Abstract: In order to service for failed spacecraft running out of fuel, a SDRE based differential game approach is proposed as an on-line attitude controller to realize attitude takeover control through microsatellites coordination. Firstly, based on the nonlinear attitude dynamics of the combined spacecraft formed by multiple microsatellites and the target spacecraft, and the performance index functions of multiple microsatellites, the multi-microsatellite differential game model is established. The attitude takeover control problem is formulated as a differential game problem among multiple microsatellites, where each microsatellite optimizes individual performance index function to get the control strategy. Secondly, the SDRE method is applied to transform the nonlinear differential game to a state-dependent pseudo-linear quadratic differential game by the state-dependent coefficient matrix. The coupled state-dependent Riccati equations is derived to approximate the Nash equilibrium strategies of microsatellites. The set of the coupled equations can be solved iteratively by using the Lyapunov iterations to obtain the state feedback control of each microsatellite with high accuracy. Finally, the numerical simulations verify the effectiveness and fault tolerance of the SDRE based differential game approach for the attitude takeover control of the failed spacecraft.

Key words: Microsatellite, Differential game, State-dependent Riccati Equation (SDRE), Attitude takeover control