## 4 Experiments and Results
### Experiments
#### 4.3.2 Dynamic Environment Experiments  
In the following experiments, an obstacle is placed dynamically in the robot's impending path to test navigation algorithms' ability to handle unexpected obstacles. The obstacle is a square with varying sizes (0.5 or 1.0 m) at varying distances (0.6, 1, and 1.5 m) from the running robot. The two sizes and three distances produce six experiment scenarios labeled (a) to (f), as shown in Figure 7. The experimental results are presented in Figure 8 and Table 2.  
DDPG can avoid small and distant obstacles (Figure 7d,e) but fails to avoid massive obstacles in near range. In contrast, KDDPG can avoid obstacles in most cases, and two global-information-aided algorithms, D*-KDDPG and D*-DWA, successfully avoid obstacles in all scenarios. For the latter two models, D*-DWA performs unnecessary actions in some cases because it fails to locate an avoidance obstacle in time, leading to sharp shifts in curvature and extended PL. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & **a** & **b** & **c** & **d** & **e** & **f** \\ \hline D*-DWA & 4819 & 6546 & 17,661 & 1.71 & 190 & 2792 \\ DDPG & collision & collision & collision & 74 & 1.35 & collision \\ KDDPG & 20 & 2.79 & collision & 1.28 & 1.30 & 419 \\ D*-KDDPG & 2.61 & 1.03 & 137 & 0.666 & 0.519 & 11.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Curvature Smoothness of Dynamic Environment. Figure 6: Path date of four algorithms in different static environments. More specifically, per path planning efficiency, D*-KDDFG improves the average NT by 34.1%, 22.2%, and 16.2% than DDPG, KDDPG, and D*-DWA, respectively, featuring relatively minor variance (less than 3.98). On the other hand, the average PL produced  
Figure 8: Dynamic Environment Path data. Figure 7: Performance comparison of four algorithms in different dynamic environments is depicted in subfigures **(a–f)**, where each subfigure represents a unique setup with varying dimensions and distances of dynamic obstacles. The green dots represent target points, and the red squares represent dynamic obstacles. The black lines indicate the D*-DWA paths, the yellow lines indicate the DDPG paths, the red lines indicate the KDDPG paths, and the green lines indicate the D*-KDDPG paths. by D*-KDDPG is approximately equal to that of D*-DWA, with an increase of 1.8%. As a comparison, D*-KDDPG outperforms DDPG and KDDPG significantly by a 24.2% shorter average PL and 15.9% less variable. Per path safety, D*-KDDPG and KDDPG maintain a high average SD, where D*-KDDPG shows a minor variance. D*-KDDPG improves SD by 72.1% compared to D*-DWA. Per path smoothness, D*-KDDPG shows significant improvements in curvature smoothness compared to other methods. D*-DWA exhibits large curvature changes when facing dynamic obstacles due to the high weight of movements in DWA's evaluation function and the resulting sharp adjustments in speed. In contrast, D*-KDDPG effectively diminishes large curvature changes thanks to its long-term planning and continuous action space planning capabilities. Moreover, Figure 9 illustrates the curvature of paths planned by D*-DWA and D*-KDDPG in scenario (c) as a validation. In the ENV-L, static and dynamic obstacles were added to compare D*-DWA and D*-KDDPG within such a complicated environment. Static obstacles of size 0.5 m \(\times\) 0.4 m are placed at coordinates (6.5, 7) and (9.25, 8.5), respectively. Additionally, a cylindrical dynamic obstacle with a diameter of 1 m and a speed of 0.26 m/s is introduced along the route from (5, 5) to (1, 1). Figure 10 illustrates the resulting paths, with experimental data listed in Table 3. The data indicates that D*-KDDPG shows improvements in the other three metrics compared to D*-DWA while maintaining a comparable PL. In summary, compared to D*-DWA, D*-KDDPG reduces navigation time and improves navigation efficiency when facing dynamic obstacles.