## 4 Results
### Results PATH 2  
Further exploration of other possible industrial uses of the controlled surface was deemed valuable for the second round of simulations. The application in this case was primarily concerned with package sorting along the line. The envisioned scenario includes an intermediate section of a transport line with side exits, where packages must be directed based on their codes. A graphical example of this is illustrated in Figure 14.  
As before, initial and final positions, package characteristics, the surface inputs, and the layout were all predetermined. Instead, the actuation of the modules underneath the transported body at each instant was determined in real time. The _Matlab_ visualization in Figure 15 displays the solutions for carrying out these processes. Both the symbols and the input values, such as the initial speed (0.05 m/s), the surface inclination (8\({}^{\circ}\)), and other parameters, are identical to those in the previous subsection. In this case, the only differences are in the target positions (named \(P_{2}1\), \(P_{2}2\), \(P_{2}3\), and \(P_{2}4\)), which are at the sides of the line at angles of \(\pm 45^{\circ}\), and the layout (footprint 3 m \(\times\) 2 m). The simulation time was also extended to nine seconds in light of the longer surface that was selected. Although they differ significantly from the PATH 1 case and from one another, the intended configurations are achieved, as seen in Figure 15. This means that the selected controller coefficients \(K_{p}\), \(K_{i}\), and \(K_{d}\) are still in use. Quantitative reference values are provided for this application as well by reporting the numerical values of the errors at each instant and the settling times. Figure 16 contains the errors data, where trends and oscillations similar to PATH 1 can be observed. Furthermore, for \(P_{2}1\), \(P_{2}2\) and \(P_{2}3\) of Figure 16, the package halting in the desired position is visible. In fact, appreciably earlier than 9 s, as also highlighted by the settling times of Table 4, the errors remain constant as the package maintains its target position. This demonstrates that the  
Figure 14: PATH 2 task’s schematic illustration [22]. Figure 13: PATH 1, \(x\), \(y\), \(\theta\) errors between the four desired and real outcomes: \(P_{1}1\), \(P_{1}2\), \(P_{1}3\) and \(P_{1}4\). surface's effect is continuous throughout the work rather than immediate, with errors not just approaching zero at the chosen simulation time. Although the issue of sensor delay is explicitly addressed in the context of the threshold-based control, similar considerations are equally relevant for the PID-based strategy. In fact, accurate estimation and management of sensor and processing latency are critical for achieving reliable closed-loop control performance. This aspect has been a key motivation for adopting a digital simulation environment rather than relying solely on the physical prototype. As discussed in Sections 2 and 4, the current experimental setup is limited by the response time of its onboard sensors, which at present does not yet meet the timing requirements for effective PID implementation. Specifically, the combined delay from sensing, processing, and actuation would need to remain below 0.01 s to align with the performance observed in simulation results, a condition that is still under development in the physical platform. The simulation environment, by contrast, at the moment is not constrained by hardware latency and allows for rapid testing and optimization under idealized timing conditions. Nevertheless, for future physical implementation, the digital model will also require computational efficiency: each simulation cycle must remain fast enough to avoid introducing artificial delays that could compromise control performance. In summary, one of the layouts selected for these simulations was created in response to the request of the industrial partner, while the other was a possible real-world use case.