Parameter space design of nonlinear feedback control for spacecraft reorientation

Presented in this paper is a nonlinear method which, incorporating the procedure of input-output feedback linearization and Lyapunov stability analysis, can be applied the problem of large angle reorientation of a rigid spacecraft. The attitude of a spacecraft, represented by four Euler parameters, is regarded as confined to the surface of a four-dimensional sphere. Instead of forming attitude transformation relation, error vector by direct attitude subtraction from present to final orientation is utilized. The error vector is a projection from the geodesic between two attitudes on the sphere which can be used as minimum path reference for the control system to follow. Through feedback linearization, the control law is formulated from the attitude error dynamics as a second-order linear ordinary differential matrix equation. Constant coefficients of the equation become the gain matrices of the attitude control law. Overall control system stability can be achieved by tuning the control gains in the anaylsis process and it will not be affected with constrained control. Geometrically, the attitude trajectory obtained from the proposed method is a minimum path trajectory. Proper selection of control coefficients and control constraint can achieve a trajectory with both minimum maneuver time and control effort.