This study explores the trajectory tracking control problem of a free-flying space manipulator subject to parametric uncertainties, external disturbance, and actuator saturation. An adaptive control strategy, employing the fully actuated system (FAS) approach, is designed, wherein the radial basis function neural network (RBFNN) is incorporated to offset lumped uncertainties. As a result, a constant linear closed-loop system is obtained with an arbitrarily assigned eigenstructure. Then the parametric method is utilized for controller parameter selection. In the context of Lyapunov theory, the presented controller ensures robust convergence of position and velocity tracking errors to a small neighborhood of the origin. A numerical simulation is finally performed to validate the efficacy of the presented controllers.