# Grasp Analysis for the Robot-Based Manipulation of Pre-Assembled Cables with Electrical Connectors
## 3 Methodology
### Scenario Generation and Cable Load Quantification  
As a basis for the scenario generation in the physics simulation, data must first be provided by the user. This includes the CAD data of plugs and sockets, their supply, and the product to be assembled. In addition, the supply pose and mating pose are necessary for each plug. This data is typically already available, at least preliminarily, during assembly planning and can be derived from assembly planning software.  
For the physics simulation in this work, high accuracy in modeling of the dynamic and mechanical cable behavior is required. A rough topological representation is, therefore, not sufficient. As shown by [30], for modeling DLOs, the nonlinear mechanics of elastic rod methods outperform other modeling techniques, such as the mass-spring method or the finite-element method, in terms of accuracy. Therefore, we build on software that is based on rod-based modeling in this work, more precisely on _IPS Cable Simulation_ ([[https://flexstructures.com/products/ips-cable-simulation/](https://flexstructures.com/products/ips-cable-simulation/)]([https://flexstructures.com/products/ips-cable-simulation/](https://flexstructures.com/products/ips-cable-simulation/)), accessed on 22 February 2023). For an in-depth comparison of the different physics simulation techniques for DLOs, please refer to [30].  
For the mechanical description of the cables, the parameters listed in Table 1 are required.  
With the CAD data and cable parameters given, the scenario can be generated automatically. For this purpose, the CAD models are placed, and the cables are created. In each case, the two cable ends are connected to the two plugs. The cables are generated without deformation and load. Subsequently, two trajectories are initialized for each cable, mapping the temporal courses of the two grippers, as shown in Figure 3.  
Linear movements are used for the removal of cables from the supply and the mating of the plugs into the sockets. The transfer motions in between up to the pre-pose for mating are carried out via straight-line translations. Thereby, necessary pose changes of the two plugs for mating occur with a constant rate of change in rotation. The two trajectories are synchronized in their velocity so that both plugs are mated into the sockets at the same time. The removal height from the supply and the pre-pose for mating can be configured individually.  
The initialized trajectories can now be used to quantify the dynamic cable wrenches. For this, the user can select the number of waypoints (WPs) to be sampled. The quantity  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Abbreviation** & **Unit** \\ \hline Tensile stiffness & \(EA\) & N \\ Bending stiffness 1 & \(EI_{1}\) & Nm\({}^{2}\) \\ Bending stiffness 2 & \(EI_{2}\) & Nm\({}^{2}\) \\ Torsional stiffness & \(GJ\) & Nm\({}^{2}\) \\ Length density & \(\rho_{L}\) & \(\frac{\text{kg}}{\text{m}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Effective parameters to describe a cable mechanically in the software _IPS Cable Simulation_. If a cable has different bending characteristics in both material directions, bending stiffness 1 and 2 show different values [31].  
should be chosen depending on the length of the trajectories and the expected cable deformations. The cables are then manipulated along the trajectories, and the wrenches are tapped at each of the two cable ends in their local coordinate system, as shown in Figure 4.  
The dynamic cable wrenches are subsequently evaluated by the contact model, which is described in the following section.