## 5 Simulation and Experiments
### DRL Training Results  
The results of this training are shown in Table 4, presenting the performance metrics for each of the three scenarios. The first scenario, shown in Figure 7, featured an environment with only static obstacles, where the robot with our method achieved a successful target reach in \((SR=92\%)\) of the simulation, with a minimal collision rate of \((CR=1\%)\) and a Time Out Rate (TOR) of 7%, indicating instances where the robot could not reach the goal within the specified time. On average, the robot took \((t=10.99\) (s)) to reach the goal, with an average speed of \((S=0.77\) m/s) and covering an average path length of \((PL=13.85\) m) during the simulation. Figure 8 illustrates the second scenario, which involved 10 dynamically positioned objects with random speeds, the robot performed remarkably well, achieving a high success rate of 94% and a collision rate of only 6%. The average time to reach the goal was 13.00 s, with an average speed of 0.68 m/s and an average trajectory length of 11.95 m. The third scenario, depicted in Figure 9, featured 10 objects randomly positioned between static and dynamic motions.The robot with the proposed method achieved a slightly lower success rate of 86% compared to the other two scenarios, with a collision rate of 14%. The average time to reach the goal increased to 16.84 s due to the higher difficulty of the scenario, with an average speed of 0.67 m/s and an average trajectory length of 11.60 m. These performance metrics provide valuable insights into our policy regarding the robot's navigation abilities in different scenarios, demonstrating its adaptability and effectiveness in dealing with various configurations and tests. In contrast, the CADRL method consistently exhibited the lowest success rate (SR) and the highest collision rate (CR) across all scenarios, as is shown in Table 4. LSTM-RL leverages LSTM recurrent neural networks to model pairwise interactions, improving navigation SR and CR. However, the LSTM's strategy resulted in longer arrival times and PL. On the other hand, the SARL method analyzes the spatio-temporal dynamics of the robot-human interactions and performs better than the CADRL and LSTM methods. The simulation results validate the efficacy of our proposed method, which surpasses the performance of other state-of-the-art baselines. The integration of BiGRU enables the model to learn and exploit complex temporal dependencies within the input data, resulting in improved decision-making and navigation performance. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Scenario** & **Method** & **SR** & **CR** & **TOR** & **t (s)** & **S (m/s)** & **PL (m)** \\ \hline \multirow{4}{*}{Static} & CADRL & 0.88 & 0.06 & 0.06 & 17.10 & 0.76 & 12.99 \\  & LSTM & 0.88 & 0.04 & 0.08 & 17.23 & 0.75 & 12.92 \\  & SARL & 0.90 & 0.03 & 0.07 & 16.01 & 0.76 & 12.17 \\  & Ours & 0.92 & 0.01 & 0.07 & 14.99 & 0.77 & 11.54 \\ \hline \multirow{4}{*}{Dynamic} & CADRL & 0.83 & 0.15 & 0.02 & 17.91 & 0.66 & 11.82 \\  & LSTM & 0.80 & 0.14 & 0.06 & 18.43 & 0.65 & 11.97 \\  & SARL & 0.84 & 0.16 & 0.00 & 17.85 & 0.66 & 11.78 \\  & Ours & 0.87 & 0.13 & 0.00 & 16.84 & 0.67 & 11.28 \\ \hline \multirow{4}{*}{Stat-Dyn} & CADRL & 0.89 & 0.11 & 0.00 & 19.71 & 0.65 & 12.81 \\  & LSTM & 0.91 & 0.08 & 0.01 & 18.80 & 0.67 & 12.59 \\  & SARL & 0.91 & 0.07 & 0.02 & 18.82 & 0.67 & 12.60 \\  & Ours & 0.94 & 0.06 & 0.00 & 17.20 & 0.68 & 11.60 \\ \hline \multirow{4}{*}{Average} & CADRL & 0.87 & 0.10 & 0.03 & 18.24 & 0.69 & 12.54 \\  & LSTM & 0.86 & 0.08 & 0.05 & 18.15 & 0.69 & 12.49 \\ \cline{1-1}  & SARL & 0.88 & 0.08 & 0.03 & 17.56 & 0.70 & 12.18 \\ \cline{1-1}  & Ours & 0.91 & 0.07 & 0.02 & 16.34 & 0.71 & 11.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance metrics. tracking of the robot's movement. The system ensures reliable and consistent operation by fusing data from these sensors, compensating for individual sensor limitations. Data processing and action execution occur at frequencies ranging from 8 to 30 Hz.