Graphbots: Mobility in discrete spaces

Abstract

Most previous theoretical work on motion planning has addressed the problem of path planning for geometrically simple robots in geometrically simple regions of Euclidean space (e.g., a planar region containing polygonal obstacles). In this paper we define a natural version of the motion planning problem in a graph theoretic setting. We establish conditions under which a “robot” or team of robots having a particular graph structure can move from any start location to any goal destination in a graph-structured space.