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Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011

VCCA-2011
Real-time Control and Hardware-in-the-Loop Simulation of Surface
Vessels for Multitask Missions at Seas
Điều khiển thời gian thực và mô phỏng phần cứng trong vòng lặp các tầu mặt
nước để làm đa nhiệm vụ trên biển
Hung Duc Nguyen
University of Tasmania / Australian Maritime College
e-Mail:


Abstract
This paper presents an experimental approach to
develop a real-time control system and hardware-in-
the-loop simulation of surface vessels for multitask
missions at seas. A multitask mission control system
has many functions as an autopilot, rudder-roll
damping, speed control, dynamic positioning,
automatic mooring and anchoring, berthing and
unberthing. A model-scaled container vessel is used
for this work. Model-scaled experiments are
conducted using a model test basin in order to verify
feasibility of the automatic multitask mission control
system. The paper first summarises control
algorithms, then describes the experimental facility
and development of real-time control programs.

Tóm tắt: Bài báo này trình bày phương pháp thử
nghiệm phát triển hệ thống điều khiển thời gian thực
và mô phỏng phần cứng trong vòng lặp cho tầu mặt


nước thực hiện đa nhiệm vụ trên biển. Hệ thống điều
khiển thực hiện đa nhiệm vụ có các chức năng như
máy lái tự động, giảm lắc ngang, điều khiển tốc độ,
định vị động, neo buộc tầu tự động và ra vào cầu tự
động. Một tầu mô hình đuợc sử dụng cho công trình
này. Các thí nghiệm mô hình được thực hiện sử dụng
bể thử mô hình nhằm kiểm chứng tính khả thi của hệ
thống điều khiển đa nhiệm vụ. Bài báo trước hết tóm
tắt các thuật toán điều khiển và tiếp theo mô tả thiết bị
thí nghiệm và phát triển chương trình điểu khiển thời
gian thực.

Nomenclature
Symbol
Unit
Meaning
U
d

m/s
Desired velocity
d


rad
Desired heading angle
x
i
, y
i


m
Position coordinates

Abbreviation
RRD/S
Rudder roll damping/stabilisation
IMO
International Maritime Organization
CCP
Controllable pitch propeller
LQG
Linear quadratic Gaussian

1. Introduction
Surface vessels are the main means of marine
transport. New generation surface vessels require
automation at a high level. Design of automatic
control systems for surface vessels involves an
understanding of their manoeuvrability, seakeeping
and seaworthiness. The most important motions for
surface vessels are surge, sway and yaw while
unnecessary motions are heave, pitch and roll.
Small autonomous surface vessels have recently been
applied in various missions in rivers and seas in
remote areas, for example, a river water sample taking
vessel is used to take water samples at certain time
and take measurement of water sample and send data
to the control centre. Another example of autonomous
surface vessel is for littoral surveillance [2].

This article is about the second step to realise an
automatic multitask mission manoeuvring system for
surface vessels. The article focuses on applied aspects
of the system and experimental approach.
The main purpose of this paper is to:
 do feasibility study of the automatic multitask
mission manoeuvring systems by computer
simulation;
 develop real-time control programs for the
multitask mission manoeuvring system;
 describe experimental facilities;
 realise multitask mission manoeuvring system;
and
 propose applications of autonomous surface
vessels for some missions at remote sea areas
where human being find it difficult to access.
This article is organised as follows: Section 1
Introduction, Section 2 Mathematical background,
Section 3 Brief description of AMC experimental
facilities, Section 4 Software controller diagrams,
Section 4 Development of software controller
programs, Section 5 Design of experiment; Section 6
Possible applications and Section 7 Conclusions.

2. Mathematical Background for
Multitask Mission Manoeuvrves
Nguyen [12][14] proposed a multitask mission
manoeuvring system based on the recursive optimal
method in which a recursive estimation algorithm is
combined with an optimal control algorithm. The

main functions of the multitask mission manoeuvring
system are:
 autopilot: course keeping and changing;
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 rudder-roll stabilisation;
 dynamic positioning;
 manoeuvre tests and estimation of
manoeuvrability indices;
 ship motion information providing and
monitoring;
 automatic berthing and unberthing
manoeuvres; and
 Automatic mooring and anchoring manoeuvres
The multitask mission manoeuvring system consists
of three subsytems (guidance, navigation and control)
as shown in Fig. 1.

Fig. 1 Three subsystems (guidance, navigation and control)
for a surface vessel

2.1 Guidance System – Waypoint positions/LOS
technique
The guidance system generating a reference trajectory
includes desired courses, speed, way-points and
position is constructed by using the waypoint and
light of sight and exponential decay techniques
[12][14]. The guidance system receives prior

information data, position of waypoints and weather
information. For various missions at seas the guidance
system will generate trajectory for the following
cases:
 IMO search and rescue expanding square
pattern and sector pattern;
 weather routing navigation trajectory;
 trawling trajectory;
 dredging trajectory;
 subsea pipe and device laying and installation
trajectory; and
 seismic survey trajectory.
The outputs of the guidance system often are
Desired way-point positions:
wpt.pos: {(x
0
,y
0
), (x
1
,y
1
), , (x
k
,y
k
)} (1)
Desired speeds between way-points:
wpt.speed: U
d

= {u
0
, u
1
, u
2
, , u
k
} (2)
Desired heading angles:
wpt.heading:
d

= {
d1

,
d2

,
d3

, ,
dk

} (3)
The guidance system also receives navigation signals
from the navigation system and computes errors
including position errors (path tangential tracking and
cross-track errors), heading error and speed error.


2.2 Navigation System
The navigation system has the main function of
providing accurate measurements of position and ship
motion. The navigation is equipped with D-GNSS or
RTK-GNSS and GNSS receivers when the surface
vessel is running along a coast where D-GNSS and
correction signals are available. A gyro- or satellite-
compass is used to measure the ship’s heading.
For autonomous surface vessels running in a lake or
model test basin a 6-DOF IMU device is used. In the
in-door model test basin where there is no GNSS
signal, an indoor navigation device is applied to get
the vessel’s measurement.
The GNSS/IMU signals are often including noisy. A
Kalman filter and/or low-pass filter may be used to
estimate state variables that are not measured and to
remove noisy, respectively. An adaptive observer is
also applied for enhancement of accuracy and
reliability of the obtained signals.

2.3 Control System
As shown in Fig. 1 the control system consists of two
blocks: motion control and controller allocation. The
control system synthesises an appropriate control
algorithm to compute control signals and allocate
control actions by actuators. The control algorithms
can be one of the following:
 conventional PID control;
 self-tuning PID control algorithm;

 recursive optimal control algorithm [11];
 optimal control algorithm;
 model reference adaptive control;
 robust (H-infinity) control;
 fuzzy logic PID control;
 neural networks-based control; or
 genetic algorithm-based control.
The control algorithm adopted in the control system is
often complicated because of MIMO control system
which controls many output variables.
For an automatic multi-task control systems used in
marine vessels equipped with a propeller and rudder
the control program should include the following
control modes:
 one control (autopilot) without RRD: course
control by rudder;
 one control (autopilot) with RRD: course
control and roll damping by rudder;
 two controls (course and speed) by rudder and
engine shaft rpm or CCP pitch angle without
and/or with RRD; and
 three controls (course, speed and positions)
without and/or with RRD.
The recursive optimal control algorithm is a
combination of an optimal LQG control law and
recursive identification algorithm. The recursive
identification algorithm is either the recursive least
squares algorithm or the recursive prediction error
algorithm. Interested readers can find more
information on this control algorithm in Appendix 1

and in [12][14].

3. Brief Description of Model-scaled
Vessel and Electronics
Estimated
position and
velocities
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2.1 Model-scaled Container Vessel
In order to develop software control programs and
verify the control algorithms for multitask mission
control systems model-scaled surface vessels
equipped with propulsion system and steering
mechanisms and instrumentation electronics are
needed. It is very ideal if a full-scaled vessel for
experiments is available. However operating a full-
scaled vessel costs a lot of money. A model-scaled
container vessel named “P and O Nedlloyd” is shown
in Fig. 2. The main particulars of the full-scaled
vessel and the model are given in Table 1.


Fig. 2 Model-scaled vessel for experiments

Table 1 Vessel and model main particulars

Full Scale

Vessel
Model (Scale
1:100)
LBP
247 m
2470 mm
B
32 m
320 mm
Draught
12 m
120 mm
Δ
64000 tonnes
62.4 kg
L/B
7.72
7.72
B/T
2.67
2.67

Fig 3 shows onboard electronic devices. The model is
equipped with a twin propeller operated by a dc
motor, rudder controlled by a servo motor and
controller, mass carriage mechanism operated by a dc
motor, a mobile (target) computer (PC\104) with
wireless/Ethernet and DAQ cards, a 6-DOF IMU and
GPS device (Crossbow NAV420CA) and batteries.
The mass carriage mechanism is used to investigate

parametric roll motion and rudder-roll damping
system.

Fig. 3 Onboard electronic devices
As shown in Fig. 3 the target computer communicates
with a host computer via an Ethernet cable or wireless
communication device. In the host computer there is
an integrated environment of software that allows the
user to develop control programs. Software includes
MATLAB/Simulink, Real-time Workshop, RT-LAB
(product of Opal-RT), MS Visual Studio, LabVIEW
and Control Design and Simulation Module and
Python.

2.2 Prototype “GreenLiner” with Electrically-
operated Waterjet
At the AMC propulsion lab there is a prototype of 11-
metre boat equipped with an electrically-operated
waterjet as shown in Fig. 4. The heading is control by
a waterjet nozzle. This prototype allows one man to
ride. GreenLiner’s principal particulars are given in
Table 2.


Fig. 4 GreenLiner, a prototype boat equipped with
electrically-operated waterjet

Table 2 Principal particulars of GreenLiner)
Item
Original

Spec
48V Electric
Spec
96V HiPo
Config
Built: 1999
Greg Cox,



L.O.A:
7.75 m


L.W.L:
6.15 m
TBA
TBA
B.O.A:
1.06 m


Draught:
164 mm
244 mm.
200 mm.
Displacement:
348 kg
648 kg.
540 kg.

Powering



Fuel
Petrol (a
cup full)
4off 210A-
hr LA
Batteries
8off HiPo
80 A-hr.
LA
Batteries
Engine/
motor
B&S 18 hp
Vanguard
engine
2 cylinder,
4-stroke,
air-cooled.
4hp
HiTorque
Industrial
Technik DC
electric
Motor.
Parallel
fields

10 hp
HiTorque
Industrial
Technik
DC
electric
motor
Series
fields
Construction
Ply
(Australian
Plantation
Hoop Pine)


Cruise Speed:
17 knots
7 knots.
11 knots.
Propulsor:
Doen DJ60
water-jet
16B5.
12A4.
16B5.
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In order to develop automatic control systems for
GreenLiner, the current steering system must be
upgraded with an electro-hydraulic steering machine
and data acquisition card.

2.3 Full-scaled and Model-scaled Bluefin
AMC has a training fishing vessel that can be used for
full-scaled experiments as shown in Fig. 5. Main
particulars of full-scaled Bluefin are given in Table 3.



Fig. 5 Full scaled Bluefin

Table 3 Main particulars of Bluefin

Length OA
34.50 m
Length BP
32.00 m
Breadth
10.00 m
Maximum draft
4.40 m
Deadweight
53.60 t

AMC also has a model scaled Bluefin as shown in
Fig. 6.




Fig. 6 Model-scaled Bluefin (scale 1:20)

4. Development of Software Controller
Programs
Computer simulation study done with non-linear
mathematical models of two vessels in [11] has
shown the feasibility of the automatic multitask
manoeuvring system using recursive optional control
algorithm. As the second step to realise the multitask
manoeuvring system, model-scaled experiments need
to be conducted to verify the methods.
Real-time measurement and control of a surface
vessel is done by MATLAB/Simulink and RT-LAB
software. The equipment for real-time measurement
and control is shown in Fig. 6. The model-scaled boat
with target computer and electronics is shown in Fig.
9. The target computer is installed with real-time
operating system QNX 6.3 and RT-LAB software,
and the host PC (with Windows) is installed with
MATLAB/Simulink and RT-LAB software.
Controller programs are developed with Simulink. A
sample real-time control program is given in Fig. 8.















Fig. 7 Arrangement of target and host PCs with
sensors and actuators



Fig. 8 Real-time control program developed with Simulink
Target
computer
& DAQ
Host
computer
Ethernet or
wireless
Actuators (propeller motor drive, mass
carriage motor drive, rudder servo
motor controller
Sensors: GPS/6-DOF
IMU, encoders etc.
Sensors:
Required software:
MATLAB/Simulink, Real-
time Workshop, RT-LAB

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A real-time control program was made with Simulink
in the RT-LAB environment. An RT-LAB program of
Oral-RT (www.opal-rt.com), fully integrated with
MATLAB/Simulink®, is a real-time simulation
software environment that provides with a
revolutionised way in which model-based design is
performed. Fig. 9 shows the RT-LAB window. The
software required consists of RT-LAB software,
MATLAB/Simulink, Real-time Workshop and a
C/C++ Compiler. Using the RT-LAB software the
real-time control program is made and run in the
following procedure:
 create and edit Simulink model
 compile the Simulink model to C code;
 assign nodes (target) for the Simulink
program;
 load the Simulink program to the target
computer, then the user-interface console
window (as shown in Fig. 11) that allows user
to run the control program appears; and
 execute the Simulink program.



Fig. 9 RT-LAB Window



Fig. 10 P and O Netlloyd with electronics


Fig. 11 Real-time control program (SC-Console window) developed with Simulink
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A series of real-time control programs have been
developed with Simulink and RT-LAB as follows:
 Program 1: Simulink model to control
propeller;
 Program 2: Simulink model to control servo
motor (rudder angle);
 Program 3: Simulink model to control both
propeller and servo motor
 Program 4: Simulink model to receive data
from Crossbow NAV420CA (GPS/IMU)
 Program 5: Simulink model to control load
carriage mass to investigate effect of changing
load.
 Program 6: Combined program for tasks in 1,
2, 3, 4, and 5 to test functionality of the open-
loop system;
 Program 7: Simulink model for autopilot (e.g.
PID control, recursive optimal control);
 Program 8: Simulink model for autopilot and
rudder-roll damping, to investigate of mass

carriage mechanism on roll motion;
 Program 9: Simulink model for autopilot,
rudder-roll damping and speed control, to
investigate effect of mass carriage mechanism,
speed and course on roll motion (parametric
roll);
 Program 10: Simulink model for trajectory
tracking manoeuvres (search and rescue
mission);
 Program 11: Simulink model for trajectory
tracking (trawling);
 Program 12: Simulink model for automatic
berthing and unberthing manoeuvres;
 Program 13: Simulink model for automatic
mooring and anchoring;
 Program 14: Simulink model for an integrated
bridge with all above functions;

5. Design of Experiments

Experiments can be conducted using a free-running
model in the AMC model test basin (MTB) (Fig. 11).


Fig. 11 Model test basin and free-running model

Table 4 General specifications of MTB

Length


35 metres

Width

12 metres

Water depth

0 to 1.0 metres

Model towing carriage speed

0 to 3.8 metres/second

Typical model lengths

2 to 6 metres


The MTB has been equipped with the following
ancillary equipment and instrumentation devices:
 multi-element wave generator;
 non-contact digital video motion capture
system;
 variable speed model towing mechanism;
 variable speed wind generator;
 votating arm mechanism;
 multiple wave damping devices;
 wide array of single and multi-axis force
transducers;

 wide array of wave measurement devices
 wide array of video cameras (including
underwater);
 acoustic Doppler Velocimeter (measurement
of currents);
 pressure transducers;
 displacement transducers;
 accelerometers; and
 multi-channel digital data acquisition systems.
The following experiments will be conducted:
 Experiment 1: zigzag test (open-loop system);
 Experiment 2: turning circle test (open-loop
system);
 Experiment 3: Course keeping and changing
(autopilot);
 Experiment 4: Autopilot and rudder-roll
damping
 Experiment 5: Autopilot, rudder-roll damping
and speed control;
 Experiment 6: Trajectory tracking control for
search and rescue mission;
 Experiment 7: Trajectory tracking control for
trawling;
 Experiment 8: Automatic berthing and
unberthing manoeuvres; and
 Experiment 9: Automatic mooring and
anchoring manoeuvres.
Some proposed experiments are shown in Fig. 12
through 15.


Fig. 12 IMO expanding square pattern with 1 and 2
controls
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Fig. 13 IMO sector search pattern with 1 and 2 controls



Fig. 14 Rudder roll stabilisation to reduce parametric roll
in head seas



Fig. 15 Berthing and unberthing

6. Possible Applications
The automatic multitask manoeuvring system is
suggested to be working in some modes as follows
 autopilot and RRD at high seas;
 the function of manoeuvres for maritime
search and rescue mission should be
compulsory for all merchant vessels in order
to enhance safety at seas;
 manoeuvring information and monitoring
system for the captain (deck officers) and
pilot; and

 manoeuvrability test system.
Fig. 17 illustrates a proposed multi-task automatic
manoeuvring system with an LCD and Control Panel
in which there are different working mode buttons
and keyboard. The multitask manoeuvring system can
be developed with a microcontroller and/or embedded
computer.













Fig 17 A proposed application for various modes (AUTO =
autopilot, RRS = rudder-roll stabiliser, MT =
manoeuvrability tests, SAR = maritime search and rescue
mission, INFO = information when manoeuvring, GNSS =
global navigation satellite system receiver

In addition to the above proposed system the
multitask manoeuvring system can be developed
further to the following for educational and research
purposes:

 automatic berthing/unberthing system;
 automatic mooring and anchoring system;
 dynamic positioning system;
 water sample taker;
 spilling area measuring autonomous vessel;
 power control and management system.
In comparison with ROVs/AUVs, advantages of using
autonomous surface vessels for various missions at
seas are:
 solution to energy issue;
 solar energy; and
 difficulty in communication between the target
computer and the host computer.

7. Conclusions
In conclusion the paper has discussed the following
points:
 background of the multitask manoeuvring
system;
 description of experimental facilities;
 development of software controller programs;
 proposed experiments using model-scaled
vessel and model test basin; and
 proposal of possible applications.
Recommendations for future work are:
 continue to develop real-time control programs
with Simulink and LabVIEW;
 conduct model-scaled experiments and collect
data for analysis;
 analyse experimental data and develop

nonlinear mathematical models for vessels;
and
 develop hardware and software for a multitask
mission manoeuvring system and test its
functionalities under lab conditions.
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Acknowledgements
This paper is a continuity of the AMC IGS granted
research project financially supported by the AMC
Research and Higher Degrees by Research Committee
during 2005-2007. The author would like to thank the
Research Office for financial support.

References
[1] Leonessa, A., Madello, J., Morel, Y. and Vidal,
M Design of a Small, Multi-Purpose,
Autonomous Surface Vessel. DOI: 0-933957-
30-0.
[2] Caccia, M Autonomous Surface Craft:
Prototypes and Basic Research Issues.
[3] Baumann, M. and Baur, O Autonomous
Surface Vessel for Toxic Cynobacteria Bloom
Examination.
[4] Caccia, M., Bono, R., Bruzzone, Ga., Bruzzone,
Gi. And Stortini, A.M Design and Exploitation
of an Autonomous Surface Vessel for the Study
of Sea-Air Interatcions. IEEE Explore. 0-7803-

8914-x/05. 2005.
[5] Munjal, A Development of Automatic
Manoeuvring Systems for Surface Vessels –
Simulation and Design of Model Scale
Experiments, BE (MOS) Thesis. AMC,
Launceston, 2011.
[6] Roberts, G.N. and Sutton, R (Editors).
Advances in Unmanned Marine Vehicles. The
Institute of Electrical Engineers, 2006.
[7] Fossen, T.I Nonlinear Modelling and Control
of Underwater Vehicles, PhD Thesis.
Norwegian Institute of Technology, 1991.
[8] Fossen, T.I Handbook of Marine Craft
Hydrodynamics and Motion Control. John
Wiley and Sons Inc. 2011.
[9] Fossen, T.I Marine Control Systems –
Guidance, Navigation and Control of Ships,
Rigs and Underwater Vehicles. Marine
Cybernetics, Trondheim, Norway, 2002.
[10] Fossen, T.I Guidance and Control of Ocean
Vehicles. John Wiley and Sons, 1994.
[11] Wadoo, S.A. and Kachoroo, P Autonomous
Underwater Vehicles: Modeling, Control
Design, and Simulation. CRC Press, 2011.
[12] Nguyen, H.D Multitask Manoeuvring Systems
Using Recursive Optimal Control Algorithms.
Proceedings of HUT-ICCE 2008, pp. 54-59 Hoi
An, Vietnam, 2008.
[13] Nguyen, H.D Recursive Identification of Ship
Manoeuvring Dynamics and Hydrodynamics.

Proceedings of EMAC 2007 (ANZIAM), pp.
681-697, 2008.
[14] Nguyen, H.D Recursive Optimal Manoeuvring
Systems for Maritime Search and Rescue
Mission, Proceedings of OCEANS'04
MTS/IEEE/TECHNO-OCEAN'04 (OTO’04),
pp. 911-918, Kobe, Japan, 2004.
[15] West, W.J. Remotely Operated Underwater
Vehicle, BE Thesis. Australian Maritime
College, UTAS, Launceston, 2009.
[16] Gaskin, C.R Design and Development of
ROV/AUV, BE Thesis. Australian Maritime
College, UTAS, Launceston, 2000.
[17] Woods, R.L. and Lawrence, K.L Modeling and
Simulation of Dynamic Systems. Prentice-Hall
Inc. Upper Saddle River, NJ, 1997.
[18] Kulakowski, B.T., Gardner, J.F. and Shearer,
J.L Dynamic Modeling and Control of
Engineering Systems. Cambridge University
Press, 2007.
[19] Antonelli, G Underwater Robots – Motion and
Force Control of Vehicle-Manipulated Systems,
2
nd
Edition. Springer, 2006.
[20] Bose, N., Lewis, R., Adams, S Use of an
Explorer Class Autonomous Underwater Vehicle
for Missions under Sea Ice, 3rd International
Conference in Ocean Engineering, ICOE 2009,
IIT Madras, Chennai, India. Keynote

presentation, 2009.
[21] Burcher, R. and L. Rydill Concepts in
Submarine Design. Cambridge University Press.
[22] Christ, R.D. and R.L. Wernli Sr (2007). The
ROV Manual – A User Guide for Observation
Class Remotely Operated Vehicles. Butter-
Heinemann (Elsevier). Oxford, 1994.
[23] Griffiths, G. (Editor) (2003). Technology and
Applications of Autonomous Underwater
Vehicles. Taylor and Francis.
[24] Groves, P.D GNSS, Inertial, and Multisensor
Integrated Navigation Systems. Artech House,
2008.

Biography

Dr. Hung Nguyen is a lecturer
in Marine Control Engineering
at National Centre for
Maritime Engineering and
Hydrodynamics, Australian
Maritime College, Australia.
He obtained his BE degree in
Nautical Science at Vietnam
Maritime University in 1991,
then he worked as a lecturer there until 1995. He
completed the MSc in Marine Systems Engineering in
1998 at Tokyo University of Marine Science and
Technology and then the PhD degree in Marine
Control Engineering at the same university in 2001.

During April 2001 to July 2002 he worked as a
research and development engineer at Fieldtech Co.
Ltd., a civil engineering related nuclear instrument
manufacturing company, in Japan. He moved to the
Australian Maritime College, Australia in August
2002. His research interests include guidance,
navigation and control of marine vehicles, self-tuning
and optimal control, recursive system identification,
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real-time control and hardware-in-the-loop simulation
of marine vehicles and dynamics of marine vehicles.

Appendix 1 Summary of Control
Algorithms
The desired trajectory is one of the following
manoeuvres:
 IMO expanding square pattern for search and
rescue mission (Fig. A1);
 IMO sector pattern for search and rescue
mission (Fig. A2)
 Williams’ turning circle manoeuvre;
 Any trawling trajectory; and
 Any planned manoeuvres;
The reference trajectory generator in the guidance
system is a vessel simulator using the Nomoto’s first-
order manoeuvring model. Details can be found in
[12][14].

The desired heading angle
d

is calculated by the
LOS technique as follows:
k+1
dk
k1
yy
atan2
xx







(A1)
When the ship is moving along the desired trajectory,
a switching mechanism for selecting the next way-
point is necessary. The next way-point (x
k+1
,y
k+1
) is
selected when the ship lies within a circle of
acceptance with a radius R0 around the current
waypoint (x
k

,y
k
) satisfying:
   
22
2
k k 0
x x y y R   
(A2)
















Fig. A1 IMO expanding square pattern

The value of R
0
is often chosen as two ship lengths,

i.e. R
0
= 2L
pp
in [8][12][14].
A reference trajectory generator using a vessel
simulator is constructed. The vessel model used in
this paper is of Nomoto’s first-order model with
forward speed dynamics and described as follows:
 
d d d
x U cos
(A3)
 
d d d
y U sin
(A4)
where (x
d,
y
d
) is the desired position, U
d
> 0 is the
desired speed and ψ
d
is the desired heading. The
forward speed dynamics is
 
2

x d w d d x
m m U 0.5 C AU    
(A5)


















Fig. A2 IMO sector pattern


















Fig. A3 LOS technique

where ρ
w
is the density of sea water, C
d
is the drag
coefficient, A is the projected cross-sectional area of
the submerged hull of ship in the x-direction, and (m
– mx) is the mass included hydrodynamic added
mass. The course dynamics is chosen as
dd
r
(A6)
d d r
Tr r K  
(A7)
where T and K are ship manoeuvrability indices, r
d
is
the desired yaw rate and δ

r
is rudder angle. The
guidance system has two inputs, thrust τ
x
and rudder
angle δr. The guidance controllers can be chosen as PI
and/or PID types.
When the ship goes along the desired trajectory, the
reference heading angle can be adjusted by the
exponential decay technique as shown in Fig. A4.
Heading and position errors when the ship is moving
along the desired trajectory are calculated as follows

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1 d d
2 d d
3d
e (x x)cos (y y)sin
e (x x)sin (y y)cos
e
    
   
   
       
   
   
  

   
e
(A8)
where e
1
= path tangential tracking error
e
2
= cross-track error (normal to path)
e
3
= heading error








Fig. A4. Exponential decay technique
If the rudder-roll damping controller is switched on
the vector of errors including roll error (e
4
) becomes
1
dd
2
dd
3

d
4
e
(x x)cos (y y)sin
e
(x x)sin (y y)cos
e
e
0
    




     





  





e
(A9)
If the speed controller is on the speed error will be
calculated

5d
e U U
(A10)

Recursive Optimal Control Algorithm
In order to design control systems with multitask
missions, mathematical models for the steering and
manoeuvring dynamics are applied. For example, the
ship steering dynamics for the automatic manoeuvring
system is represented by an MAXR as follows

(t 1) ( ) (t) ( ) (t)  xFθ xGθ u
(A11)

(t) ( ) (t)yCθ x
(A12)
where x(t) is the state vector, u(t) is the input vector,
y(t) the output vector and F(θ), G(θ) and C(θ) are
system matrices dependent on parameter vector θ.
The unknown system parameters are estimated by one
of appropriate recursive estimation methods. An
optimal control law is applied. The optimal recursive
control algorithm is illustrated by the flowchart as
shown Fig. A5.
Summary of RPE Algorithm: The RPE algorithm is to
minimize the following criterion function:
       
T1
1
V t t t

2

θ ε Λε
(A13)
where
Λ
is a positive definite matrix, and Gauss-
Newton search direction is chosen as:
       
11
f t t t, t,

 H ψ θ Λε θ
(A14)
where H(t) is the Hessian, the second derivative of the
criterion function with respect to θ and ψ(t,θ) is the
gradient of the predicted output with respect to θ and
ε(t,θ) is the vector of the predicted errors. The RPE
algorithm consists of the following steps:

Fig. A5 Flowchart for the optimal recursive control
algorithm [12]

Step 1: Calculate the predicted error vector using
     
ˆ
t t tε yy
(A15)
Step 2: Update the weighting matrix by
           

T
t t 1 t t t t 1

     

Λ Λ ε ε Λ
(A16)
Step 3: Update the Hessian:
             
1T
t t 1 t t t t t 1


    

HH ψ Λψ H
(A17)
Step 4: Update the estimated parameters:
             
11
t t 1 t t t t t

  θ θ H ψ Λε
(A18)
Step 5: Update the predicted output:
     
T
ˆ
t t ty 
(A19)

Step 6: Calculate the gradient of the predicted output
by
   
d
ˆ
t t,
d






y
(A20)
Step 7: Update data and loop back to Step 1.
Note that the step size factor α(t) is calculated as
 
1
t
1t


(A21)
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