The estimation of the 2D relative motion of an indoor robot using monocular vision is presented. The camera calibration is known, and its motion is limited to be planar. These constraints are included in the robust regression of epipolar geometry from point matches. Motion is derived from the epipolar geometry. A sequence of 54 real images is used to test the algorithm. Accurate motion, both in rotation and translation angles of 0.4 and 1.7 deg, is successfully derived.