# Position Control of a Mobile Robot through Deep Reinforcement Learning
## 5 Experiments and Results
### Results
#### 5.3.2 Multiple Target Points  
Next, it will be analyzed what happens with the control of the robot's position in front of multiple target points--specifically, three target points for environments without and with obstacles. Target points 1, 2 and 3 are located 0.95 m from the robot, with an angular difference from the robot's orientation of \(178^{\circ},135^{\circ}\) and \(45^{\circ}\), respectively.  
The objective of the multiple targets experiment is to evaluate the robustness of the proposed algorithms with respect to changes produced by the robot orientation versus the target point position. This experiment allows us to evaluate the control algorithms, since they exhibit low performance when the orientations of the target point and the robot have a high angular error--for example, when \(O_{c}\approx 180^{\circ}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Villela** & **IPC** & **DQN** & **DDPG** \\ \hline ISE & 30.94 & 22.62 & 19.53 & **18.04** \\ IAE & 28.92 & 23.42 & 21.08 & **19.66** \\ ITSE & 301.92 & 195.92 & 158.02 & **131.99** \\ ITAE & 351.39 & 254.32 & 213.51 & **187.5** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance indices for the environment without obstacles.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Times (s)** \\ \hline Villela & 33.95 \\ IPC & 30.40 \\ DQN & 28.75 \\ DDPG & **27.40** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Time to reach the target point for the experiment without an obstacle.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Villela-Braitenberg** & **IPC–Braitenberg** & **DQN** & **DDPG** \\ \hline ISE & 33.64 & 27.96 & 22.79 & **19.07** \\ IAE & 33.45 & 32.20 & 26.05 & **21.32** \\ ITSE & 386.75 & 343.27 & 233.22 & **154.48** \\ ITAE & 498.41 & 533.28 & 346.31 & **226.06** \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance indices for the environment with obstacles.  
Figure 13 shows a graph with the trajectories made by the robot for the environment without obstacles. All of the algorithms manage to reach their target points; however, DDPG and DQN have trajectories that react earlier, reaching the target before Villela and IPC, which adjust more to reach the target point. Figure 14 shows the trajectory of the robot in an environment with obstacles. The DDPG agent has the shortest trajectory, allowing it to reach the target point faster, followed by DQN. In contrast, the agents controlled by the Villela and IPC methods move away from obstacles, maintaining a distance of approximately 20 cm, which corresponds to the maximum distance of its sensor's measurement.  
To make a better comparison of the times used in the experiments, Table 6 shows the time taken to reach the targets for the experiment without obstacles. Note how DDPG and DQN obtain the lowest times on average compared to the control algorithms; however, in some cases, the control algorithms obtain a performance comparable to that of the RL agents. Table 7 shows the time taken to reach the target points in the case of the obstacle experiment. The excellent performance of DDPG is observed, reaching its TPs in 22.68 s, on average.  
Figure 14: Graph of the trajectory for the three target points in the environment with obstacles.  
Figure 13: Graph of the trajectory for the three target points in the environment without obstacles.  
To finish the analysis, Tables 8 and 9 were added, showing the average performance indices for each algorithm in the experiments without and with obstacles, respectively. From Table 8, it is observed how the RL algorithms once again present very favorable results, indicating that the control of the position of a mobile robot can be performed efficiently with RL algorithms. Table 9 shows that DDPG obtains very low metrics, it being the algorithm to choose to perform this type of task.