Abstract: In the torque-free case, the attitude motion of coupled rigid bodies spacecraft can be controled by a universal-joint model. This system is underactuated and characterized by the fact that there are more degrees of freedom than actuators. The attitude motion control of the underactuated system of coupled rigid bodies is investigated using angular momentum conservation in this paper. The control system of a coupled rigid-body spacecraft with an universal-joint model is obtained by using dynamics of multibody systems. The control problem of the system can be converted to the motion planning problem for a driftless system. The optimal control technique and wavelet analysis method is utilized and a numerical algorithm for motion planning of an underactuated system is proposed. The wavelet approximation is used to the optimal control and to generate an optimal trajectory for a coupled rigid body spacecraft. The effectiveness of the numerical algorithm is demonstrated for motion planning of an underactuated spacecraft by numerical simulation.