Visual navigation using planar homographies

We introduce three new results, which allow homographies of the ground plane to support visual navigation functions for mobile robots using uncalibrated cameras. Firstly, we illustrate how, for pure translation, a homography can be computed from just two pairs of corresponding corner features. Secondly, we show how, for pure translation, we can determine the height of corner features above the ground plane using the recovered homography and a construct based on the cross ratio. This allows us to detect points which can be driven over, as their height is measured to be close to zero, and points which are sufficiently high to drive under. Finally, we show how, in the case of general planar motion, homographies can be used to determine the rotation of the camera and robot.