## 3 Marker-Assisted Region Scanning
### Update Robot State
As the robot moves, the map is continuously updated to reflect the current state of the environment. ## 5 Results

In this section, the results of the experiments conducted to evaluate the efficiency and stability of the proposed MARS-SLAM method are presented. The experiments are obtained for three distinct scenarios, aiming to analyze the performance of the approach in various contexts. The maps of the virtual environments used in the simulations are shown in Figure 5. The maps are designed with increasing levels of complexity, with Map 1 being the least complex, followed by the more challenging Map 2, and culminating in the highly complex Map 3, to thoroughly test the adaptability of the MARS-SLAM method. The simulations are performed on a computer with the following specifications: Intel(R)Core(TM) i7-10750H CPU @ 2.59 GHz, 24 GB of RAM, and Microsoft Windows 11 Home operating system (version 10.0.22631). The development environment and tools used for the implementation and simulations included Python 3.7.7 and the necessary libraries for calculations and visualization of the results. ### Experiments

To provide a robust comparison of MARS-SLAM, two alternative routes are created. The objective of these simulations is to establish a solid basis for comparison with the new proposal. To achieve this, a pragmatic approach is developed that, under the assumption of prior knowledge of the map, allows for the distribution of markers in a grid format, with a distance proportional to the LiDAR scan limit. This distribution ensures that by visiting all the markers, the mapping is complete. These routes will provide an order of magnitude for evaluating the efficiency of MARS-SLAM. Comparing MARS-SLAM with these routes will help determine whether the method maps the whole map with a similar number of poses, even without prior knowledge of the environment. If MARS-SLAM yields comparable results to the alternative routes, this would indicate that the method is efficient, as it can achieve similar results even though it has no prior knowledge of the map. To compare MARS-SLAM, two alternative routes are developed using markers distributed in a grid:

1. Standard Zigzag Route: In this route, the robot is positioned at the first marker of the first row and navigates from left to right in even rows and from right to left in odd rows, creating a zigzag pattern. 2. ACO-Optimized Route: Here, a heuristic based on the Ant Colony Optimization (ACO) algorithm [37] is applied to construct a route that is close to the optimal route. These routes are generated for the three virtual scenarios shown in Figure 5. Figure 6 presents the final mapping results (100% completion) for all three maps, comparing the performance of the Zigzag, ACO, and MARS-SLAM methods. The already-mapped areas are shaded in pink, red dots represent the markers added by the robot, and the small pink dots indicate the robot's recorded poses throughout the mapping process. The simulations demonstrate that MARS-SLAM successfully achieves its main objective, which is to perform a complete mapping of the environment, utilizing an efficient stopping criterion to identify the conclusion of the navigation task. Each simulation is repeated 10 times to ensure the robustness of the results. Table 4 presents the averages and standard deviations for the number of poses require for complete mapping by each method, as well as the mapping completeness. Table 5 presents the average times and standard deviations related to three time categories: preprocessing, navigation, and total simulation time. The preprocessing time refers to the initial phase before navigation, which includes setting up specific parameters for each method. Navigation time, on the other hand, represents the

\[v=\frac{v_{l}+v_{r}}{2} \tag{1}\]0 Maps of the virtual environments used in the simulations, designed with different levels of complexity to test the adaptability of the MARS-SLAM method.