Spatial Trajectory Tracking of Underactuated Autonomous Underwater Vehicles by Model–Data-Driven Learning Adaptive Robust Control
Abstract
:1. Introduction
- (1)
- The serial ILC is introduced as feedforward compensation control, and the corresponding trajectory tracking error dynamics, Feedforward Compensation–Line of Sight (FFC-LOS) guidance law, and feedforward compensation-based kinematics controller are proposed, which can significantly improve trajectory tracking performance for repetitive tasks in 3D space.
- (2)
- In order to solve the problem of uncertain dynamics parameters, the projection-type adaptation law with rate limits is applied, and the parameter estimation process is designed based on the least squares estimation technique. The nonlinear robust feedback control and fast dynamic compensation term are designed to deal with the nonlinear complex external disturbances.
- (3)
- The proposed LARC strategy for underactuated AUVs includes the data-driven ILC feedforward part, the adaptive control part, and the robust control and fast dynamic compensation part, using the advantages of both model-based control and data-driven control. The stability of the kinematics controller and dynamics controller are ensured by Lyapunov analysis. The effectiveness of the proposed control strategy is verified by comparison and multi-case study.
2. Modeling and Control Objective
2.1. Mathematical Models of Underactuated AUV
2.2. Control Objective
3. Controller Design
3.1. ILC Part in Kinematics Controller
3.2. Trajectory Tracking Error Dynamics Model
3.3. Kinematics Controller Design
3.4. Dynamics Controller Design
3.4.1. Parameter Adaptation Law
3.4.2. Velocity Tracking Controller Design
4. Simulation Study
4.1. Combined Reference Trajectory Tracking
4.2. Helical Dive Reference Trajectory Tracking
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Nomenclature | Definition |
---|---|
AUV | Autonomous underwater vehicle |
ARC | Adaptive robust control |
DIARC | Integrated direct/indirect adaptive robust control |
ILC | Iterative learning control |
LARC | Learning adaptive robust control |
FFC-LOS | Feedforward Compensation–Line of Sight |
ISMC | Integral sliding mode control |
Earth-fixed inertial reference frame | |
Body-fixed frame | |
Serret–Frenet frame | |
The position vector in | |
The attitude vector in | |
The desired trajectory in | |
The desired attitude in | |
The velocity in | |
The angular velocity in | |
Terms of inertia and added mass | |
, , , , | Linear drag hydrodynamic coefficients |
, , , , | Nonlinear drag hydrodynamic coefficients |
, , , , | Oceanic external disturbance |
, , | Propeller thrust and rudder torques |
ILC compensation term in | |
The kinematics control law | |
, | FFC-LOS guidance law |
The dynamics control law | |
, , , | Linear feedback term, adjustable model compensation term, nonlinear robust feedback term, fast dynamic compensation term in the dynamics control law |
Regressor vectors | |
System parameters | |
Adaptation rate matrices | |
Adaptation functions | |
Adaptation rates in fast dynamic compensation term | |
Velocity and angular velocity tracking errors |
Appendix B
Appendix C
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Performance Indices | LARC | DIARC | ISMC |
---|---|---|---|
Total MAE | 1.4208 | 2.0879 | 3.0263 |
Total MSE | 1.2513 | 2.5514 | 4.7696 |
MAE | 0.0209 | 0.0299 | 0.0536 |
MSE | 0.0021 | 0.0024 | 0.0045 |
MAE | 0.0824 | 0.1232 | 0.1715 |
MSE | 0.0117 | 0.0235 | 0.0461 |
MAE | 0.0371 | 0.0534 | 0.0995 |
MSE | 0.0018 | 0.0036 | 0.0126 |
MAE | 0.8522 | 1.2666 | 1.6016 |
MSE | 1.0073 | 2.0605 | 3.2048 |
MAE | 0.4282 | 0.6148 | 1.1001 |
MSE | 0.2285 | 0.4614 | 1.5015 |
Performance Indices | LARC | DIARC | ISMC |
---|---|---|---|
Total MAE | 1.5013 | 2.2084 | 3.4047 |
Total MSE | 1.3958 | 2.8627 | 5.4221 |
MAE | 0.0214 | 0.0312 | 0.2671 |
MSE | 0.0020 | 0.0024 | 0.0729 |
MAE | 0.0833 | 0.1236 | 0.1581 |
MSE | 0.0110 | 0.0215 | 0.0348 |
MAE | 0.0382 | 0.0550 | 0.1029 |
MSE | 0.0018 | 0.0038 | 0.0133 |
MAE | 0.9137 | 1.3599 | 1.6988 |
MSE | 1.1365 | 2.3395 | 3.6014 |
MAE | 0.4447 | 0.6388 | 1.1779 |
MSE | 0.2444 | 0.4954 | 1.6998 |
Performance Indices | LARC | DIARC | ISMC |
---|---|---|---|
Total MAE | 1.4609 | 2.0931 | 3.0078 |
Total MSE | 2.5752 | 3.4832 | 5.2508 |
MAE | 0.0232 | 0.0328 | 0.0654 |
MSE | 0.0044 | 0.0047 | 0.0081 |
MAE | 0.0879 | 0.1296 | 0.1753 |
MSE | 0.0199 | 0.0332 | 0.0548 |
MAE | 0.0379 | 0.0538 | 0.0994 |
MSE | 0.0021 | 0.0039 | 0.0127 |
MAE | 0.8517 | 1.2420 | 1.5823 |
MSE | 1.8165 | 2.5747 | 3.6042 |
MAE | 0.4602 | 0.6349 | 1.0855 |
MSE | 0.7324 | 0.8667 | 1.5710 |
Performance Indices | LARC-2 Iteration | LARC-1 Iteration | DIARC | ISMC |
---|---|---|---|---|
Total MAE | 1.0766 | 1.5504 | 2.2279 | 3.3942 |
Total MSE | 2.3505 | 2.6816 | 3.7884 | 5.8889 |
MAE | 0.0174 | 0.0234 | 0.0338 | 0.2883 |
MSE | 0.0041 | 0.0042 | 0.0046 | 0.0855 |
MAE | 0.0597 | 0.0897 | 0.1316 | 0.1661 |
MSE | 0.0136 | 0.0197 | 0.0318 | 0.0466 |
MAE | 0.0280 | 0.0393 | 0.0558 | 0.1026 |
MSE | 0.0013 | 0.0022 | 0.0041 | 0.0132 |
MAE | 0.6178 | 0.9214 | 1.3495 | 1.6781 |
MSE | 1.6288 | 1.9145 | 2.8622 | 3.9934 |
MAE | 0.3537 | 0.4765 | 0.6571 | 1.1591 |
MSE | 0.7028 | 0.7411 | 0.8858 | 1.7502 |
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Guo, L.; Zhou, R.; Guo, Q.; Ma, L.; Hu, C.; Luo, J. Spatial Trajectory Tracking of Underactuated Autonomous Underwater Vehicles by Model–Data-Driven Learning Adaptive Robust Control. J. Mar. Sci. Eng. 2025, 13, 1151. https://doi.org/10.3390/jmse13061151
Guo L, Zhou R, Guo Q, Ma L, Hu C, Luo J. Spatial Trajectory Tracking of Underactuated Autonomous Underwater Vehicles by Model–Data-Driven Learning Adaptive Robust Control. Journal of Marine Science and Engineering. 2025; 13(6):1151. https://doi.org/10.3390/jmse13061151
Chicago/Turabian StyleGuo, Linyuan, Ran Zhou, Qingchang Guo, Liran Ma, Chuxiong Hu, and Jianbin Luo. 2025. "Spatial Trajectory Tracking of Underactuated Autonomous Underwater Vehicles by Model–Data-Driven Learning Adaptive Robust Control" Journal of Marine Science and Engineering 13, no. 6: 1151. https://doi.org/10.3390/jmse13061151
APA StyleGuo, L., Zhou, R., Guo, Q., Ma, L., Hu, C., & Luo, J. (2025). Spatial Trajectory Tracking of Underactuated Autonomous Underwater Vehicles by Model–Data-Driven Learning Adaptive Robust Control. Journal of Marine Science and Engineering, 13(6), 1151. https://doi.org/10.3390/jmse13061151