A vehicle equipped with a cemputer vision system moves on a plane. We show that subject to certain constraints, the system can determine the motion of the vehicle (one rotational and two translational degrees of freedom) and the depth of the scene in front of the vehicle. The constraints include limits on the speed of the vehicle, presence of texture on the plane and absence of pitch and roll in the vehicular motion. It is possible to decouple the problems of finding the vehicle's motion and the depth of the scene in front of the vehicle by using two rigidly connected cameras. One views a field with known depth (i.e. the ground plane) and estimates the motion parameters and the other determines the depth map knowing the motion parameters. The motion is constrained to be planar to increase robustness. We use a least squares method of fitting the vehicle motion to observer brightness gradients. With this method, no correspondence between image points needs to be established and information fran the entire image is used in calculating notion. The algorithm performs very reliably on real image sequences and these results have been included. The results compare favourably to the performance of the algorithm of Negandaripour and Horn  where six degrees of freedom are assumed.