## 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 originally located at a point s on the boundary of a street polygon. A street is a simple polygon with two distinguished points s and g, which 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 minimise 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 a series of strategies all of which follow the same general high level strategy. In the first part we present a class of strategies any of which can be shown to have a competitive ratio of π + 1. These strategies are robust under small navigational errors and their analysis is very simple.
In the second part we present the strategy Continuous Lad which is based on the heuristic optimality criterion of minimising the Local Absolute Detour. We show an upper bound on the competitive ratio of Continuous Lad of ~2.03. Finally, we also 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. This about halves the gap between the known sqrt(2) lower bound for this problem and the previously best known competitive ratio of ~2.05.