Walking in streets with minimal sensing

Abstract

We consider the problem of walking a robot in an unknown polygon called "street", starting from a point $$s$$s to reach a target $$t$$t. The robot is assumed to have minimal sensing capability in a way that cannot infer any geometric properties of the environment, such as its coordinates, angles or distances; but it is equipped with a sensor that can only detect the discontinuities in the depth information (or gaps). Our robot can also locate the target point $$t$$t as soon as it enters in robot's visibility region. In addition, one pebble is assumed to be available to the robot to be used as an identifiable point and to mark any position of the street. Our goal is to generate a shortest possible path for such robot from $$s$$s to $$t$$t in such a scene. We offer a data structure similar to Gap Navigation Tree to maintain the essential sensed data of the explored street. We present an online strategy that guides our robot to navigate the scene and reach the target. The strategy is based only on what is sensed at each point, and on what is saved in the data structure. Although the robot has a limited capability, we show that the robot's detour from the shortest path can be restricted such that our generated path is at most 11 times as long as the shortest path to the target. We also consider a special case of the problem in which the street is rectilinear and the search path has to be rectilinear. We propose a search strategy for this case that generates an $$L_1$$L1-shortest path from $$s$$s to $$t$$t.