## 5 Experiments
### Comparison Between FastSLAM and FastSLAM-PSO  
#### 5.2.1 Small-Scale Scenario  
As shown in Figure 4, the true trajectory is depicted in orange, with FastSLAM in green, FastSLAM-PSO in brown, FastSLAM-DE in pink, FastSLAM-MO-DE in purple, and our proposed FastSLAM-MO-PSO in red. Figure 4a presents a comparative analysis of the estimated particle paths, revealing that the red path, representing FastSLAM-MO-PSO, exhibits the least overall deviation from the actual orange path. The figures depict the deviation of the estimated paths from the true path. A lower deviation indicates a closer alignment with the true path, signifying better performance. The \(y\)-axis in Figures 4-6 represents this deviation, measured in the consistent arbitrary units used throughout our simulation. The performance of the SLAM algorithms is thus inversely related to the deviation shown; the smaller the deviation, the more accurate and robust the SLAM solution. This suggests a superior alignment with the true trajectory, underscoring the enhanced accuracy afforded by the integration of multi-objective optimization with PSO.  
Figure 4b delves into the discrepancies between the algorithmic solutions and the true path along the \(x\)-axis. Here, FastSLAM-MO-PSO demonstrates consistent performance, closely followed by FastSLAM-PSO. While FastSLAM-MO-PSO experiences an increase in deviation mid-way, it recovers with improved accuracy in the later stages, potentially due to the inherent high-performance capabilities. Collectively, the algorithms augmented with evolutionary strategies, particularly FastSLAM-MO-PSO, significantly outperform the  
Figure 4: Comparative results in the small-scale scenario.  
conventional FastSLAM, indicating the substantial benefits of incorporating evolutionary components. The initial segment of FastSLAM-MO-DE appears promising; however, it suffers from significant drift in the later stages. This could be attributed to the inherent search capabilities of DE, which may not be as adept as PSO in navigating complex environments. Overall, the PSO-based algorithms consistently demonstrate stronger performance than their DE counterparts.  
This distinction is further accentuated in Figure 4c, where DE-integrated algorithms underperform in comparison to the original FastSLAM. This is likely due to the vertical distribution of the map scenario, creating a narrow, elongated structure along the \(Y\)-axis that challenges precise localization. Algorithms based on PSO, however, exhibit commendable performance, with FastSLAM-MO-PSO leading the pack. The superior performance of FastSLAM-MO-PSO can be attributed to the multi-objective optimization approach, which allows for a more nuanced exploration of the solution space. By simultaneously optimizing for multiple objectives, such as mapping accuracy and trajectory fidelity, the algorithm can better adapt to the intricacies of the environment. The PSO component significantly bolsters the algorithm's performance by adeptly navigating through the intricate landscape, optimizing the distribution of particles, and swiftly adapting to local environmental variations. Its well-known balance of exploration and exploitation likely plays a crucial role in enhancing the precision with which sensor data-derived estimates are refined.  
Figure 5: Comparative results in the medium-scale scenario.  
Figure 6: Comparative results in the large-scale scenario.