## 4 Experimental Evaluation
### Results and Analysis
We test 50 episodes, and the results are shown in Figures 13-15 and Table 3.  
Figure 12: The training performance of Graph-STNN and the removal of some of its components on randomly generated simulation environments, with the size of 20 m \(\times\) 20 m.  
The results show that the convergence speed of the models without spatial or temporal information (no temporal encoder, no spatial encoder, no spatial and temporal encoder) is close to Graph-STNN. However, they obtain fewer rewards and have worse efficiency. Besides, we can see that without state features (no state encoder, no spatial and state encoder, no temporal and state encoder) the performance of convergence speed, mapping accuracy, and exploration efficiency are all not very good, and they are difficult to converge. The reason is that spatial and temporal information tend to guide robots to reduce the environment's uncertainty, which leads to fast exploration. In the meanwhile, the state information tends to balance the exploration speed and the map accuracy, since it always contains the global information during the exploration progress. To further check the model's robustness and generalization, we directly extend the trained model to 30 m \(\times\) 30 m and 40 m \(\times\) 40 m environment. Figure 13: The results of 50 exploration trials of Graph-STNN and the removal of its components, with the model trained in 20 m \(\times\) 20 m maps and the same initialized landmarks and robot’s start locations, on 20 m \(\times\) 20 m maps. (**a**) One of the test result of 50 exploration trials. (**b**) Average exploration rate (left), trajectory error (middle), and exploration efficiency (right). Figure 14: The results of 50 exploration trials of Graph-STNN and the removal of its components, with the model trained in 20 m \(\times\) 20 m maps and the same initialized landmarks and robot’s start locations, on 30 m \(\times\) 30 m maps. (**a**) One of the test result of 50 exploration trials. (**b**) Average exploration rate (left), trajectory error (middle), and exploration efficiency (right). \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**e**} & \multicolumn{3}{c}{**\(\boldsymbol{\eta}\)**} \\ \cline{2-7}  & **20 m \(\times\) 20 m** & **30 m \(\times\) 30 m** & **40 m \(\times\) 40 m** & **20 m \(\times\) 20 m** & **30 m \(\times\) 30 m** & **40 m \(\times\) 40 m** \\ \hline Graph-STNN & 1.0160 & 1.3088 & 1.7588 & 1.7051 & 1.5085 & 1.4032 \\ \hline no state & 1.9370 & 2.3748 & 2.7195 & 0.9039 & 0.9304 & 0.9153 \\ \hline no temporal & 1.4761 & 1.8144 & 2.2950 & 1.5585 & 1.4389 & 1.3101 \\ \hline no spatial & 1.6475 & 1.8303 & 2.5787 & 1.0854 & 1.4828 & 1.1593 \\ \hline no temporal and state & 1.5732 & 2.2140 & 2.5679 & 1.2563 & 0.9476 & 0.9950 \\ \hline no spatial and state & 1.9935 & 2.5510 & 2.7051 & 0.8231 & 0.7813 & 0.8142 \\ \hline no spatial and temporal & 1.7770 & 2.5523 & 2.3844 & 0.9823 & 1.3127 & 1.0719 \\ \hline \end{tabular}
\end{table} 
Table 3: The trajectory error and exploration efficiency of Graph-STNN and its removal of some components with the size of 20 m \(\times\) 20 m, 30 m \(\times\) 30 m and 40 m \(\times\) 40 m.  
As shown in Figures 14 and 15, the complete Graph-STNN achieves the best results compared to the models using temporal, spatial, and state features alone or in part. These results once again confirm our claim (ii): Graph-STNN can better adapt to the exploration problem using temporal and spatial information and lead to more accurate exploration. As we can see, the state encoder can promote exploration speed and efficiency, which plays a major role in improving the model's generalization. Meanwhile, the temporal and spatial encoders mainly play a role in improving the mapping accuracy. Finally, we use a physical robot model and a lifelike environment to further validate our approach on Stage. Stage is a simulation tool for researching mobile robots and intelligent sensor systems, which can simulate objects such as mobile robots, sensors, and obstacles.