Robotic exploration as graph construction

Addressed is the problem of robotic exploration of a graphlike world, where no distance or orientation metric is assumed of the world. The robot is assumed to be able to autonomously traverse graph edges, recognize when it has reached a vertex, and enumerate edges incident upon the current vertex relative to the edge via which it entered the current vertex. The robot cannot measure distances, and it does not have a compass. It is demonstrated that this exploration problem is unsolvable in general without markers, and, to solve it, the robot is equipped with one or more distinct markers that can be put down or picked up at will and that can be recognized by the robot if they are at the same vertex as the robot. An exploration algorithm is developed and proven correct. Its performance is shown on several example worlds, and heuristics for improving its performance are discussed