# A 6 DOF Virtual Environment Space Docking Operation with Human Supervision
## 2 Real and Virtual Setup Description  
The Berthing Docking Mechanism (BDM) is a mechatronic system that is capable of performing successful rendezvous/contact operations via either docking or berthing. It is designed for the low-impact docking of a spacecraft by actively reducing the impact forces on the platform during progressive contact. The structural design of the BDM is a 6 DOF parallel manipulator, based on the Stewart-Gough platform [8; 9]. Lab-scale 6 DOF Stewart systems controlled with robust integer-order controllers have already been presented in [10; 11; 12; 13]. However, the main difference to the lab-scale application is that BDM structures have high LPV dynamic properties. Since the leg's dynamics depend on the experienced inertial load, each relative mass corresponds to a model with different dynamics. In other words, each model represents the dynamics of a particular leg in a particular pose when a certain force is exerted on the platform's upper ring. Since every executable trajectory of the platform can be seen as a succession of different states, it is clear that the LEMA dynamics change constantly during spacecraft docking. How they become active during the contact process is briefly described as follows. During docking, the mechanism consists of an active and a passive module, as illustrated in Figure 1, which can be viewed as two sub-systems with an interaction when in contact. The ring-shaped interfaces of the active module can be moved with 6 DOF by means of six telescopic extensible legs. The length of the legs is controlled for each leg individually by  
Figure 1: Illustration of the active and passive modules for space IBDM (International Berthing and Docking Mechanism) rendezvous/contact. In the context described in our methodological approach, each module is a dynamic sub-system. a brushless DC motor, based on the force signals measured by the load cells. Considering the platform's 6 DOF, the net power the legs have to deliver in order to move the spacecraft in a certain direction might differ, depending on the pose of the platform. When the actuator is oriented in the direction in which the platform has to be accelerated, the legs will experience low-load behavior, which is less demanding in terms of actuator effort. The variations in the load are referred to as the reflected mass. From an LPV perspective, this 6 DOF platform has to be controlled with respect to a varying-load system conditions. The real picture of the platform is depicted in Figure 2a, while the coordinate system of the virtual and real platform is illustrated in Figure 2b. In this figure, the \(O_{vw}\) is the origin of the virtual world, the \(O_{vwp}\) is the central coordinate of the virtual platform and \(O_{rw}\) and \(O_{rwp}\) represent the coordinates of the real world and of the real platform, respectively. \(H_{rp}=H_{vp}=50\) cm represents the height of the platform, \(D=10\) cm is the distance between the real ad the virtual platform, and the diameter of the platform plate is \(70\) cm. The real 6 DOF platform from Figure 2a represents the first part of the co-simulation setup system and is considered to be the active module of the BMD setup. It uses the position control of each leg (Figure 3a) to achieve global positioning and determine the angle of the platform. Given that the position of the platform is known, the position of each connection \(C(x_{c},y_{c},z_{c})\) is also known (as specified by the controller). The position of the servo \(A(x_{a},y_{a},z_{a})\) and its orientation \(\theta\) are determined by the motion platform construction. The connection of the servo lever and the vertical rod is indicated as \(B(x_{b},y_{b},z_{b})\). Let \(r\) be the length of the servo arm (\(AB\)) while \(BC\) is the shaft that connects the servo arm with the platform in the point \(C\) and has the length \(\ell\). The absolute distance between point \(A\) and \(C\) is denoted by \(\ell_{1}\).