Abstract: A second-order sliding mode finite-time adaptive control method is designed for the base-attitude-controlled space robot with output constraints and random disturbances. The dynamic model of the disturbed space robot system is established using Lagrange method. Considering the output constraints of the space robot, an barrier Lyapunov function is designed to limit the system output within a preset range. In order to handle the random disturbances of the space robot, a second-order sliding mode finite-time controller is constructed using the power-adding integration method, which eliminates the dependence of existing sliding mode control methods on the upper bound information of the disturbance terms, solves the problem of gain overestimation in traditional adaptive control methods, and weakens the phenomenon of torque chattering. The simulation results demonstrate that the proposed control method can achieve error convergence within 2 seconds and enforce full-state output constraints strictly, outperforming the existing controllers without the mechanism of output constraint. Moreover, it exhibits smoother output torque, faster response, stronger robustness, and higher safety, thereby significantly enhancing the overall control performance of space robots.