## 5 Experiments
### Analysis of Mapping Results  
As illustrated in Figure 7, our experiments in Scenario 1 systematically varied the particle count \(N\) from 20 to 100, commencing from \(N=20\) due to the poor mapping observed at \(N=10\). The results indicate a positive correlation between particle count and the quality  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **FastSLAM** & **FastSLAM-DE** & **FastSLAM-PSO** & **FastSLAM-MO-DE** & **FastSLAM-MO-PSO** \\ \hline Scene\_1 & 4101.973994 (s) & 7867.448255 (s) & 7140.355758 (s) & 7311.061464 (s) & 6462.207688 (s) \\ Scene\_2 & 7334.884456 (s) & 16,145.49226 (s) & 15,157.19925 (s) & 13,401.55571 (s) & 11,099.08987 (s) \\ Scene\_3 & 6159.537662 (s) & 12,651.76538 (s) & 11,456.88336 (s) & 8440.059285 (s) & 70,362.45773 (s) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The time analysis results.  
of mapping and localization, underscoring the effectiveness of our algorithm and its dependence on an adequate number of particles for precise environmental representation.  
The performance of the SLAM algorithm notably improves beyond a particle count of 70, suggesting this threshold as a critical point for the algorithm to efficiently model the environment. Particularly at \(N=100\), the algorithm yields mapping results that are not only accurate, but also stable in terms of overall direction, indicating a high level of performance. The maps generated are ready for direct application with minimal further optimization, signifying the algorithm's readiness for practical use. While the outcomes at \(N=80\) and \(N=90\) are satisfactory, minor deficits in detail suggest room for fine-tuning to achieve perfection. The performance enhancement with an increased number of particles can be attributed to the algorithm's ability to better approximate the posterior distribution of the robot's pose and landmarks. A higher particle count facilitates a more detailed exploration of the state space, reducing uncertainty in the mapping process and leading to more precise localization.  
Figure 7: Analysis of the population parameters \(N\) in the small-scale scenario. The green represents the route estimated by the SLAM process.  
However, the slight decrease in detail at \(N=80\) and \(N=90\) suggests that while a higher particle count improves overall performance, it also increases the computational load, potentially affecting the algorithm's ability to refine details. This observation indicates an optimal range for the particle count, beyond which the law of diminishing returns may apply. In conclusion, the experiments conducted in Scenario 1 provide compelling evidence of the FastSLAM-MO-PSO algorithm's sensitivity to the number of particles and its impact on mapping quality. The results validate the algorithm's effectiveness within an optimal particle count range and highlight the need for a balanced approach to ensure both accuracy and computational efficiency.  
In summary, the comprehensive experimental evaluation across varying scales and complexities has conclusively demonstrated the superior performance of the FastSLAM-MO-PSO algorithm in comparison to the conventional FastSLAM and its DE counterpart. The FastSLAM-MO-PSO algorithm, with its integration of Particle Swarm Optimization, has exhibited a heightened level of accuracy and robustness in mapping and trajectory tracking. This enhancement is attributed to the ability to effectively manage the optimization of particles, thereby mitigating the degradation typically associated with traditional SLAM approaches. The global search capabilities of PSO have been instrumental in refining the particle distribution, leading to a more reliable and precise estimation of the robot pose and the surrounding environmental landmarks. The experimental outcomes consistently show that FastSLAM-MO-PSO maintains its superiority in terms of mapping quality and localization accuracy, highlighting the benefits of integrating multi-objective optimization strategies into SLAM algorithms.