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An algorithm is proposed to answer the challenges of autonomous corridor navigation and mapping by a mobile robot equipped with a single forward-facing camera. Using a combination of corridor ceiling lights, visual homing, and entropy, the robot is able to perform straight line navigation down the center of an unknown corridor. Turning at the end of a corridor is accomplished using Jeffrey divergence and time-to-collision, while deflection from dead ends and blank walls uses a scalar entropy measure of the entire image. When combined, these metrics allow the robot to navigate in both textured and untextured environments. The robot can autonomously explore an unknown indoor environment, recovering from difficult situations like corners, blank walls, and initial heading toward a wall. While exploring, the algorithm constructs a Voronoi-based topo-geometric map with nodes representing distinctive places like doors, water fountains, and other corridors. Because the algorithm is based entirely upon low-resolution (32 times 24) grayscale images, processing occurs at over 1000 frames per second.