One of the most pressing issues in the field of mobile robotics is that of power delivery. By being fundamentally unattached to the environment, these systems often employ batteries. However, this can have some limitations related to cost, battery life etc.; a promising approach is that of powered floors, where a specially designed contact array is connected to the robot, and slides on a surface in which conducting bands are laid out, providing a continuous and uninterrupted electrical connection. In this paper, we provide a complete framework for the analysis and synthesis of these systems, to be used in the field of mobile robotics. We study the problem both in terms of feasibility and in quantitative terms; in particular, we illustrate a methodology related to n-sided polygons which takes into account a fuzzy representation of the bands, useful to analyze tolerances in the bands boundaries or in the position of the individual brushes. We support the theoretical framework with both numerical and experimental campaigns, and compare the results with existing state-of-the art solutions. Finally, we discuss possible further developments.
