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Path following controller for autonomous ships: simulation, experiment, and application in shallow water

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Abstract

This study aims to develop a practical path following controller and examine its control effects for large-sized ships in shallow water. First, a new controller is designed and implemented in a ship manoeuvring simulator, and the controller’s tracking capacity is evaluated via controlling a 6 DOF math model following a prescribed path at various speeds and water depths. Then, towing tank tests are conducted with the corresponding physical model to validate the simulation results. Based on experimental results, comparisons are executed between the proposed controller and the traditional controllers (e.g. fuzzy controller). Finally, the applicability of the controller is investigated through simulations of the ship transiting the Panama Canal, meanwhile, the bank effects on the controller’s performance are discussed. The results show that the designed controller offers satisfactory tracking performance. Simulation results match well with the experimental results despite slight discrepancies. Additionally, satisfactory path following performance is obtained by the simulations in the canal. To conclude, the proposed controller is able to fulfill path following missions in shallow water with high precision and can be applied in the manoeuvring simulator.

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Data Availability

Data sets used in this study are confidential therefore not publicly available.

Abbreviations

\(B\) :

Breadth (m)

\(C\) :

Internal model controller (–)

\({C}_{{\text{B}}}\) :

Block coefficient (–)

\({d}_{1}\), \({d}_{2}\) :

Input and output disturbance (–)

\(GM\) :

Metacentric height (m)

\(\widehat{G}\) :

Plant model (–)

\({\widehat{G}}_{{\text{inv}}}\) :

Inverse model of plant model (–)

\(h\) :

Water depth (m)

\(K\) :

Gain of Nomoto model (s−1)

\({K}_{{\text{d}}}\) :

Derivative coefficient (s)

\({K}_{{\text{d}}n}\) :

Adaptive derivative coefficient (–)

\({K}_{{\text{i}}}\) :

Integral coefficient (s−1)

\({K}_{{\text{i}}n}\) :

Adaptive integral coefficient (–)

\({K}_{{\text{p}}}\) :

Proportional coefficient (–)

\({K}_{{\text{p}}n}\) :

Adaptive proportional coefficient (–)

\({L}_{{\text{PP}}}\) :

Length between perpendiculars (m)

\({L}_{{\text{OA}}}\) :

Length over all (m)

\(m\) :

Ship’s mass (kg)

\(n\) :

Propeller rate (rps)

\(Oxyz\) :

Body-bound coordinate system (–)

\({O}_{0}{x}_{0}{y}_{0}{z}_{0}\) :

Earth-bound coordinate system(–)

\(p\) :

Roll angular velocity (rad s−1)

\(q\) :

Pitch angular velocity (rad s−1)

\(Q\) :

Design transfer function (–)

\(r\) :

Yaw angular velocity (rad s−1)

\(s\) :

Laplace operator (–)

\(T\) :

Time constant (s)

\({T}_{{\text{e}}}\) :

Cross track error (m)

\({T}_{{\text{M}}}\) :

Draft at midship (m)

\(u\) :

Surge speed (m s−1, knots)

\(v\) :

Sway speed (m s−1, knots)

\(\beta\) :

Drift angle (°)

\({\beta }_{{\text{c}}}, \gamma\) :

Internal model control coefficient (–)

\(\delta\) :

Rudder angle (°)

\(\Psi\) :

Heading angle (°)

\({\Psi }_{{\text{d}}}\) :

Desired heading angle (°)

\({\Psi }_{{\text{e}}}\) :

Heading angle error (°)

\(\nabla\) :

Displacement volume (m3)

DOF:

Degrees of freedom

Exp.:

Experiment

FHR:

Flanders hydraulics research

GA:

Genetic algorithm

H∞:

H-infinity

IMC:

Internal model control

IMO:

International maritime organization

LNG:

Liquefied natural gas

LQG:

Linear quadratic Gaussian

MASS:

Maritime autonomous surface ships

mHEI:

Mean heading error integral

mRI:

Mean rudder integral

mRTV:

Mean rudder total variation

mTEI:

Mean track error integral

MTE:

Maximum track error

NN:

Neural network

PID :

Proportional integral derivative

Ref.:

Reference

R.E.:

Relative error

Sim.:

Simulation

UKC:

Under keel clearance

USVs:

Unmanned surface vessels

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Acknowledgements

This work is supported by the program of China Scholarship Council (201706570007) and Special Research Fund—Cofounding for Chinese candidates holding a CSC-grant (01SC8418).

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Authors and Affiliations

  1. Ghent University, Ghent, Belgium

    Changyuan Chen, Guillaume Delefortrie, Marc Mansuy & Evert Lataire

  2. Flanders Hydraulics Research, Antwerp, Belgium

    Guillaume Delefortrie

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  1. Changyuan Chen
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  2. Guillaume Delefortrie
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Correspondence to Changyuan Chen.

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Chen, C., Delefortrie, G., Mansuy, M. et al. Path following controller for autonomous ships: simulation, experiment, and application in shallow water. J Mar Sci Technol 29, 181–199 (2024). https://doi.org/10.1007/s00773-023-00980-3

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