## 4 Simulation of Robotino's Path  
We can now simulate the motion of Robotino along the planned path. We build the model first and then start a simulation run using the following parameters: simulation interval 50 s, output interval 0.02 s, maximum time step size 0.02 s, errors 1 \(\times\) 10\({}^{-6}\). The simulations are performed on a PC with a x64-based processor, AMD Ryzen 7 PRO 4750 G (AMD, Santa Clara, CA, USA), with Radeon Graphics 3.60 GHz. The total elapsed time is 0.51 s. After that, we repeat the simulation with the same parameters, and this time, we enable communication between the dynamic and virtual models. Communication isestablished using the IPC pipe component (inter-process communication), shown as a red ring in Figure 31, which enables the dynamic model to send some information. In our case, these are joint angle values, which are sent to the virtual model 30 times per second. When the dynamic model is connected to the virtual one, the total elapsed time is 46.83 s. Having tested the behavior of Robotino using both these models, in future investigations, we plan to connect them with a real physical robot according to the digital twin concept. The BondSim3 DVisual application also enables the mechanism movements to be written over the screen on a video file in the MP4 format. We start writing using the command Start Video and end it with the command End Video under the File menu. We can read this file using various applications, such as Media Player, Movies & TV, and similar. We uploaded this file to YouTube under the name Project Robotino, where readers can view it. When the video writing is underway, the process is somewhat slower, but it remains at about 50 s.  
Some generated plots are shown in the figures below. The path coordinates in the plane motion sent to the virtual model force the latter to change its position on the screen, i.e., it moves. The corresponding virtual path coordinates are picked up by the probe element (Figure 10a) and sent back over the named pipe; they appear at the output of the IPC element. Figure 32a shows the corresponding path, as seen on the display connected to this IPC port. The difference between these signals and the signals of the Robotino's base coordinates, which are evaluated using the simulation, i.e., the same signals that we previously sent over the pipe, are evaluated by the block below and to the right of IPC's output port. They are displayed on the display component on the right. The resulting plot is shown in Figure 32b. To further explain the obtained results, we put the \(x\)-coordinates of the center point XC and XCvisual on the same y-axis on the display at the right of the IPC component. This is shown in Figure 33a. At first glance, they appear to be a single curve. We expand a small rectangle around a point on the curve. The generated enlarged plot is shown in Figure 33b. There are really two curves, displaced by 30 ms (milliseconds). Thus, the signal sent back over the pipe is delayed by this time value; as a result, the accuracy of this curve is moderate, as shown in Figure 32b. The accuracy depends on the frequency with which data packs are sent over the pipe. In this simulation, it is exactly the same number, i.e., 30 ms.  
Figure 32: Simulation results: (**a**) path traversed in the virtual space; (**b**) differences in the \(X_{C}\) and \(Y_{C}\) coordinates obtained due to the behavior of the virtual and dynamic models. To verify the developed dynamic model and control algorithm, we compared the coordinates of the robot center and its orientation as obtained during the simulation with the reference values. Figure 34 depicts the deviations in the obtained coordinates of the Robotino's center (\(X_{C}\) and \(Y_{C}\)) and its orientation (angle \(\varphi\) in radians) with reference to the reference values defined by (24) and (29). They are of the order of several \(10^{-6}\) m for \(Xc\), less than \(2\cdot 10^{-5}\) m for \(Yc\), and \(10^{-6}\) rad for the angle \(\varphi\) (after the initial transient processes).