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MMG Standard model with extensions for winds, currents and shallow water

In here you find an implementation of the MMG standard model by Yasukawa, H., Yoshimura, Y. (2015).

Installation

Install the package via pip:

pip install git+https://github.com/nikpau/mmgdynamics

Dynamics

The system's dynamics can be found in the dynamics.py file. The model can be used straight out of the box with any vessel in the calibrated_vessels.py file. If you want to embed this model into your framework, use the step() or the pstep() function. The step() function takes in initial values of surge, sway, and yaw rate, as well as parameters about the simulated vessel and optionally environmental disturbances such as water depth, wind speed, and direction, current speed, and direction. It returns the raw first derivatives of surge sway and yaw rates, which must be further post-processes.

If, instead, you want to directly return the new position in the earth-fixed position together with the new surge, sway, and yaw rates, call the pstep() function. It additionally takes the global position of the vessel as an input. This function is easy to use and will likely be the starting point for integrating the MMG dynamics into your project. See the example below on how to use the model

import math
import mmgdynamics as mmg
import mmgdynamics.calibrated_vessels as cvs
import matplotlib.pyplot as plt # Just for demostration

# Load a pre-calibrated vessel
vessel = mmg.Vessel(**cvs.kvlcc2_l64)

# Let the vessel drive with a rudder angle
# of 10° for 1000 seconds
# -------------------------------------
# Inital position
pos = [0,0] # x,y [m]

# Initial heading
psi = 0 # [rad]

# Random initial values (replace these with yours)
uvr = [3.85, 0, 0] # u,v,r [m/s, m/s, rad/s]

positions = []
for _ in range(1000):
    uvr, eta = mmg.pstep(
        X           = uvr,
        pos         = pos,
        vessel      = vessel,
        dT          = 1,    # 1 second
        nps         = 4,    # 4 revs per second
        delta       = 10 * (math.pi / 180), # Convert to radians
        psi         = psi,  # Heading
        water_depth = None, # No water depth
        fl_psi      = None, # No current angle
        fl_vel      = None, # No current velocity
        w_vel       = None, # No wind velocity
        beta_w      = None  # No wind angle
    )
    x,y,psi = eta # Unpack new position and heading
    positions.append([x,y]) # Store the new position
    pos = [x,y] # Update the position
    
# Quick plot of the trajectory
ps = list(zip(*positions))
plt.plot(ps[0], ps[1])
plt.show()

Calibrate custom vessel

To calibrate a vessel not present in the calibrated_vessels.py file, you can define a minimal dict with basic information about the vessel and use calibrate() to make it usable in the step() function. Several empirical formulas will be used to estimate the relevant hydrodynamic derivatives for your vessel and return a dict, which can be used as an input to the step() function.

Disclaimer: The quality of the empirical estimations for hydrodynamic derivatives varies greatly for different ships. Please consider comprehensive testing before using a custom vessel.

Calibration process:

Under src/structs.py, you will find the dataclasses responsible for modeling the vessel objects. For using a minimal dict as a vessel, you must define it as seen below and then pass it into the calibrate() function which returns a full vessel object.

The empirical estimations need at least the following information:

from mmgdynamics.structs import MinimalVessel
from mmgdynamics.dynamics import calibrate

my_vessel = {
  "m":        0.0, # Vessel displacement [m³]
  "B":        0.0, # Vessel Breadth (width)
  "Lpp":      0.0, # Length between perpendiculars
  "C_b":      0.0, # Block coefficient (< 0.8)
  "D_p":      0.0, # Propeller Diameter
  "eta":      0.0, # Ratio of propeller diameter to rudder span
  "f_alpha":  0.0  # Rudder lift gradient coefficient 
                   # (If not given you will be asked for the rudder aspect ratio)
}

# To create a complete vessel object, you must pass
# the minimal dict and the water density of your environment 
# into the calibrate function as a minimal Vessel:
full_vessel = calibrate(MinimalVessel(**my_vessel),rho = 1000)

Extension for winds and currents

Current and wind forces are calculated according to Fossen, 2011. The angle of attack for currents is set as an angle from the global reference frame. 0° current are parallel to the x-axis. Angles rotate clockwise, directions are modeled as coming from. (Wind direction of 90° means wind flows from east to west.)

Shallow water adaption

The effects of shallow water are incorporated using various semi-empirical formulas summarized in Taimuri et. al. (2020)

Examples

You can find common test cases for vessel maneuvering, such as the ZigZag or turning maneuver test, in the example.py file.

Citation

If you use this code in one of your projects or papers, please cite it as follows:

@misc{mmgdynamics,
  author = {Niklas Paulig},
  title = {MMG standard model for ship maneuvering},
  year = {2024},
  publisher = {GitHub},
  journal = {GitHub Repository},
  howpublished = {\url{https://github.com/nikpau/mmgdynamics}}
}