Three-Dimensional Trajectory Tracking for a Heterogeneous XAUV via Finite-Time Robust Nonlinear Control and Optimal Rudder Allocation
Abstract
:1. Introduction
- (1)
- The finite-time convergence strategy is deeply integrated with the whole controller design process. The novel FTLOS guidance law and finite-time feedback kinematics control law is designed for the kinematics control loop. Improved global finite-time terminal sliding mode control (FTTSMC) laws are proposed for heading control, pitching control, and surge velocity tracking control in the dynamics control loop, where finite time convergence is considered in both the approaching stage and sliding mode holding stage. The FTEDOs are designed to tackle the multi-source unknown uncertainties existing in both the kinematics and dynamics loops. Compared with the existing literature on finite-time control [20,21], this paper not only focuses on the finite convergence of dynamics control, but also proposes a new finite-time convergence guidance algorithm that is easy to implement, making the finite-time control method more comprehensive and effective.
- (2)
- The influences of actuator dynamics are fully considered, including not only the propeller input saturation problem, but also the complex dynamics mechanism and various constraints of the heterogeneous X-rudder. To deal with the propeller input saturation problem, an adaptive RBFNN compensator is integrated into the surge velocity tracking control law, while for X-rudder dynamics and constraints, a multi-objective optimal rudder allocator is proposed that can realize the rudder angle allocation and energy consumption optimization at the same time, as well as meet the saturation constraints of rudder angle and rudder steering velocity. Compared with the general literatures on actuator characteristics, the research in this paper is more comprehensive.
- (3)
- Multi-source disturbances are considered in both the kinematics model and dynamics model. In particular, and are treated as unknown uncertainties, rather than directly obtained by differential calculation, taking into account the noise problem in the measurement process, which makes the controller design more practical. For the multi-source unknown disturbances, FTEDOs are designed to realize fast and accurate disturbance estimation based on motion state, which greatly improves the robustness of the system. Compared with the conventional disturbance observer, this method can realize the estimation of both the disturbance and its derivative, and shows finite time convergence.
2. XAUV Modeling and Problem Formulation
2.1. Preliminaries and Nomenclatures
2.2. XAUV Modeling
2.3. Problem Formulation
2.4. Assumptions
3. Control Methodology
3.1. Finite-Time Extended Disturbance Observer
3.2. Finite-Time Kinematics Control
3.3. Finite-Time Dynamics Control
3.3.1. Finite-Time Heading Control
3.3.2. Finite-Time Pitching Control
3.3.3. Finite-Time Velocity Tracking Control
3.4. Optimal Rudder Allocation
4. Simulation
4.1. Simulation Preparation
- According to the parameter range mentioned above, prepare a group of basic parameters and make the system converge through debugging. In the process of adjustment, adjust the conventional parameters first and then the exponential parameters;
- On the basis of system convergence, the kinematic control parameters are adjusted to improve the convergence speed;
- Further adjust the dynamic control parameters to optimize the tracking control accuracy and convergence speed;
- Adjust the parameters of rudder allocation to optimize the energy consumption.
4.2. Case 1
4.3. Case 2
5. Conclusions and Future Works
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Parameters | Expressions |
---|---|
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Nomenclature | Definition |
---|---|
XAUV | X-rudder autonomous underwater vehicle |
FTLOS | Finite-time line-of-sight |
FTEDO | Finite-time extended disturbance observer |
FTTSMC | Finite-time terminal sliding mode control |
DOF | Degree of freedom |
RBFNN | Radial basis function neural network |
SQP | Sequential quadratic programming |
{I} | Inertial reference frame |
{B} | Body-fixed frame |
{F} | Frenet–Serret frame |
The position and orientation variables in {I} | |
The linear and angular velocities in {B} | |
Desired position and orientation variables in {I} | |
The tracking error vectors in {F} | |
The propeller thrust | |
The X-rudder forces and torques | |
The X-rudder angles | |
The proposed FTLOS guidance laws | |
The kinematics control laws | |
The desired rudder torques generated by dynamics control |
Algorithm: Three-dimensional trajectory tracking |
Given control parameters |
Procedure: |
Input: Collect the data from the integrated navigation system; Calculate the reference trajectory . |
Finite-time kinematics control law: (1) according to Equation (15); (2) according to Equation (13); (3) according to Equation (20); (4) according to Equation (18). |
Finite-time dynamics control law: Heading control law: (1) according to Equation (28); (2) utilizing Equation (29); (3) according to Equation (15); (4) utilizing the finite-time control law Equation (31). Pitching control law: (1) according to Equation (39); (2) utilizing Equation (39); (3) according to Equation (15); (4) utilizing the finite-time control law Equation (41). Velocity tracking control law: (1) according to Equation (43); (2) utilizing Equation (43); (3) according to Equation (15); (4) according to Equation (47); (5) utilizing Equation (46); (6) utilizing the finite-time control law Equation (45). |
Optimal rudder allocation: (1) according to Equation (49); (2) utilizing Equation (48). |
The X-rudder equations Equation (10) update (For simulation) Dynamics equations Equation (9) update (For simulation) Kinematics equations Equation (7) update (For simulation) |
End procedure |
Repeat procedure |
Subcases | Disturbance Settings |
---|---|
Subcase 1.1 | |
Subcase 1.2 | |
Subcase 1.3 | |
Subcase 1.4 |
Subcase 1.1 | Subcase 1.2 | Subcase 1.3 | Subcase 1.4 | |
---|---|---|---|---|
0.0018 | 0.0025 | 0.0012 | 0.2502 | |
0.0212 | 0.0492 | 0.0061 | 0.0086 | |
0.0001 | 0.0003 | |||
0.0085 | 0.0195 | 0.0070 | 0.0064 | |
Name | Method |
---|---|
Proposed method | The control method proposed in Section 3 |
Method 1 | LOS + ISMC [39]: (1) Kinematics control: LOS guidance law; (2) Dynamics control: integral terminal sliding mode controller; (3) Rudder allocation: pseudo inverse method. |
Method 2 | LOS + FPID [40]: (1) Kinematics control: LOS guidance law; (2) Dynamics control: Fuzzy PID method; (3) Rudder allocation: pseudo inverse method. |
Method 3 | LOS + Backstepping [41]: (1) Kinematics control: LOS guidance law; (2) Dynamics control: Backstepping method; (3) Rudder allocation: pseudo inverse method. |
Proposed | Method 1 | Method 2 | Method 3 | |
---|---|---|---|---|
0.0017 | 0.0021 | 0.2725 | 0.0020 | |
0.0010 | ||||
0.0034 | 0.0035 | 0.1655 | 0.0254 | |
0.0168 | 0.0009 | |||
0.0014 | 0.0031 | 0.0379 | 0.0316 | |
0.0014 | 0.0014 |
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Xia, Y.; Huang, Z.; Xu, K.; Xu, G.; Li, Y. Three-Dimensional Trajectory Tracking for a Heterogeneous XAUV via Finite-Time Robust Nonlinear Control and Optimal Rudder Allocation. J. Mar. Sci. Eng. 2022, 10, 1297. https://doi.org/10.3390/jmse10091297
Xia Y, Huang Z, Xu K, Xu G, Li Y. Three-Dimensional Trajectory Tracking for a Heterogeneous XAUV via Finite-Time Robust Nonlinear Control and Optimal Rudder Allocation. Journal of Marine Science and Engineering. 2022; 10(9):1297. https://doi.org/10.3390/jmse10091297
Chicago/Turabian StyleXia, Yingkai, Zhemin Huang, Kan Xu, Guohua Xu, and Ye Li. 2022. "Three-Dimensional Trajectory Tracking for a Heterogeneous XAUV via Finite-Time Robust Nonlinear Control and Optimal Rudder Allocation" Journal of Marine Science and Engineering 10, no. 9: 1297. https://doi.org/10.3390/jmse10091297
APA StyleXia, Y., Huang, Z., Xu, K., Xu, G., & Li, Y. (2022). Three-Dimensional Trajectory Tracking for a Heterogeneous XAUV via Finite-Time Robust Nonlinear Control and Optimal Rudder Allocation. Journal of Marine Science and Engineering, 10(9), 1297. https://doi.org/10.3390/jmse10091297