## Active Debris Removal
### Proximity Operations  
Guidance, navigation and control problems typically have a nonlinear design space, several constraints as well as competing objectives. Therefore, a simulation-based design approach--as depicted in Figure 12--is being developed to achieve efficient and high TRL design processes. Preliminary design stages are performed in lower fidelity environments to assure fast concept verification and low development costs. To this purpose, a Mathematica-based symbolic simulation environment has been created. De-Orbit, Formation Flight and Re-Entry Analytical Toolbox (DIFFRACT) provides a modular set of analytical and semi-analytical tools employed to model motion dynamics, perturbation forces and guidance schemes. The relative motion is modeled using state transition matrices based on a quasi-nonlinear parametrization of relative orbital elements (ROE) [55]. For more advanced design stages, the closed loop performance of several subsystems need to be evaluated. SpaceCraft ATTitude and Orbit numERical simulator (SCATTER) is a  
Figure 12: Simulation-based design approach. Matlab/Simulink-based (2017b, MathWorks, Natick, MA, USA) high fidelity simulation environment developed to this purpose. Compared to the symbolic simulation environment, SCATTER allows the additional modeling of Clohessy-Wiltshire (CW) equations, nonlinear relative motion and attitude dynamics (six degrees of freedom), detailed perturbative forces and Torques, and major subsystems of the spacecraft such as propulsion and attitude determination and control subsystems. The environment is composed of several Matlab scripts and a Simulink library of standard (modified) and own-created blocks. This enables the interconnection of different models to assemble the components of the system to be designed. Both stated environments have been verified, demonstrating their successful implementation and the achievement of design requirements. The verification process included the following steps: sanity checks by comparing simulation results to the analytical solution for simplified models (e.g., CW equations), comparison of SCATTER and DIFFRACT against each other, and comparison to already validated and verified software such as the NEPTUNE propagator. The results show good concordance. Figure 13 depicts the relative trajectory during the closing phase of a rendezvous mission simulated via DIFFRACT (Figure 13a) and SCATTER (Figure 13b). The symbolic simulation uses an unperturbed quasi-nonlinear relative motion model and an idealized impulsive maneuver scheme, while the numerical simulation uses a nonlinear motion model, a reaction wheel model, and thruster model and thus includes an Linear Quadratic Regulation (LQR) position controller and a PD attitude controller. The figure shows that the computed radial impulsive guidance scheme works well for ideal conditions and even under the presence of actuator uncertainties due to the good performance of the closed-loop attitude and position control. The maneuver execution errors result in additional hops during the closing. To refine the design for on-orbit qualification and achieve advanced TRL, a Hardware-In-the-Loop (HIL) simulation environment has been constructed. The Experimental Lab for proxlmity operations and Space Situational Awareness (ELISSA) uses an air-bearing table to emulate orbital relative motion and the contact dynamics during the docking phase. The air-bearing table consists of modular aeromechanical platforms with embedded nozzles, which are supported by an aluminum structure. The airflow is supplied by two side channel blowers to the platforms, which generate an air cushion to support propeller driven satellite mockups. The mockup's thrust control is achieved via Pulse Width Modulation (PWM). An optical capture system has been installed and tested, achieving position uncertainties under \(\approx\)1 mm. ELISSA provides the possibility of replacing inaccurate or complex models (such as docking mechanisms) with real-world counterparts and test the system under real-time constraints.