A Receding Horizon Navigation and Control System for Autonomous Merchant Ships: Reducing Fuel Costs and Carbon Emissions under the Premise of Safety
Abstract
:1. Introduction
- The design of a new autonomous navigation system is proposed, which accomplishes the economic and green goals of navigation in the path planning module and ensures the safety of navigation in the control module;
- Based on the superposition of fields, cost and emission fields according to their consumption rate are constructed, and guided fields are designed to transform the path search problem into a gradient descent optimization problem to solve the multi-objective path planning problem of MASS;
- A navigation and control system framework for path planning and rolling NMPC tracking control co-optimization is designed for the problem of determining whether the reference trajectory and tracking controller track with high accuracy during multi-objective planning.
2. Problem Statement
2.1. Problem Description
- (i)
- A guidance module for multi-objective path planning;
- (ii)
- A control module for precise trajectory tracking and to guarantee navigation safety;
- (iii)
- The collaborative optimization of guidance and control for information interaction and synergy optimization between navigation and control modules.
2.2. Framework of Receding Horizon Navigation and Control System
3. Guidance Module
3.1. Fields Based on Cost and Emission
3.2. Guidance Field
3.3. Field Renewable Local Path Planning Algorithm
3.3.1. Superposition of Fields
3.3.2. Event Trigger Mechanism
3.3.3. Path Planning Based on Superposition Field
- Calculate guide field Gk and initial superposition field according to Equations (1)–(6).
- Judge whether the vessel is in the collision avoidance state. If the distance between the vessel and the obstacle is greater than or equal to danger range , the vessel is judged to be in the regular navigation state; if the distance between the vessel and the obstacle is less than danger range , the vessel is judged to be in the regular collision avoidance state. In that case, when the coordinates of the vessel on both the X and Y axes exceed the obstacle or other vessel, the vessel is transferred from the collision avoidance to regular navigation state.
- If the ship is in the state of collision avoidance, calculate gradient ▽(p(k)) from ; if in the state of regular navigation, calculate the gradient from .
- Obtain path points p(k + ) = p(k) − (k) ∗ ▽(p(k)).
Algorithm 1 Local path planning. |
Input: Gradient of field |
Output: Trajectory of MASS p(x) |
|
4. NMPC-Based Trajectory Tracking Control and Collision Avoidance
4.1. Maritime Autonomous Surface Ship System Modeling
4.2. Trajectory Tracking Control
- The optimization problem (23) is solved with the current state error as the initial state and , (k = 0, 1, 2,…, N − 1) as a set of optimal solutions to the control problem.
- The system only uses the first optimal solution as the control output for one sampling period , as a control decision for the MASS.
- At moment at the beginning of the next sampling period, the optimization problem (23) is solved again using the latest measurement data .
5. Collaborative Optimization of Path Planning and Tracking Control
5.1. Interface I for Path Planning
5.2. Process of the Closed-Loop Structure
Algorithm 2 Path planning and trajectory tracking control. |
Input: Field and reference trajectory |
Output: Optimum control and real trajectory |
|
6. Simulation
6.1. Experimental Design
6.1.1. Marine Environment
6.1.2. Experimental Parameters
6.1.3. Experimental Design
6.2. Simulation Results
6.2.1. Contrast Experiments Considering Carbon Emissions and No Carbon Emissions in Local Path Planning
6.2.2. Simulation Experiments of Receding Horizon Navigation and Control System in Global Planning
6.2.3. Simulation Experiments of Real-Time Path Planning and Tracking Control with Collision Avoidance
Scenario: Static Collision Avoidance
Scenario: Head-on
6.2.4. RHNC System with Collision Avoidance and Event Triggering
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Parameters | Meanings |
---|---|
K | Propeller efficiency |
Propulsion efficiency (0.6 to 0.7) | |
Significant wave height | |
Still water power | |
Water density | |
Still water drag coefficient | |
S | Wetted surface |
Additional power for wave resistance | |
Drag coefficient for wave resistance | |
g | Vertical force |
B | Ship width |
L | Ship length |
Additional power for wave resistance | |
Drag coefficient for aerodynamic | |
A | Surface area projected for wind |
u | Wave speed |
Wind speed | |
m | Cargo on board the vessel |
n | Cargo weight constant |
r | Wave constant (0.1) |
Parameters | Value | Unit |
---|---|---|
897.77 | kg | |
1718 | kg | |
105.34 | kg | |
42.77 | kg/s | |
863 | kg/s | |
51.88 | kg/s | |
S (wetted surface) | 9424 | m |
A (wind area) | 2200.43 | m |
L | 230 | m |
B | 32.2 | m |
1 | ||
1 | ||
16 | ||
0.57e | ||
1.27e | m/s | |
0.1 |
Navigation and Control System | EC (USD) | EM (t) | EM per n mile (USD) | EM per n mile (kg) | Time (min) |
---|---|---|---|---|---|
RHNC | 1.047 | 31.2642 | 80.74 | 241.10 | 480 |
Offline-SPNC | 1.1656 | 37.8385 | 88.81 | 288.31 | 460 |
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Zheng, J.; Sun, W.; Li, Y.; Hu, J. A Receding Horizon Navigation and Control System for Autonomous Merchant Ships: Reducing Fuel Costs and Carbon Emissions under the Premise of Safety. J. Mar. Sci. Eng. 2023, 11, 127. https://doi.org/10.3390/jmse11010127
Zheng J, Sun W, Li Y, Hu J. A Receding Horizon Navigation and Control System for Autonomous Merchant Ships: Reducing Fuel Costs and Carbon Emissions under the Premise of Safety. Journal of Marine Science and Engineering. 2023; 11(1):127. https://doi.org/10.3390/jmse11010127
Chicago/Turabian StyleZheng, Jian, Wenjun Sun, Yun Li, and Jiayin Hu. 2023. "A Receding Horizon Navigation and Control System for Autonomous Merchant Ships: Reducing Fuel Costs and Carbon Emissions under the Premise of Safety" Journal of Marine Science and Engineering 11, no. 1: 127. https://doi.org/10.3390/jmse11010127
APA StyleZheng, J., Sun, W., Li, Y., & Hu, J. (2023). A Receding Horizon Navigation and Control System for Autonomous Merchant Ships: Reducing Fuel Costs and Carbon Emissions under the Premise of Safety. Journal of Marine Science and Engineering, 11(1), 127. https://doi.org/10.3390/jmse11010127