Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rather, it nds out about obstacles as it encounters them. We compare the distance walked by the robot in going from s to t to the length of the shortest (obstacle-free) path between s and t in the scene.

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... describe and analyze robot strategies that minimize this ratio for di erent kinds of scenes. In particular, we consider the cases of rectangular obstacles aligned with the axes, rectangularobstacles in more general orientations, and wider classes of convex bodies both in two and three dimensions. For many of these situations, our algorithms are optimal up to constant factors. We study scenes with non-convex obstacles, which are related to the study of maze-traversal. We also show scenes where randomized algorithms are provably better than deterministic algorithms.