Impedance-controlled robots are widely used on Earth to perform interaction-rich tasks and will be a key enabler for In-Space Servicing, Assembly and Manufacturing (ISAM) activities. This paper introduces the software architecture used on the On-Board Computer (OBC) for the planned SpaceDREAM mission aiming to validate such robotic arm in Lower Earth Orbit (LEO) conducted by the German Aerospace Center (DLR) in cooperation with KINETIK Space GmbH and the Technical University of Munich (TUM). During the mission several free motion as well as contact tasks are to be performed in order to verify proper functionality of the robot in position and impedance control on joint level as well as in cartesian control. The tasks are selected to be representative for subsequent servicing missions e.g. requiring interface docking or precise manipulation. The software on the OBC commands the robot's joints via SpaceWire to perform those mission tasks, reads camera images and data from additional sensors and sends telemetry data through an Ethernet link via the spacecraft down to Earth. It is set up to execute a predefined mission after receiving a start signal from the spacecraft while it should be extendable to receive commands from Earth for later missions. Core design principle was to reuse as much existing software and to stay as close as possible to existing robot software stacks at DLR. This allowed for a quick full operational start of the robot arm compared to a custom development of all robot software, a lower entry barrier for software developers as well as a reuse of existing libraries. While not every line of code can be tested with this design, most of the software has already proven its functionality through daily execution on multiple robot systems.