## 6 Conclusions  
In response to the issue of underwater robots facing difficulties in determining model parameters and external disturbances, and the inability of traditional fixed-parameter controllers to achieve optimal control performance for the controlled object, an online parameter tuning strategy based on active disturbance rejection control has been proposed: the DDPG-LADRC algorithm.  
1. Based on the nonlinear model of underwater robots, dynamic parameter uncertainty was considered, and a linear active disturbance rejection controller was designed. The convergence of the extended state observer in the linear active disturbance rejection controller and the stability of the closed-loop control were proven using the Lyapunov method. To address the issue that fixed parameter controllers in nonlinear systems cannot achieve optimal control performance, a DDPG-LADRC control strategy was designed, which improved the performance of the LESO by online adjusting control parameters, resulting in the reward curve of DDPG. A feasibility analysis of parameter optimization for LESO was conducted in numerical simulations, demonstrating the effectiveness of the DDPG-LADRC strategy.
2. Compared to PID, fixed-parameter LADRC, and the latest nonlinear observer-based double closed-loop sliding mode control method (NESO-DSMC), the DDPG-LADRC method can generate optimal parameters for the controller, thereby improving control accuracy. Experiments show that this control strategy outperforms PID, fixed-parameter LADRC, and NESO-DSMC control strategies in terms of transient performance and anti-interference capability. Therefore, it can be said that DDPG-LADRC has significant advantages in tracking and anti-interference capabilities.
3. The algorithm, although demonstrating good performance in simulations, still faces significant challenges when being translated into practical engineering applications. For instance, the accurate determination of an ROV's rotational inertia and hydrodynamic coefficients presents a notable challenge. In the future, the parameter adaptation concept based on DDPG can be combined with other control methods to achieve asymptotic stability and optimal control performance.  
G.L.: Writing--review and editing, Writing--original draft, Validation, Supervision, Software, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. D.Z.: Writing--review and editing, Writing--original draft, Visualization, Validation, Software, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. W.F.: Conceptualization, Funding acquisition, Investigation, Resources, Supervision, Writing--review and editing. Z.J.: Data curation, Investigation, Resources, Supervision, Validation, Writing--review and editing. X.L.: Data curation, Investigation, Supervision, Visualization. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the project [2024]52 funded by the Guangdong Provincial Department of Natural Resources and the Guangdong Provincial Natural Resources Research Committee. We appreciate the support you provided. It was also funded by the Shanghai Municipal Industrial Collaborative Innovation Technology Project (ATCX-KJ-2023-2-15). We sincerely thank you for your valuable help and support.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to copyright issues with co-developers.  
Conflicts of Interest: Author [PERSON] was employed by the company Lanqi Robot Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.