Space access and satellites lifespan are increasingly threatened by the great amount of debris in Low Earth Orbits. Among the many solutions proposed in the literature so far, the emphasis is put here on a robotic arm mounted on a “chaser” satellite to capture massive debris, such as dead satellites or launch vehicle upper stages. The modeling and control of such systems are investigated throughout the paper. Dynamic models rely on an adapted Newton–Euler algorithm, and control algorithms are based on the fixed-structure synthesis, recently implemented in an efficient Matlab toolbox. The main goal is to efficiently track a target point on the debris while using PD-like controllers to reduce computational burden. The fixed-structure framework proves to be a suitable tool to design a reduced-order robust controller that catches up with external disturbances and is simultaneously compatible with current space processors capabilities.