We provide a competitive strategy for a mobile robot with vision, that has to explore an unknown simple polygon starting from and returning to a given point x0 on the boundary. Our strategy creates a tour that does not exceed in length 133 times the length of the shortest watchman route from x0. It has been claimed before by other authors that a competitive strategy with factor 2016 exists for this problem; but no proof has appeared except for the easy rectilinear case.
