This paper presents an obstacle detection and tracking framework for mobile robots and autonomous vehicles equipped with LiDAR (Light Detecting and Range finding) sensors. The framework contains a detection module (DM) for clustering the point cloud and modeling the obstacles, and a tracking module (TM) for recognizing the obstacles and estimating their velocities. In order to detect the obstacles, DM segments the point cloud by finding the gaps in it. Detected obstacles are modeled by one or two line segments depending on their geometry. TM gets the line segments returned by DM as the obstacles to track. To this end, first, the obstacles are labeled and their features are stored. Thereafter, a set of equations are solved to recognize the labeled obstacles. Finally, the Kalman filter is used to calculate the translational and rotational velocities of the obstacles. The framework is evaluated in experiments on a robot platform and using the KITTI dataset. The results indicate satisfactory performance in terms of effectiveness and quickness and confirm that DM and TM are qualified enough to perform in real time as ancillary modules of mobile robots and autonomous vehicles. Especially, because of robust and accurate obstacle modeling, the velocity diagrams are smooth and coherent, a point which is not seen in similar researches.