Robotic manipulators mounted on spacecraft experience a number of kinematic, dynamic, and control problems because the motion of the spacecraft is affected by the robot motion. In this paper, the general three dimensional equations of motion are derived for an n link manipulator mounted on a non-fixed base object. Instead of performing a single inverse kinematic calculation at the beginning of a movement to determine the required joint setpoints, multiple inverse kinematic updates are done throughout a movement. The updating sequence is determined by an optimal inverse kinematic updating algorithm. This motion control algorithm is based on experimental simulation results performed in Matlab and a set of performance indices that are used as guidelines. Simple PD joint controllers and a special joint trajectory generator are used for servoing the manipulator joints for a planar robot application. The derived motion control techniques incorporate the base motion without base motion control.