## 5 Simulation Analysis
### Scenario 1
It can be seen that even in the presence of disturbances, the DDPG-LADRC control scheme can achieve precise trajectory tracking, with control performance superior to that of the PID controller and the fixed parameter LADRC controller, demonstrating stronger robustness. Therefore, parameter optimization based on DDPG can enhance the control performance of LADRC. The selected evaluation indicators for transient performance are overshoot, settling time, and peak time. In underwater robot control, overshoot is an important indicator used to describe the dynamic performance of a system. Overshoot is typically measured by the difference between the maximum output value and the steady-state value, and it can also be expressed as a percentage of this difference relative to the steady-state value. The system without overshoot typically stabilizes at the setpoint without deviating too much from the target value, indicating that there is no significant overreaction or oscillation during the response process. From Table 4, we can see that DDPG-LADRC maintains response speed without overshoot, while PID and LADRC exhibit overshoot. When the overshoot is too large, the control system is prone to oscillation. The results indicate that DDPG-LADRC ensures the dynamic response process of the system, maintaining high robustness even in the face of model uncertainty or external disturbances. The parameter optimization effect of DDPG-LADRC is evident, effectively meeting the dynamic performance requirements of the system. Figure 9: Trajectory tracking results of the ROV under three control schemes. In underwater robot trajectory tracking control, the adjustment time is an important dynamic performance indicator. It reflects the robot's sensitivity to changes in control signals and its ability to respond quickly, defined as the time required for the ROV to respond and maintain within a certain allowable error range (usually \(\pm 2\%\) or \(\pm 5\%\) of the final value) after initially reaching the target value. A shorter adjustment time means that the ROV can stabilize more quickly around the target value, reducing oscillations or instability during the transition process. Additionally, a rapid response can better handle external disturbances and changes in the internal parameters of the ROV, enhancing the system's robustness and stability. Referring to Table 5, it can be seen that the adjustment time of DDPG-LADRC for the ROV in the \(X\)-direction is significantly better than the other two control strategies, reducing by 93% and 98%, respectively. In the \(Y\)-direction, the reductions are 93% and 86%, respectively, and in the \(Z\)-direction, the reductions are 66.7% and 90%, respectively. The attitude angles \(Phi\) were reduced by 64% and 89%, respectively. Even if the overshoot is 0, the system response may still have a \"peak,\" which does not refer to a deviation exceeding the steady-state value, but rather to the maximum value during the response process. In the underwater robot trajectory tracking control system, the peak time is an important dynamic performance indicator that describes the time required for the system response to exceed its steady-state value and reach the first peak. Referring to Table 6, the comparison of peak times shows that in the \(X\)-direction, DDPG-LADRC significantly outperforms the other two control strategies, reducing by 93% and 98%, respectively. In the \(Y\)-direction, it reduces by 82% and 90%, respectively, and in the \(Z\)-direction, it reduces by 80% and 98%, respectively. The attitude angles \(Phi\) are reduced by 93% and 89%, respectively. In summary, through a comparative analysis of transient performance under different control methods, the results indicate the superiority of the DDPG-LADRC control strategy in terms of transient performance. Compared to PID controllers and traditional LADRC controllers, the proposed DDPG-LADRC is more suitable for underwater robotic systems that are multivariable, strongly coupled, have significant randomness, and are subject to unknown disturbances.