**5. Conclusions**

Aiming at the problem of AUV trajectory tracking control, this paper designs a novel tracking control method based on NTSM-ADRDC. Firstly, the AUV 5-DOF model is decoupled by introducing the ADRC technology. Secondly, the 3D trajectory tracking controller based on NTSM-ADRDC is designed. The controller uses LESO to observe the state variable values of the AUV and estimate the sum of the unmodeled dynamics and external disturbances of the system. By introducing the exponential reaching law into NTSM, a nonlinear error feedback law is designed to compensate for the total disturbance of the system. Combining NTSMC and ADRC technology can retain the advantages of the two control algorithms to the maximum. The NTSMC strategy can make the AUV quickly approach the reference trajectory, and the ADRC can suppress model uncertainty and external disturbance. Finally, the simulation verifies the effectiveness of the designed controller by comparing it with LADRC.

In future work, we will investigate the theory of optimization of the control parameters of the NTSM-ADRDC algorithm to improve the engineering applicability of the designed algorithm. Meanwhile, considering the input and state constraints existing in the AUV system, we will combine other methods, such as model predictive control, in the design process of the ADRC controller. In addition, in order to match the configuration of AUV actuators in actual applications, thrust allocation schemes will be investigated for the design of the controller.

**Author Contributions:** Methodology, W.W.; Validation, Z.Y.; Investigation, Z.L.; Data curation, X.D.; Writing—original draft, W.W.; Writing—review & editing, W.W.; Funding acquisition, W.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China under grant E1102/52071108, and in part by National Natural Science Foundation of China under grant 5217110332, and the Natural Science Foundation of Heilongjiang Province under grant JJ2021JQ0075.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
