Abstract: This paper studies the optimal control of the nonholonomic motion planning for the free-floating space robot with prismatic joint. A hybrid optimization strategy based on the Gauss pseudospectral method (GPM) and the direct shooting method (DSM) is proposed. First, a dynamics model for the space robot is established based on the multibody dynamics theory. For a given initial and flnal conflgurations, the motion planning problem is described as an optimal control problem in the Bolza form. Then, the continuous optimal control problem is transformed into a nonlinear programming problem based on the GPM. With fewer Legendre-Gauss (LG) points, the feasible solution of the state variables and the control variables can be obtained. Finally, the control variables are discretized at the LG points and used as the initial values of the DSM, the optimal trajectory and the optimal control inputs are obtained by the sequential quadratic programming (SQP) algorithm. As shown by the numerical simulation, the optimal trajectory of the system is stable with no detours, and the control inputs match the various constraints under actual conditions. The results indicate that the hybrid optimization strategy is efiective with a good robustness.