## 4 Simulation Studies
### Robot Motion for Membrane Laser Welding  
As mentioned earlier, discrepancies such as position and velocity errors between the simulation and the actual robot were addressed through a dedicated calibration algorithm. Therefore, validating the operation of the developed software through simulations is important.  
To validate the robot motions, a physical implementation was conducted in a scaled-down demo environment of the large LNG cargo hold being produced, as shown in Figure 11. Although Figure 11 consists of a single layer, simulation verification of robot motions is adequate, as inter-layer movement in this development is manually controlled by the operator. The working space, which is composed of membranes, has a height of 3400 mm and is structured with three membranes.  
The robot model features a mobile robot with a 6-DOF manipulator mounted on top. To secure the workspace both above and below, a vertical movement axis was added to the mobile robot. The mobile robot has dimensions of 1200 mm in width and 600 mm in height, and an additional vertical stroke of 500 mm. The manipulator used for welding is the same as that described in Section 4.1, with a maximum reach of 1808 mm. While the actual model is an industrial robot with a payload capacity of 35 kg, the payload is irrelevant in the simulation because the dynamics are not considered.  
Figure 11: Simulation configuration: 1 layer of LNG cargo with laser welding mobile manipulator.  
Figure 10: Membrane configuration forming a two-layer sample environment.  
The membranes targeted for welding by the robot are shown in Figure 12. The model has dimensions of 2500 mm in width and 950 mm in height, with six corrugations on the top and bottom edges and three on the right and left edges. As illustrated in Figure 12, the characteristic feature of the corrugation path is a symmetrical conical shape consisting of three sections, S1, S2, and S3, each with different curvatures. S1, S2, and S3 represent round shapes with various curvatures. Simulation confirms the ability to trace the path; however, actual robot motions considering welding quality through integration with the welding device need to be validated through process research on actual membranes. Although the detailed robot motions may differ through the study of laser welding processes, simulation-based seam tracking allows for macroscopic verification of robot and environment collisions and confirmation of robot motion range and speed during membrane welding considering corrugations.  
The seam-tracking sequence was determined as shown in Figure 13. When numbering the three membranes in the sample process from bottom to top, as shown in (1), (2), and (3), the welding sequence is a straightforward sequential welding from bottom to top. In overlapping sections, where membranes (1) and (2) overlap and (2) and (3) overlap, the top edge of the lower membrane slightly overlaps the bottom edge of the upper membrane.  
The simulation of the robot's motion in welding the lowest membrane of the three is depicted in Figure 14. The sequence followed was the top, right, bottom, and left edges. As the membrane was positioned at a lower level, the vertical linear drive axis of the mobile robot was in its home position. The angles and angular velocities of the six joints of the manipulator are shown in Figure 15 and Figure 16, respectively. These figures confirm the suitability of the robot's joint motion range and speed range for the intended task, when compared to the industrial robot intended for use. In particular, the corrugation section, which requires an extensive joint motion range and abrupt speed, falls within the normal operating range of the robot.  
Figure 12: Membrane and corrugation configuration used in simulation.  
Figure 14: The order in which the mobile robot laser welds the membrane and the operating posture at each edge.  
Figure 13: Seam welding sequence for the designed environment.