Trajectory Estimation Using Relative Distances Extracted from Inter-image Homographies

Abstract

The main idea of this paper is to use distances between camera positions to recover the trajectory of a mobile robot. We consider a mobile platform equipped with a single fixed camera using images of the floor and their associated inter-image homographies to find these distances. We show that under the assumptions that the camera is rigidly mounted with a constant tilt and travelling at a constant height above the floor, the distance between two camera positions may be expressed in terms of the condition number of the inter-image homography. Experiments are conducted on synthetic data to verify that the derived distance formula gives distances close to the true ones and is not too sensitive to noise. We also describe how the robot trajectory may be represented as a graph with edge lengths determined by the distances computed using the formula above, and present one possible method to construct this graph given some of these distances. The experiments show promising results.