Signal strength-based adjacency matrix and its eigenvalue in mobile robotic networks

Abstract

Generally the adjacency matrix is constructed as the function of distance between two nodes in unit disk graph. Although the distance between both robots meet the requirement to form adjacency matrix, however, actually the reliable communication is determined by the function of distance. In this paper, the adjacency matrix that express connectivity in mobile robotic networks are expressed by means of the quality of received wireless signal, which is indicated by received signal strength indicator (RSSI) value. The metric measured in this paper is second semallest eigenvalue or λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , that represents the connectedness of communication topology in mobile robotics networks. As the results from the simulation, it is shown that the rssi-based adjacency model still satisfy the requirement of connectedness, that is λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> > 0.