A formal framework for navigating a robot in a geometric terrain by an unknown set of obstacles is considered. Here the terrain model is not a priori known, but the robot is equipped with a sensor system (vision or touch) employed for the purpose of navigation. The focus is restricted to the non-heuristic algorithms which can be theoretically shown to be correct within a given framework of models for the robot, terrain and sensor system. These formulations, although abstract and simplified compared to real-life scenarios, provide foundations for practical systems by highlighting the underlying critical issues. First, the authors consider the algorithms that are shown to navigate correctly without much consideration given to the performance parameters such as distance traversed, etc. Second, they consider non-heuristic algorithms that guarantee bounds on the distance traversed or the ratio of the distance traversed to the shortest path length (computed if the terrain model is known). Then they consider the navigation of robots with very limited computational capabilities such as finite automata, etc.