## 4 Experiments
### Comparison between FastSLAM and FastSLAM-PSO  
#### 4.2.1 Small-Scale Scenario  
In the small-scale scenario, the final mapping results are visually presented in Figure 2, which compares the mapping outcomes of FastSLAM, FastSLAM-PSO, and FastSLAM  
Figure 1: Three problem scenarios. The gray color represents obstacles, and during algorithm operation, the vehicle constructs a map and confirms its trajectory based on the existing path using the FastSLAM algorithm, with the white part being the traversable area.  
DE. The Ground Truth represents the actual trajectory of the simulated environment, while the Estimated corresponds to the mapping results generated by the FastSLAM algorithm. The green line indicates the predicted trajectory by the SLAM algorithm. Within this confined setting, both the FastSLAM-PSO and FastSLAM-DE algorithms were tested against the conventional FastSLAM. As depicted in Figure 2, FastSLAM-PSO outperforms its counterpart in both mapping and trajectory tracking, aligning more closely with the actual trajectory. This enhancement is attributed to the optimization of particles by the PSO algorithm, which enhances the precision of particle filtering and, consequently, the fidelity of the estimated path to the real environment. The integration of PSO postulates that the performance is heightened, excelling in mapping and trajectory tracking and approximating the simulated scenario with greater accuracy. The FastSLAM-DE, while showing overall mapping accuracy, exhibits noticeable distortions, suggesting that while its global alignment is generally correct, the local adjustments require refinement. This statement indeed suggests that the integration of PSO has been more effective in enhancing the performance of the FastSLAM algorithm, particularly in terms of mapping accuracy and trajectory tracking, than DE. The success of PSO in this context can be attributed to its ability to navigate the solution space more effectively, optimize particle distribution, and enhance responsiveness to local environmental changes. The capacity of PSO to balance exploration and exploitation likely contributes to its superior performance in refining the estimates derived from sensor data.  
Figure 2: _Cont_.  
To further scrutinize the disparity between FastSLAM and FastSLAM-PSO, Figure 3 juxtaposes their trajectories in a single frame, contrasting the estimated paths with the true trajectory along the X and Y axes. In Figure 3, \"Difference\" refers to the deviation between the estimated paths of the FastSLAM and FastSLAM-PSO algorithms and the true trajectory in both the X and Y axes. It is evident from Figure 3 that the FastSLAM algorithm, due to the random selection of particles without targeted optimization, yields suboptimal path results that deviate from the actual path. In contrast, the incorporation of PSO refines the particles prior to particle filtering, leading to outcomes that are more congruent with the true scenario. The FastSLAM-DE, despite good alignment with the true trajectory along the \(X\)-axis, exhibits larger deviations in the \(Y\)-axis, likely due to overall distortions in its mapping approach. This suggests that while the global positioning along the \(X\)-axis is well-maintained by FastSLAM-DE, the algorithm struggles with local accuracy along the \(Y\)-axis, potentially because of greater overall distortions not adequately compensated by its evolutionary strategy. Regarding the deviation in the X and Y axes, FastSLAM-PSO generally outperforms FastSLAM and FastSLAM-DE, with minor exceptions in the \(Y\)-axis, potentially due to alignment discrepancies in post-processing. Overall, FastSLAM-PSO exhibits smaller deviations in the majority of cases, indicating that the introduction of PSO significantly bolsters the accuracy and robustness.  
Figure 3: Comparative results of FastSLAM, FastSLAM-PSO and FastSLAM-DE in the small-scale scenario scene_1.  
Figure 2: Visual comparison of SLAM results between FastSLAM, FastSLAM-PSO and FastSLAM-DE in the small-scale scenario scene_1.