### Technical Report No. 103, July - Abstract

**Al\'ejandro L\'opez-Ortiz, Sven Schuierer< **

* *

A fundamental problem in robotics is to compute a path for a robot
from its current location to a given target. In this paper we consider
the problem of a robot equipped with an on-board vision system
searching for a target * t * 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 * t * are located on the polygon boundary and the
part of the polygon boundary from * s * to * t * is
weakly visible to the part from * t * to * s * and vice
versa.

We are interested in the ratio of the length of the path traveled by
the robot to the length of the shortest path from * s * to *
t * which is called the competitive ratio of the strategy. In
this work we present the first * exact * analysis of the
* continuous angular bisector * (CAB) strategy, which has been
considered several times before, and show that it has a competitive
ratio of 1.6837 in the worst case.

Report No. 103(PostScript)