Satellite Servicing becomes a more and more important application in the field of space robotics. It provides an option for maintenance, repair and life time extension of satellite systems. Since operating satellite systems are not yet prepared for such kind of servicing tasks, our current scenarios are focused on docking of servicing vehicles which are acting as attached attitude control modules when docked to the target system. This method offers both a kind of satellite re-fuelling [1] and an option for a well controlled satellite de-orbiting (ROSAT, [2]) if the satellite is not able to be controlled anymore. For successful grasping and docking at the target satellite the manipulator system onboard the servicing vehicle plays a central role. In most of the mission scenarios the robotic system is based on a kinematically redundant manipulator, equipped with at least seven joints due to the increased skill performance and operational flexibility. However, the problem of solving the Inverse Kinematics increases accordingly to the number of manipulator joints. Moreover, for space applications the free floating robot base has to be taken into account inside the solution algorithm. In our environment the algorithm for solving the Inverse Kinematics problem is formulated as a Lagrangian constraint optimization. It provides joint motion solutions with respect to a large variety of optional optimization criteria concerning joint motion parameters like minimum joint speed / acceleration / torque / power but also criteria concerning physical limitations of the robotic system (e.g. max. joint angle range, max. joint speed etc.) and last but not least concerning the free floating motion of the robot base satellite in space. Moreover, the algorithm supports standard serial robot kinematics but also tree-like systems including kinematic loops. The paper focuses on the modularity of the algorithm’s implementation concerning description of the robot kinematics as well as adaptation to different operation environments (e.g. fixed on ground, free floating in space).