In this paper, we propose a novel method for the on-ground simulation of a space robotic mission, while exploiting a robotic hardware-in-the-loop facility. The simulated dynamics replicated by the robots are defined with respect to a nominal motion. This approach enables simulating the motion of large satellites. In particular, we exploit a Lagrangian matching relative to the nominal motion for a satellite (client) and a manipulatorequipped spacecraft (servicer), which are modeled as a rigid body and a multi-body system, respectively. Stability of the proposed method is also analyzed. The effectiveness of the method is demonstrated through experiments on the OOS-Sim facility for the capture of Envisat, a free-tumbling satellite and the largest space debris in Low-Earth-Orbit.