— This paper presents a metric-based matching algorithm to estimate the robot planar displacement by matching dense two-dimensional range scans. The contribution is a geometric distance that takes into account the translation and orientation of the sensor at the same time. This result is used in the two steps of the matching - estimation process. The correspondences between scans are established with this measure and the minimization of the error is also carried out in terms of this distance. As a result, the translation and rotation are compensated in this framework simultaneously. In fact, this is the contribution with respect to previous work that addressed only translation or translation and rotation but separately. The new technique has been implemented and tested on a real vehicle. The experiments illustrate how it is more robust and accurate than prior techniques. At the end of the paper, we give an extension of our distance measure to 3D range-data matching problems.