# Adaptive Compensation for Robotic Joint Failures Using Partially Observable Reinforcement Learning
## 5 Results and Discussion  
### RL Training Results  
We trained the robot for 24,000 episodes, as described in Section 3.3 utilizing an NVIDIA GeForce 2070 Super GPU. The training, which took approximately 40 min, aimed to optimize the robot's performance on drawer-opening tasks under various joint malfunction \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(E_{x}\) **(rad)** & \(E_{y}\) **(rad)** & \(E_{z}\) **(rad)** & \(x\) & \(y\) & \(z\) \\ \hline \(p_{i}\) & 0.5\(\pi\) & 0 & \(\pi\) & 0.500 & 0 & 0.625 \\ \(p_{d}\) & 0 & 0 & 0.5\(\pi\) & 0.750 & 0 & 0.317 \\ \(p_{p}\) & 0.5\(\pi\) & 0 & \(\pi\) & 0.371 & 0 & 0.317 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Position of the three points constructing the end-effector trajectory: the initial position (\(p_{i}\)), the drawer position (\(p_{d}\)), and the pulled-out position (\(p_{p}\)). Euler angles (\(E_{x}\), \(E_{y}\), \(E_{z}\)) and translation vectors (\(x\), \(y\), \(z\)). scenarios. The reward plot of the robot training is shown in Figure 2, in which we show the four reward functions that we describe in Section 3.1.3. As illustrated in Figure 2a, the distance reward showed a sharp increase initially, stabilizing around the 1.8 to 1.9 log value range after approximately 2000 steps. This indicates that the robot quickly learned to minimize the distance required to open the drawer, achieving and maintaining high performance early in the training process. However, the rotation reward showed a more variable trend, with an initial increase peaking around 0.05 log value, followed by a decrease and some fluctuations, as shown in Figure 2b. The value eventually stabilized around \(-0.075\) to \(-0.025\) log value after 20,000 steps. This variability suggests that the robot had more difficulty optimizing the rotational aspect of the task compared to the distance, which is likely due to the complexity of the rotation movements required for the task. Figure 2c shows that the opening reward showed a consistent increase, stabilizing around a log value of 2.0 after 7500 steps. This indicates a steady improvement in the robot's ability to perform the opening action of the drawer, reflecting the effectiveness of the training in teaching the robot this aspect of the task. The total reward shown in Figure 2d, which likely aggregated the individual rewards, demonstrated a steady increase, stabilizing around a log value of 3.5 to 4.0 after 20,000 steps. This overall upward trend indicates successful training, with the robot improving its performance across all aspects of the task over time. In addition to showing task completion rewards, we conducted experiments under different fault conditions to evaluate the performance of our RL framework under various joint malfunction scenarios. Following previous research [46], we calculated the successful task completion rate under different fault scenarios, including permanently broken joints,  
Figure 2: Reward from the training. (**a**) Distance reward. (**b**) Rotation reward. (**c**) Opening reward. (**d**) Total reward. intermittently functioning joints, the joint working in the first half of testing and not working in the second half of testing, and vice versa. For the task completion rate, this metric was used to measure the effectiveness of the robot's ability to complete the drawer-opening task, even in the presence of joint malfunctions. A higher completion rate indicates a more reliable and adaptable system, demonstrating the robot's capacity to overcome joint failures. Additionally, we analyzed the time taken to complete the task to assess the robot's efficiency. A lower time suggests more efficient performance, while an increase in time indicates that the robot had to adjust its strategy to compensate for joint malfunctions. The success rate and average completion time for each scenario are presented in Table 3.  
The results presented in Table 3 provide valuable insights into the robustness and efficiency of our RL framework when subjected to various joint malfunction scenarios.