## 4 Experimental Evaluation
### Results and Analysis
The experimental value of \(e\) and \(\eta\) of different methods in 20 m \(\times\) 20 m and 40 m \(\times\) 40 m environments are shown in Table 2.  
Figure 10: The results of 50 exploration trials of Graph-STNN, GCN-obs, GCN-no_obs, entropy-based, uncertainty-based and random methods, with the same randomly initialized landmarks and robot 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 11: The results of 50 exploration trials of Graph-STNN, GCN-obs, GCN-no_obs, entropy-based, uncertainty-based and random methods, with the same randomly initialized landmarks and robot start locations, on 40 m \(\times\) 40 m maps (the models are trained in 20 m \(\times\) 20 m grid maps, and the results shown are plotted per time-step of the simulation). (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} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**e**} & \multicolumn{2}{c}{**\(\eta\)**} \\ \cline{2-5}  & **20 m \(\times\) 20 m** & **40 m \(\times\) 40 m** & **20 m \(\times\) 20 m** & **40 m \(\times\) 40 m** \\ \hline Graph-STNN & 0.8761 & 1.4607 & 1.7051 & 1.4032 \\ \hline GCN-no\_obs & 1.2328 & 2.0179 & 1.4630 & 0.8719 \\ \hline GCN-obs & 0.9665 & 1.6894 & 1.5573 & 1.0270 \\ \hline Entropy & 1.5038 & 1.7454 & 1.0219 & 1.0571 \\ \hline Uncertainty & 1.2304 & 1.7406 & 1.1676 & 1.0651 \\ \hline Random & 1.9614 & 3.1803 & 0.7536 & 0.7779 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average trajectory error and average exploration efficiency of different methods with the size of 20 m \(\times\) 20 m and 40 m \(\times\) 40 m.  
The result shows that Graph-STNN gets the shortest path, the smallest trajectory error, and the largest exploration efficiency. Besides, the Random method has the worst performance in all three metrics. In addition, by introducing Uncertainty in reference [25] and Entropy in reference [15], we can see that the performance is better than the Random method. However, both of them are still not good enough. Intuitively, it is evident in Figure 11 that Graph-STNN with obstacle information consideration has a better performance compared with the model without that (GCN-no_obs), which is closer to the actual situation. Because we take the obstacles as nodes in the graph, which enriches graphical representation. Meanwhile, by adding path planning, the approach can learn the path changes due to obstacle avoidance, which supports our claim (i): our approach chooses more reasonable target points by taking into obstacle information. Furthermore, it can be seen in Figure 11a, in the test of 50 episodes, Graph-STNN finish exploring the environment fastest, with the highest accuracy and efficiency of mapping compared with GCN-based and information entropy-based methods. Meanwhile, the advantage is more significant than in the 20 m \(\times\) 20 m environment, showing higher robustness and generalization, as our claim (iii). Eventually, the results verify that the global spatiotemporal information plays a more critical role in the exploration problem than single structural information, as our claim (ii). To verify the role of the spatial encoder, temporal encoder, state encoder, and their combination in Graph-STNN, we train the networks with different components separately. The reward curves change during the training process are as shown in Figure 12, in which the rewards are averaged every ten thousand steps. Furthermore, as shown in the picture, the approaches considering separately state features and action features converge faster and obtain more rewards, as our claim (iv). Next, we test the trained network with the map size of 20 m \(\times\) 20 m, 30 m \(\times\) 30 m and 40 m \(\times\) 40 m, with different obstacle and landmark distributions.