## 5 Conclusions  
This paper is dedicated to the development and testing of a control system for a novel modular surface for package handling that has been recently investigated. The study begins with an overview of the main features of the concept, its functioning, the digital model, and the objectives. In summary, the concept is an under-actuated rotor-based system, with a camera on top to monitor package motion, and the only controllable variable is the discrete orientation of the rotor axis. This design inherently imposes specific constraints on the system's controllability and responsiveness. The under-actuation means that direct control over all degrees of freedom is not possible, limiting the ways the package can be influenced at any given time. Furthermore, the discrete nature of the rotor axis orientation restricts continuous adjustment, confining the system to a finite set of actuation states. These constraints stem directly from the modular and rotor-based architecture chosen to achieve simplicity, modularity, and cost-effectiveness, but they also create challenges in precisely steering the packages, especially under varying conditions. Due to these characteristics and the working principle, the control strategies proposed in the literature were not directly applicable; therefore, tailored modeling and control methods had to be developed. As a result, two methods were selected: a practical threshold-based control strategy and a dynamic closed-loop control with a PID controller. For the first method, an existing experimental setup is presented, along with the logic behind its definition. In more detail, the actuation of the surface modules is predefined, and the input condition is governed by the achievement of a limit condition. Practically, two main handling tasks were considered for evaluating the control strategy and system operation with this setup: sorting and orientation. For the sorting task, the threshold condition was simply the package IDs, which determined the type of sorting to be performed. Instead, in the orientation task, the angle variable was continuously monitored throughout the package's motion. When the angle reached the predefined limit, the actuation was adjusted accordingly. The results in both cases were promising. The sorting and orientation \begin{table}
\begin{tabular}{c c c c} \hline  & \(\mathbf{St_{x}}\) **[s]** & \(\mathbf{St_{y}}\) **[s]** & \(\mathbf{St_{\theta}}\) **[s]** \\ \hline \(P_{2}1\) & 8.748 & 6.748 & 8.381 \\ \hline \(P_{2}2\) & 8.744 & 8.543 & 8.715 \\ \hline \(P_{2}3\) & 8.197 & 8.457 & 8.631 \\ \hline \(P_{2}4\) & 8.984 & 8.957 & 8.983 \\ \hline \end{tabular}
\end{table} 
Table 4: Settling time (\(\mathbf{St}\)) with 2% threshold for the two displacements \(x\), \(y\) and the orientation \(\theta\) in the four outputs cases of PATH2. objectives were successfully achieved, with an error of approximately 4.4% in the second task, where a precise target value had to be reached for the monitored variable. On the other hand, for the PID control method, the analysis was challenged on two fronts that required some discussion: first, the managing of the severe non-linearities that stem from the under-actuation, over-constrained contact, passive driving and discrete actuation; second, the system modeling had to incorporate novel adjustments to address issues specific to the non-prehensile planar device. As a result, the proposed solution consisted of a feedback system that used the dynamic description of the transported item to retrieve the discrete system's input variable via minimization. In this context, the developed control was tested using a previously validated software environment, which implements the system's analytical model. The digital test, having already been certified, provides faster and more cost-effective results without compromising reliability. Specifically, two potential industrial applications of the surface were analyzed.