacecraft is subjected to arbitrary Gauss distribution, the RRD could be obtained by assembling the time variable error ellipsoids of position. A closed-loop control system for close-range relative motion based on the linearized dynamical model with measurement and control errors was considered in the problem. The covariance matrix of spacecraft state, which defined the error ellipsoid, was analyzed by covariance analysis describing function technique (CADET). An algorithm for solving the envelope of RRD with the state covariance matrix was proposed subsequently. Comparison between the RRDs, solved in both open-loop and closed-loop systems, and the simulation result of 1 000 Monte Carlo runs demonstrates the feasibility and validity of the proposed method.