# Study and Simulation of an Under-Actuated Smart Surface for Material Flow Handling
## 1 Introduction
The former, which are the most recent in the literature, exploit multiple omnidirectional and motorized wheels called \"omnivheels\" positioned in the module with their axes fixed. The layout and number of wheels is not the same in every study, however; as a reference, three or more wheels are usually employed and their spinning axes are positioned out of alignment to create controllable forces in both directions of the plane. As first example of modules with more than three wheels, study [13] alternates units with seven wheels--one large in the center and six small on the sides, to units with five--two large on the sides and three small in the center. For both layouts, the axes of the large wheels are perpendicular to the axes of the small ones to ensure driving forces in the plane. In contrast, in [3, 11, 35], each module of the device studied, called \"Celluveyor\", contains three omnidirectional wheels with axes arranged at 120\({}^{\circ}\) to one another. Each wheel can rotate at different speeds to control the magnitude of the force exchanged with the transported object, and all three  
Figure 1: Smart surfaces classification and field of application. forces together are used to handle the body motion. On the other hand, the second group of systems, i.e., those with modules with two degrees of freedom, consist of units composed of one or more motorized and swiveling wheels. In this case, therefore, as presented in [14; 34], the basic element of the module is a simple wheel driven by a motor mounted on its axis of rotation. This wheel, however, unlike the one degree of freedom systems, is also mounted on a vertical axis, which is itself motorized and therefore swiveling. Summarizing, these devices just described are fully implemented and contain several motors per module, specifically, three or more for the first class and at least two for the second. They can actively drive, sort, and manipulate the material flow, creating a totally actuated surface with significant handling skills. However, the use of several motors and their control necessarily involves a greater effort in the management of the system, as well as increasing costs and complexity. According to the current state of the art, a simpler under-actuated device without motors is missing for the same intralogistic tasks. For that reason, seeking cost reduction and simplification of both control and design, without losing the flexibility of this class of systems, in this paper the authors propose an under-actuated surface composed of modules. Unlike existing concepts, each module contains an idle rotor instead of a motorized wheel. The axis of rotation of the mentioned rotor is not driven continuously by a motor but can be oriented in a limited number of directions in the plane of the surface, creating a directionable friction force for object handling. In order to compensate for the under-actuation, the material is moved by exploiting gravity or an initial velocity of the object provided by another system (e.g., a previous conveyor belt). Therefore, compared to the existing systems [3; 11; 13; 14; 31; 32; 33; 34; 35], the novelty that distinguishes this active surface from the literature technology lies in its simplicity. In fact, the two main characteristics of the system proposed by the authors, compared to those in the same category, are the under-actuation and the limited directions of the rotor axis, both of which are reductions to a minimal form of concept technology, but which save components and make the most of sources already present in the application environment, such as gravity and the speed of the objects in the transport line. Against potential assumptions of performance losses, the authors proved through simulations that the same goals and efficiency [3; 4; 35] of sorting and handling can be achieved with a minimal design architecture, consisting of few components, while decreasing costs and saving energy.