Traditional simultaneous localization and mapping (SLAM) back-end optimization methods typically rely on public landmarks and closed-loop detection to enhance global consistency. However, in scenarios with limited feature information or closed-loop failures, the effectiveness of optimization is often constrained. To address this issue, this study proposes a SLAM back-end optimization method based on 2D vector map constraints. The 2D vector map provides globally consistent feature point information, which can be introduced as a priori constraints in the back-end optimization process. This approach effectively compensates for the limitations of traditional methods in feature-sparse or closed-loop failure scenarios. By associating geometric features such as building contour corner points in the vector map with LiDAR sensing data, the method provides stronger global constraints for the optimization process. This enables more accurate position estimation and adjustments to the mapping results, thereby improving both the accuracy of localization and the consistency of the constructed map.

Based on a graph-based optimization algorithm for laser SLAM, this study proposes an improved graph optimization algorithm that incorporates vector maps as constraints. The standard graph-based SLAM optimization algorithm was extended by incorporating vector-building contours as nodes in the factor graph and associating them with radar perception map nodes. First, a hierarchical factor graph model was constructed to divide the optimization problem into two layers: local and global. In the local optimization layer, the factor graph consisted of LiDAR odometry, IMU, vector map a priori, and frame-to-submap alignment factors. The vector map a priori factor provided additional prior information for local optimization, enhancing the local accuracy of position estimation by extracting the building contour corner points and correlating them with the corresponding LiDAR data. In the global optimization layer, the factor map further incorporated a loopback factor and a submap-to-submap alignment factor. The loopback factor was employed to correct cumulative errors when a closed loop was detected. The submap-to-submap alignment factor optimized the relative positional relationships between submaps by aligning the point-cloud data of different submaps to construct a globally consistent point-cloud map. During the optimization process, the Levenberg?Marquardt (L?M) algorithm was employed to iteratively optimize the factor map. The maximum likelihood estimation of the reference state of the point cloud map and submaps was solved for each frame by adjusting the states of the position nodes through the minimization of the error function. Through this hierarchical optimization strategy, the consistency of the global map was enhanced while maintaining the accuracy of local position estimation, resulting in a highly accurate and robust back-end optimization.

Experiments were conducted to verify the robustness, stability, and accuracy of the proposed algorithm under various conditions by designing scenarios with fewer constraints (single building) and more constraints (multiple buildings) within a campus environment. Each scenario was further categorized into loopback and non-loopback conditions. The position errors of the proposed algorithm were compared with those of Lio-Sam and Lego-Loam. The experimental results demonstrate that the accuracy of position estimation is significantly enhanced by incorporating vector map constraints. In the scenario with fewer constraints, the loopback condition exhibits a smaller position error at the starting point, which gradually accumulates as the travel distance increases. This error is corrected upon loopback. The trajectory error of the algorithm proposed in this study is slightly higher than that of Lio-Sam and Lego-Loam, indicating that the vector constraint further improves accuracy, even though the loopback mechanism is effective in reducing error (Fig. 6). The algorithm proposed in this study, under loopback conditions, reduces the RPE by 6.3% and the APE by 11.7% on average compared with Lio-Sam and reduces the RPE by 7.3% and the APE by 20.9% on average compared with Lego-Loam. In contrast, under non-loopback conditions, the proposed algorithm shows an average reduction of 8.4% in RPE and 16.3% in APE compared with Lio-Sam and an average reduction of 11% in RPE and 23.8% in APE compared with Lego-Loam (Fig. 13(a) and (b), respectively). In the scenario with more constraints, the trajectory errors of Lio-Sam and Lego-Loam under non-loopback conditions increase significantly with the travel distance, whereas the trajectories generated by the proposed algorithm are effectively corrected at corner positions owing to the constraining effect of the vector corners, thereby improving the overall accuracy (Fig. 12). The proposed algorithm, under loopback conditions, reduces the RPE by 14.1% and the APE by 13.5% on average compared with Lio-Sam, and reduces the RPE by 17.8% and the APE by 25.3% on average compared with Lego-Loam. In contrast, under non-loopback conditions, the proposed algorithm achieves an average reduction of 15.6% in RPE and 28.4% in APE compared with Lio-Sam and an average reduction of 19.9% in RPE and 36.5% in APE compared with Lego-Loam. The error reduction under multiple-building constraints is significantly greater than that in the single-building scenario with fewer constraints, indicating that the optimization effect of vector constraints becomes more pronounced with an increased number of constraints (Fig. 13(c) and (d), respectively).

This study proposed a SLAM back-end optimization method based on 2D vector map constraints, which significantly enhances the bit position estimation accuracy and the global consistency of the map by embedding vector corner points as strong constraints in the factor graph optimization model. Compared with traditional back-end optimization methods, the approach presented in this study demonstrates greater robustness and stability in weak-feature scenarios characterized by sparse features and closed-loop failures. Experimental results indicate that the accuracy of position estimation is significantly enhanced by incorporating vector maps as a priori constraints, and the problem of odometer drift is effectively addressed. In the loopback measurement area, the vector constraint further enhances position estimation accuracy based on the loopback mechanism. In contrast, in the non-loopback measurement area, the optimization effect of the vector constraint is more pronounced, effectively reducing error accumulation. The method presented in this study offers a new technical approach for high-precision laser map construction and provides a reliable solution for SLAM system optimization in weak-feature scenarios. Future research may further explore the application of this method to map updating, using optimized map construction results to supplement the vector map with local details, thereby enhancing the richness and practical utility of the map.