The differential game barrier model for spacecraft under target maneuvering based on minimum error

This paper explores the pursuit-evasion game of two spacecrafts in low coplanar orbit under minute continuous thrust. By using differential game theory, this study verifies terminal conditions confined by controlling, target set and velocity and gives the linear game model of minimum error that is compared with nonlinear game model on sight coordinate. The terminal conditions are fixed by constructing parameter equations set, which are obtained by the optimal controlling strategy for both spacecraft. Within the linearized set of equations, there are variable parameters that are associated with the linearization process. Using differential game of kind theory, this paper obtains the expression of the barrier with the variable parameters to be established. According to extremum theory of the minimum error, the parameters to be established are achieved. This paper gives the results of theoretical derivation and numerical simulation.