Walking streets faster

Abstract

A fundamental problem in robotics is to compute a path for a robot from its current location to a given goal. In this paper we consider the problem of a robot equipped with an on-board vision system searching for a goal g in an unknown environment.

We assume that the robot is located at a point s in a polygon that belongs to the well investigated class of polygons called streets. A street is a simple polygon where s and g are located on the polygon boundary and the part of the polygon boundary from s to g is weakly visible to the part from g to s and vice versa.

Our aim is to minimize the ratio of the length of the path traveled by the robot to the length of the shortest path from s to g. In analogy to on-line algorithms this value is called the competitive ratio. We present two strategies. Our first strategy, continuous lad, extends the strategy lad which minimizes the Local Absolute Detour. We show that this extension results in a 2.03-competitive strategy, which significantly improves the best known bound of 4.44 for this class of strategies. Secondly, and most importantly, we present a hybrid strategy consisting of continuous lad and the strategy Move-in-Quadrant. We show that this combination of strategies achieves a competitive ratio of 1.73 which about halves the gap between the known √2 lower bound for this problem and the previously best known competitive ratio of 2.05.

This research is supported by the DFG-Project “Diskrete Probleme”, No. Ot 64/8-1.