Discrete Coordinate System with Isotropy on a Surface with Regular Tessellations

This paper proposes an “Isotropic” discrete coordinate system for regular tessellations in Euclidean plane, E2. Its conceivable robotics applications include: workspace description, mobile robot positioning, and configuration rendering for swarm robots. The new coordinate system, named HC/P, is generated via projection process of three-dimensional (3D) honeycomb over a two-dimensional (2D) plane. The HC/P coordinate system is composed of three axes in order for indicating 2D position. This redundancy enables HC/P to posses the isotropy that is the most significant advantage of the system. The characteristic features of HC/P, such as distance computation and rotational operation, are described in this paper with an application example.