Multi-Ship Control and Collision Avoidance Using MPC and RBF-Based Trajectory Predictions
Abstract
:1. Introduction
2. AIS-Data-Based Trajectory Prediction Models
2.1. Radial Basis Function Neural Networks
2.2. The Fuzzy Means (Fm) Training Algorithm
2.3. Data Preprocessing
Algorithm 1 Preprocessing Stage |
1: Process each entry in the common dataset so that it contains only the following: Vessel ID, timestamp, latitude, and longitude. Reject all other information. |
2: Sort dataset by vessel ID and sort each vessel data by date. |
3: Apply resampling and outlier filtering on the data of each vessel to achieve a resampling of 120 s. |
4: Split vessel data into trajectories containing ten consecutive vessel positions each. |
5: Create final preprocessed dataset, which should contain the vessel ID and final 10-position trajectories. |
2.4. Modeling Procedures
Algorithm 2 Modeling Stage |
1: Load final preprocessed dataset. |
, so that each trajectory sample is in the form . |
3: Randomly permute the trajectory samples of each vessel. |
4: Split the trajectory samples of each vessel into training, validation, and testing subsets (in this work a 50%–5%–25% percentage split is used). Do this so that all vessels contribute to all three subsets according to the chosen splitting. |
5: Merge all subset samples, e.g., all training samples of all vessels together in one single dataset that will be used for training. Do the same for the validation and testing subsets. |
6: Normalize the inputs and outputs of the training subset. Apply the normalization coefficients to the validation and testing subsets. |
− values as inputs and the last set of − values as output. |
8: Final model is in the form of Equation (11). |
3. MPC for Multi-Ship Collision Avoidance
3.1. Preliminaries on Maritime Collision Avoidance and Trajectory Generation
3.2. Collision Avoidance with Mpc and Obstacle Trajectory Prediction Models
3.3. Control Framework
4. Case Study
4.1. Multi-Ship Collision Avoidance Control for the Miami Port
4.2. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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RBF NN | ||
---|---|---|
Latitude (y) | Longitude (x) | |
Mean RMSE (deg) | 1439∙10−6 | 1567∙10−6 |
Best combined RBF models | ||
Mean RMSHFD (m) | 1200 |
Parameter | Description | Value |
---|---|---|
Controller sample time | 1′ | |
Control horizon | 5 | |
Prediction horizon | 15 | |
Risk function scaling parameter | 3 | |
Risk term weighting parameter | 1 | |
Course deviation term weighting parameter | 0.05 | |
Control action smoothness term weighting parameter | 5 |
Parameter | Description | Value |
---|---|---|
Minimum allowable DCPA for risk calculation | 750 m | |
Emergency distance | 200 m | |
Minimum allowable TCPA for risk calculation | 10′ | |
Rudder gain constant | 0.5 | |
Rudder time constant | 2 |
Scenario 1 | Scenario 2 | ||||
---|---|---|---|---|---|
s | Controlled Vessel | MPC-RBFP | MPC-SLP | MPC-RBFP | MPC-SLP |
Course deviations (1) | 1 | 1.31·104 | 2.21·104 | 0.658·104 | 0.521·104 |
2 | 1.49·104 | 2.85·104 | 0.404·104 | 0.529·104 | |
Control action smoothness (2) | 1 | 307.35 | 476.59 | 242.12 | 167.85 |
2 | 290.94 | 424.43 | 92.47 | 128.41 | |
Risk of trajectory (3) | 1 | 0 | 4.032·106 | 0 | 0 |
2 | 0 | 0 | 0 | 3.949·106 | |
Cost of trajectory (4) | 1 | 9.05·106 | 1.62·1013 | 2.63·106 | 1.49·106 |
2 | 2.63·106 | 4.15·107 | 8.58·105 | 1.55·1013 |
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Papadimitrakis, M.; Stogiannos, M.; Sarimveis, H.; Alexandridis, A. Multi-Ship Control and Collision Avoidance Using MPC and RBF-Based Trajectory Predictions. Sensors 2021, 21, 6959. https://doi.org/10.3390/s21216959
Papadimitrakis M, Stogiannos M, Sarimveis H, Alexandridis A. Multi-Ship Control and Collision Avoidance Using MPC and RBF-Based Trajectory Predictions. Sensors. 2021; 21(21):6959. https://doi.org/10.3390/s21216959
Chicago/Turabian StylePapadimitrakis, Myron, Marios Stogiannos, Haralambos Sarimveis, and Alex Alexandridis. 2021. "Multi-Ship Control and Collision Avoidance Using MPC and RBF-Based Trajectory Predictions" Sensors 21, no. 21: 6959. https://doi.org/10.3390/s21216959