## 5 Experiments
### Benchmark Introduction  
We have crafted a benchmark, as illustrated in Figure 3. Figure 3 depicts a modest environment characterized by well-defined obstacles and landmarks, which serves as a foundational testbed for evaluating the algorithm's core competencies within a confined and predictable space. Figure 3 introduces a medium-scale scenario, incorporating a mix of open areas and densely packed obstacles, emulating a real-world environment replete with diverse topographical attributes. This scenario is designed to stress-test the SLAM algorithms, assessing their flexibility and adaptability in the face of varied and intricate spatial configurations. Advancing to a more complex setting, Figure 3 portrays a vast corridor, thereby increasing the intricacy for SLAM algorithms. The extensive corridor design is purposed to scrutinize the algorithm's adeptness at managing large-scale spatial data and sustaining precise particle distribution across expansive areas. Collectively, these scenarios offer an extensive experimental framework for evaluating the performance of FastSLAM-MO-PSO. Within this simulation, all distances are represented in a single unit for consistency, which facilitates the comparison of different scenarios and the assessment of the algorithm's performance without the need for real-world unit conversion. This unit is arbitrary and used solely for the purposes of this study, allowing for a standardized evaluation of the SLAM algorithm across various simulated environments. They enable a detailed evaluation of the algorithm's map accuracy, trajectory estimation proficiency, and overall SLAM effectiveness across a spectrum of environmental scales and complexities.  
Figure 3: Three problem scenarios in benchmark. The black areas represent obstacles that are non-negotiable, while the white areas denote traversable spaces. The red dot signifies the starting point of the simulated vehicle, and the green dot indicates its destination. As the algorithm operates, the vehicle constructs a map and verifies its trajectory along the existing path, following the blue line from the starting point to the endpoint. The SLAM algorithm is utilized to build the map and simulate the vehicle’s trajectory during this process.  
Our experiments are conducted within simulated environments, which provide a controlled and reproducible testing ground. This approach offers several advantages, including the ability to systematically vary environmental parameters such as obstacle density, sensor noise levels, and initial position and orientation variations. Obstacle density, defined by the number and distribution of obstacles within the simulated environment, can significantly affect the navigation path and mapping accuracy. Sensor noise levels, which represent the degree of noise introduced into the sensor data, simulate different sensor qualities and environmental conditions, thereby influencing the algorithm's performance. Initial position and orientation variations, determining the starting points and orientations of the robot, can impact the initial localization and subsequent mapping process. The simulated setting allows for a thorough exploration of the algorithm's capabilities and limitations in a safe and controlled manner, ensuring that our findings are robust and applicable to a broad range of potential real-world applications. This methodology is not only efficient, but also aligns with best practices in algorithm development and validation, ensuring that our proposed FastSLAM-MO-PSO algorithm is rigorously tested and ready for practical deployment. Additionally, by concentrating on obstacle density, we have designed a relevant analysis in environments characterized by varying degrees of clutter.