A filtering model of sequential road edges is proposed. The solution of unclosed snakes is discussed based on traditional active contour models, the snakes. Then, it is applied to the smoothing and filtering of road edges detected from 2D LIDAR (LIght Detection And Ranging) data. Several models to depict roads and obstacles are discussed in detail. Based on these models, road edges can be acquired from a single scan 2D LIDAR data quickly and efficiently. Some problems are investigated, such as building and initialization of unclosed snakes model in the road edge filtering scenario, and acquisition of image forces of snakes from LIDAR data. The proposed algorithm is implemented on our ALV (autonomous land vehicle), and the navigation experiments demonstrate that our approach can efficiently reduce the mistakes and errors as well as improve the continuity of road edges. The resulted road edges thus are more faithful to the truth.