Leaving an Unknown Maze Using an Error-Prone Compass

Imagine you are trapped in a maze of caves. All you have is an old rusty compass and barely enough light to read it. Howmuch inaccuracy can you allow to ensure that you can leave the maze? Or you are walking in a maze of hedgerows that are on the whole orthogonal. Can you find the exit by counting left and right turns? We consider the problem of escaping from an unknown polygonal maze under limited resources and errors in inputs and motion. It is well known that the Pledge algorithm always finds a path out of an unknown maze without any means of orientation—provided that such a path exists—but it relies on fact that inputs and motions are correct.