# 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.

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