The polygon exploration problem

We present an on-line strategy that enables a mobile robot with vision to e xplore an unknown simple polygon. We prove that the resulting tour is less than 26.5 times as long as the shortest watchman tour that could be compute d off-line. Our analysis is doubly founded on a novel geometric structure called the an gle hull. Let D be a connected region inside a simple polygon, P. We de ne the angle hull of D, AH(D), to be the set of all points in P that can see t wo points of D at a right angle. We show that the perimeter of AH (D) canno t exceed in length the perimeter of D by more than a factor of 2. This uppe r bound is tight.