Autonomous space robots are crucial for performing future in-orbit operations including servicing of a spacecraft, assembly of large structures, maintenance of other space assets and debris removal. Such orbital missions require servicer spacecraft equipped with one or more dexterous manipulators. However, unlike its terrestrial counterpart, the base of the robotic manipulator is not fixed in inertial space, instead, it is mounted on the basespacecraft, which itself possess both translational and rotational motions. Additionally, the system will be subjected to extreme environmental perturbations, parametric uncertainties as well as system constraints due to the dynamic coupling between the manipulator and the base-spacecraft. This paper presents the dynamic model of the space robot and a three-stage control algorithm to control such a highly dynamic non-linear system. In this approach, Feed-Forward compensation and Feed-Forward Linearization techniques are used to decouple and linearize the highly non-linear system respectively, therefore, allowing the use of the linear Proportional-Integral-Derivative (PID) controller and Linear Quadratic Regulator (LQR)as final stages. Moreover, a simulation-based trade-off analysis was conducted to assess the efficacy of both proposed controllers. This assessment considered the requirements on precise trajectory tracking, minimizing power consumption and robustness during the close-range operation with the target spacecraft.Research highlights: orbital space robotic missions, control of space robots, freeflying and controlled-floating modes of operation, application of linear controllers