An Online Strategy for Exploring the Outer Boundary of a Convex Polygon

This paper considers an online problem where a robot has to explore the outer boundary of an unknown convex polygon. The robot starts from a vertex and walks a tour outside the polygon. The goal of it is to see all points of the polygon's outer boundary and to return to the start. The exploration tour is required to be as short as possible. We present a competitive strategy for this problem and prove that the length of the tour is at most 23.78 times longer than the shortest path. Also we give a lower bound of 5 for this problem.