Abstract: In this paper, the inverse kinematics of a free floating space manipulator system is studied, and it is shown that the Jacobian matrix is unlinearly dependent on inertial parameters. With the augmentation approach, we demonstrate that the augmented generalized Jacobian matrix can be linearly dependent on inertial parameters. According to the results, when the inertial parameters are unknown, two adaptive control schemes for a free floating space manipulator system to track the desired trajectory of workspace are proposed. A two link planar space manipulator system is simulated to verify both proposed control schemes.