The European Proximity Operation Simulator (EPOS) is a hardware-in-the-loop (HIL) system aiming, among other objectives, at emulating on-orbit docking of spacecraft for verification and validation of the docking phase. This HIL docking simulator set-up essentially consists of docking interfaces, simulating the servicing satellite called chaser satellite, the serviced satellite called target satellite, a sensor of the forces and torques during contact, and two industrial robots that hold the docking interfaces, and control satellites motion relative position and attitude. Furthermore, the EPOS includes a real-time controller interface linked to a computer-based numerical simulator of satellites orbital and attitude dynamics. A key feature of this set-up is the feedback loop that is closed on the real force sensed at the docking interfaces during contact. That feedback force is used as driving input to satellites dynamics numerical simulation. This HIL docking simulation concept has the unique advantage of using the measured contact forces and torques, but it presents significant challenges. The high stiffness of the industrial robots and the docking interfaces yields a high bandwidth contact dynamics at impact and, thus, very short contact time durations. These times might be shorter than the inherent time delay of the robot controllers. This leads to physical inconsistency in the docking dynamics and measured variables. This also causes a stability issue in the force feedback HIL system during contact and may cause catastrophic damages to the robots. Additional problems that need to be addressed are the characterization of the stability domain of operation, the compensation of the non-contact forces and torques, such as the measured forces and torques due to gravity effect. Finally, this thesis addresses the task of identifying the dynamic behavior of the robot end-effectors. This thesis addresses the above mentioned challenges and problems and presents solutions towards a stable and safe docking simulation operation of the EPOS facility. First, in order to mitigate the high stiffness and time delay problem, the thesis introduces a novel idea of simulating contact based on a concept called hybrid contact dynamics model. The method, developed in this thesis, is based on a combination of a passive compliance control introduced at the end-effector of the robot and a virtual contact model. The virtual contact model allows the operator to vary the contact parameters which can also be used as a control gain. The method also allows to solve the stability problem coming from the combination of time delay of the robot controller and high stiffness of the robot end-effector. For the passive compliance control, a new device is designed that has fairly known stiffness properties which are softer than the robot and docking interface stiffness. Second, the thesis presents a stability analysis of the proposed method via the adaptation of the pole location method to dead-time systems. The analysis is based on a linearized design model of the dynamics; linearization is performed around the docking geometrical configuration. This work first presents an analysis for the single dimensional case, which is then extended to two dimensions. The highlight of the stability analysis is the development of physically intuitive state-space model that easily unveil the modes of the contact dynamics. The application of the pole location method to the resulting second-order characteristics polynomial is straight forward. The contribution of this analysis is a closed-form relationship, and associated plots, among the system's parameter, i.e., the satellite's masses, the stiffness and damping coefficient of the contact parameters, the delay, and the geometry. In addition, the stability analysis is supported using the passivity method which is valid for three dimensions. Third, a model of the force-torque sensor is presented, and the classical weighted least-squares estimation technique is suggested for the identification and compensation of the non-contact forces and torques from the contact force and the torque measurement. Finally, it is proposed to utilize a LEICA laser tracker, a positioning measurement system, in order to identify the robot end-effectors dynamics behaviors such as the natural frequency and damping ratio. This hybrid contact dynamics model and the accompanying analysis is envisioned as a tool for safe and flexible EPOS operations. This tool shall allow emulation of the desired impact dynamics for any stiffness and damping characteristics within the stability region without recurring to a modification of the hardware. The experimental results of the robotics based hybrid docking simulator comply with experimental data from an air-bearing testbed that was independently performed by this author at the Space Robotics Laboratory of Tohoku University. It demonstrates the validity of the novel EPOS concept of operations and increases the confidence of using this approach for future on-orbit docking/contact algorithm validation, at the EPOS facility.