Tractor-trailer wheeled robots need to perform comprehensive perception tasks to enhance their operations in areas such as logistics parks and long-haul transportation. The perception of these robots face three major challenges: the relative pose change between the tractor and trailer, the asynchronous vibrations between the tractor and trailer, and the significant camera parallax caused by the large size. In this paper, we propose a novel Unified Vertex Motion Video Stabilization and Stitching framework designed for unknown environments. To establish the relationship between stabilization and stitching, the proposed Unified Vertex Motion framework comprises the Stitching Motion Field, which addresses relative positional change, and the Stabilization Motion Field, which tackles asynchronous vibrations. Then, recognizing the heterogeneity of optimization functions required for stabilization and stitching, a weighted cost function approach is proposed to address the problem of camera parallax. Furthermore, this framework has been successfully implemented in real tractor-trailer wheeled robots. The proposed Unified Vertex Motion Video Stabilization and Stitching method has been thoroughly tested in various challenging scenarios, demonstrating its accuracy and practicality in real-world robot tasks.