## 4 Experiment and Result  
Finally, several experiments will be carried out to illustrate the effectiveness of the proposed algorithm and the rationality of the topological map representation method. Relevant experiments were completed in the simulation environment, and the metric map was obtained by using the gmapping algorithm [31]. In the Gazebo simulation environment, four environments were built representing an indoor home, office, pillar, and open space. The experimental environment is shown in Figure 5. In the experiment, the turtlebot2 robot equipped with a 2D laser sensor was used as an experimental platform. All of the experiments were performed on a notebook with a memory 8G, i7 processor, and a GTX1050 graphics card. The first experiment was carried out in the indoor home environment, and each part of the whole system was tested. The experimental results are shown in Figure 6, which includes the construction of the metric map, the construction of the topological map, the adjustment of the topological map, and the preservation of the topological map. These continuous processes truly implement the process of topological mapping from build to save. In the following, relevant experiments were carried out in the office environment, pillar environment, and open space. The results are shown in Figure 7, which shows the metric map and topological map constructed in different environments. Among them, the growth radius is between 1.2-3 m, the map resolution is 0.20 m, and the control weight is one. Figure 5: Simulation environment. Figure 6: Topological map construction process. The office environment consists of many small spaces and long corridors. It can be seen that the map construction algorithm performs poorly at the door and the area is somewhat deformed. However, in the latter two examples, the map construction algorithm is more perfect: the region is more similar to the ellipse, and the dynamic growth and merging process makes the small region fully covered. Next, in the indoor environment, this paper chooses a special location (next to the dining table in the living room) to build the map, and discusses the impact of these three parameters on the map construction under the circumstances of changing the obstacle ratio, the point addition ratio, and the points pass ratio. Here, the growth radius is set to 1.5 m, the map resolution is 0.2 m, and the control value \(R_{w}\) is set to one. The details of regional growth are shown in Figure 8.  
The obstacle ratio is to prevent the region from growing into a concave region, and ensure the convexity of the topological region. As can be seen in group (**a**) of Figure 7, with the increase of the obstacle ratio, the area will grow toward a small space (such as a door) next to it, and a few obstacle points will be added continuously. The points addition ratio prevents malformation, making the growth area approximately circular or elliptical rather than elongated. It can be seen in group (**a**) of Figure 8 that when the point addition ratio is too small or too large, it is easy to cause growth malformation or insufficient growth. The points pass ratio can reflect the contrast between the growth area and the ideal area in the current state. It is used to modify the growth radius in real time, so its role is to prevent growth deficiency. When the growth area is far from the ideal area, it can make the region grow seriously. This effect is well reflected in the (**c**) group, but it also destroys the convex nature of the area. Therefore, the  
Figure 7: Occupied map (**left**) and its corresponding topological map (**right**). above three parameters need to be adjusted according to the actual situation, and the topological map will represent the environment better. In addition, map resolution is another important factor affecting the construction of topological maps. In the indoor home environment, a large number of experiments were carried out for different resolutions in order to obtain an optimal topological map.