International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 4
Number 2
June 2010
151
1 INTRODUCTION
Nowadays, many ships are equipped with thrusters
to support manoeuvring activities. By using these
thrusters, the full mission autopilot can control ves-
sel fully automatic from a quay to other quay.
During a voyage, the controlling vessel can be di-
vided into 3 phases: sailing phase (when vessel runs
at open sea); manoeuvring phase (when vessel runs
in narrow and resisted water); transitional phase
(when vessel changes from sailing mode to manoeu-
vring mode).
In the transitional phase, the vessel is reduced
speed from sailing speed (at which, the vessel can be
controlled just by the rudder) to the manoeuvring
speed (at which, the rudder’s effect is too small and
vessel mainly control by thrusters and main propel-
ler). The autopilot’s task in this phase is to reduce
the vessel speed to the required speed (manoeuvring
speed) during approaching to the waypoint and also
keep the vessel moving on the set path with the set
heading.
This paper presents the algorithm and the experi-
ences results by using simulator and scaled model of
the autopilot, which is designed and researched by
the authors (Leszek et al. 2008).
2 THE OBJECT OF CONTROL
The training ship “Blue Lady” is the floating, auton-
omous scale model of the VLCC tanker. It is used by
the Foundation for Safety of Navigation and Envi-
ronment Protection at the Silm Lake near Ilawa in
Poland for training navigators. The ship is built of
the epoxies resin laminate in 1:24 scale. It is
equipped with battery-fed electric drives and the
control steering post at the stern. The model is
equipped with the main propeller, a rudder, two tun-
nel thrusters, and two azimuth pump thrusters which
can be rotated within limited angle ranges. The con-
troller presented in the paper just controls two tunnel
thrusters and the main propeller for manoeuvring
tasks. The arrangement of the model is shown in
Figure 1, while the main characteristic data are given
in the Table 1.
Table 1. The main characteristic data of the model
___________________________________________________
Length over all LOA 13.78[m]
Beam B 2.38[m]
Draft (average) - load condition Tl 0.86[m]
Displacement - load condition D 22.83[T]
Speed 3.10[kn]
___________________________________________________
Figure 1. The arrangement of the model “Blue Lady”
Problem of Stopping Vessel at the Waypoint
for Full-Mission Control Autopilot
L. Morawski
Gdynia Maritime University, Gdynia, Poland
V. Nguyen Cong
Vietnam Maritime University, Haiphong, Vietnam
ABSTRACT: The paper presents a controlling method to control vessel of a full mission autopilot at the tran-
sitional phase when vessel reduce speed from navigation speed down to manoeuvring speed while she access-
es to the manoeuvring waypoint, where the vessel is started control in manoeuvring mode. The vessel is con-
trolled by three propellers: the bow thruster, the stern thruster and the main propeller. The autopilot is
designed with 5 fuzzy logic controllers. It works in Matlab-Simulink and tested on a scaled physical model of
a tanker in the lake environment.
152
3 THE REFERENCE FRAMES AND THE
DEFINITIONS
There are two reference frames used in control. They
are Geographic reference frame (x
n
y
n
) and Body ref-
erence frame (Fig. 2).
Geographic Reference Frame (x
n
y
n
or n-frame):
The coordinate system x
n
y
n
is defined relative to the
Earth reference ellipsoid (World Geodetic System
1984). In this coordinate system the x-axis points
towards true North, while the y-axis points towards
East (Fosen 2002).
Body Reference Frame (x
b
y
b
or b-frame): This is
moving coordinate frame which is fixed to the ves-
sel. The origin O
b
of the coordinate system is chosen
to coincide with the center of gravity (CG) when CG
is in the principal plane of symmetry. The axes are
defined as x - longitudinal axis, directed from aft to
fore and y- transversal axis, directed to starboard
(see Fig. 2) (Fosen 2002)
Figure 2. Reference frames
R – reference point, required position of the vessel
dx – position deviation in x-axis of b-frame
dy – position deviation in x-axis of b-frame
ψs – set heading
dψ – course deviation
The position of vessel is fixed by GPS in n-frame
while the signals for control (deviations) are meas-
ured in b-frame. The transfer functions of coordi-
nates and velocities between these frames as follow-
ing:
T
nn
n
b
T
T
ObnObn
n
b
T
bbb
ryxRrvu
yyxxRyx
][][
][][
=
−−= 0
ψ
(1)
where
1
100
0
0
−
−
=
ψψ
ψψ
cossin
sincos
n
b
R
(2)
Reference point R: This is a point on which the
vessel position has to be maintained. The vessel
movement will be controlled through this point
(Vinh 2007).
4 ALGORITHM OF CONTROL AND
AUTOPILOT DIAGRAM
The diagram of the autopilot is shown in Figure 3.
The Positioning regulator has task of controlling
main engine and thrusters to keep vessel at the refer-
ence point with the set heading. The Trajectory
regulator has task to steer the ship along a strait path
segment. The Trajectory controls rudder and main
engine of the ship. Depending on the control mode,
the Signals selector block switches and connects the
output signals of the regulators to the propulsion
system.
Figure 3. Regulator diagram
As mentioned in the section 1, in the transitional
mode, the autopilot has to 1) keep the vessel course
stable in the path segment direction and the vessel
movement stable on the path segment; 2) control the
braking force to obtain the speed that is within the
manoeuvring speed range when the vessel arrived
exactly at the waypoint.
The braking up of a vessel is carried out in 2
steps:
Step 1: Starting braking up at the braking distance
d
braking
. When the distance from the vessel to the
waypoint is less than or equal d
braking
, the auto pilot
changes the control mode from trajectory mode to
transitional mode.
Step 2: Adjusting the braking up force. In this
step, the autopilot controls the rudder, thrusters to
keep the vessel moving on the set path with the re-
quired heading and it also controls the main engine
to reduce the vessel speed.
The algorithm used in each steps is presented in
detail in the next subsections.
dx
dy
R
O
b
y
b
y
n
x
n
O
n
ψ
s
d
ψ
x
R
y
R
y
Ob
x
Ob
x
b
Trajectory
regulator
n
δ
Positioning
regulator
Signals selector
n
δ
p
b-th
p
s-th
p
b-th
p
s-th
Speed cal-
culation
V
ψ
k
x
k
, y
k,
x
k+1
, y
k+1
, V
k
x
R
, y
R
,
ψ
k
x, y,
ψ
, r
x, y,
ψ
, r
xPC
Inter-
face
Processing
HOST PC
xPC
x, y,
ψ
, r
n
153
4.1 Calculating a breaking distance d
braking
Figure 4. The braking distance d
braking
in transitional phase
The braking distance d
braking
is the distance to the
first waypoint of the manoeuvring segment, at this
distance the autopilot should change from the trajec-
tory mode to the transitional mode to access the
waypoint correctly (Fig. 4).
In this autopilot, the braking distance d
braking
is
calculated by using the following formula
eufdcubuaud
braking
+++++= )(
234
(3)
In the formula (3), u is the surge of the vessel.
The coefficients of equation (3) are defined from the
results of the experiment. The coefficient f is the
time taken to change the engine mode of the vessel.
Other coefficients a, b, c, d, e are defined by the ex-
periment as following: “Vessel is full loading, runs
ahead at maximum speed in the wind on a straight
path. At a moment, change engine to dead slow
astern then record the vessel speed and the passing
distance of vessel until the vessel completely stops.”
The graph in Figure 5 is an example of the exper-
iment result. On the basis of the recorded data, the
coefficients of formula (1) are defined by using
Horner’s method.
Figure 5. The relation between the braking distance d
braking
and
speed of the Blue Lady model when the engine mode is set to
dead slow astern
The dead slow astern engine mode was used for
transitional mode after many experiments on the
lake with the Blue Lady model. During braking up,
the engine runs astern while vessel moves forward,
the chaotic water flow increases and causes abnor-
mal movement of the vessel. If a higher engine
mode is used, the chaotic flow will be stronger then
the thrusters and the rudder will be not strong
enough to manage the vessel.
4.2 Adjusting the braking up force
In the transitional phase, the Processing block sets
and controls the reference point R moving along the
path segment; and sets the heading as same as direc-
tion of the path segment (see Fig. 6).
When the vessel speed is enough for rudder ef-
fect, the Trajectory regulator controls the rudders to
support thrusters keeping the vessel course. When
the speed is too low, the signal from Trajectory reg-
ulator is cut off.
The Positioning regulator controls the vessel
heading by the thrusters and braking force by main
propeller to obtain vessel speed within the manoeu-
vring speed range when the vessel reaches the way-
point.
As mentioned in subsection 4.1, the braking force
is fixed by the engine mode dead slow astern. So, to
adjust vessel speed, the autopilot just changes the
engine vessel to dead slow astern, stop or dead slow
ahead mode. The engine mode is selected by com-
paring the actual distance from vessel to the way-
point with the expected passing distance S of the
vessel.
Figure 6. Braking up a vessel
The expected passing distance S is calculated by
following formula:
a
uu
S
2
2
1
2
2
−
=
(4)
0 20 40 60 80
100 120 140 160 180 200
0
0.2
0.4
0.6
0.8
1
1.2
1.4
braking distance [m]
vessel speed [m/s]
Maneuvering
segment
Trajectory
segment
d
braking
d
braking
R
x
k+1
,
y
k+1
ψ
k
d
to waypoint
R
x
k+1
,
y
k+1
x
k
, y
k
V
u
S
R
u<0.
a)
b)
c)
u
Maneuvering control area
154
where
u
1
: actual vessel surge
u
2
: the required speed (surge) at the waypoint, it
should be within the manoeuvring speed range. In
this autopilot, the value of u
2
is set at 0
a : average acceleration of a vessel while speed
changes from u
1
to u
2
S : the distance which vessel passed while speed
changes from u
1
to u
2
.
As mentioned above, the engine mode for braking
is fixed at dead slow astern so the braking force may
be treated as a constant force. Hence, the average
acceleration a can be treated as constant and it can
be calculated as:
12
12
tt
uu
a
tt
−
−
=
(5)
The Processing block reads vessel surge every
sampling period and calculates acceleration a as
formula (5). From values of a, u
1
(actual surge), u
2
(required surge), the Processing block calculates the
expected distance S.
5 EXPERIMENTS AND RESULTS
5.1 Experiment using simulator
The experiments on braking up a vessel were per-
formed using computer simulation as well as the
model in real environment. In computer simulation,
a vessel was tested braking up from four different
speeds with respect to four engine modes: full ahead,
half ahead, slow ahead and dead slow ahead (Ta-
ble 2).
In the experiment, the vessel was running from
waypoint A(75768, 71540) to waypoint B(75314,
71540) on the course of 180
o
(Table 2). The autopi-
lot’s task was to stop the vessel at waypoint B. While
stopping vessel, the heading had to be kept at 180
o
and the vessel track had to be kept close to the path
segment AB.
While the vessel was running steadily along path
segment AB, the Processing block calculated brak-
ing distance d
braking
basing on the actual vessel speed
using formula (3). Depending on the instant speed,
these distances d
braking
were 192 m, 152 m, 100 m
and 49 m with respect to the speed of 1.25 m/s, 1.00
m/s, 0.74 m/s and 0.47 m/s (Fig. 7).
Table 2. Set path of braking up experiments
___________________________________________________
Experiment Waypoint A Waypoint B Speed[m/s]
No. X[m] Y[m] X[m] Y[m] /engine mode
___________________________________________________
No. 1 75768 71540 75314 71540 1.31/full ahead
No. 2 75768 71540 75314 71540 1.00/half ahead
No. 3 75768 71540 75314 71540 0.70
/slow ahead
No. 4 75768 71540 75314 71540 0.50
/d.slow ahead
___________________________________________________
When the distance from the vessel to waypoint B
was less than d
braking
, the autopilot changed the con-
trol mode from the trajectory mode to the transition-
al mode. From this moment t
1
in Figure 7, the main
engine was controlled by the Processing block to ad-
just braking force; two thrusters were controlled by
the Positioning regulator to maintain vessel course;
the rudder was controlled by the Trajectory regulator
until the vessel speed was less than 0.1 m/s.
Figure 7. Track of the vessel in the braking up experiment us-
ing computer simulation. Position marked every 60 s; u – surge
of vessel at the starting of the transitional mode.
When the vessel speed reached the manoeuvring
speed range or the vessel was in manoeuvring area
around waypoint B, the autopilot changed the con-
trol mode to the manoeuvring mode (t
2
). In experi-
ments 1, 2 and 3 (Fig. 7 a, b, c), the vessel speed
reached manoeuvring speed at about 10m before the
target waypoint B (position of t
2
in Fig. 7). From this
moment t
2
, the vessel was controlled using the
manoeuvring mode and it took about five minutes to
move to the waypoint B.
Figure 8. Recorded data of the braking up experiment 1
d
to WP
– the distance from the vessel to the target waypoint.
71500 20 40 60 80
75 320
75 340
75 360
75 380
75 400
75 420
75 440
75 460
75 480
75 500
75 520
75 540
75 560
75 580
East [ m]
North [m]
71500 20 40 60 80
East [ m]
71500 20 40 60 80
East [ m]
71500 20 40 60 80
East [ m]
192 m
152 m
100 m
49 m
t
1
t
2
t
2
t
1
u = 1.25
u = 1.00
u = 0.74
u = 0.47
a) Experiment 1
B
B
B
B
B
B
B
B
b) Experiment 2
c) Experiment 3
d) Experiment 4
t
1
t
2
t
1
t
2
t
1
t
2
-5
0
5
y err.
[m]
175
180
185
ψ
[
o
]
0
10
20
d
to
WP
[m]
0
1
2
u[m/s]
-1
0
1
b. thru
-1
0
1
s. thru
-500
0
500
r.p.m.
0 100 200 300 400 500 600 700 800 900
-10
0
10
δ
[
o
]
ti me [s]
155
Figure 9. Recorded data of the braking up experiment 2
d
to WP
– the distance from the vessel to the target waypoint.
Figure 10. Recorded data of the braking up experiment 3
d
to WP
– the distance from the vessel to the target waypoint.
Figure 11. Recorded data of the braking up experiment 4
d
to WP
– the distance from the vessel to the target waypoint.
In the experiment 4, the vessel approached the
maneuvering area of waypoint B but the speed was
higher than the maneuvering speed. In this situation,
the autopilot changed also the control mode to the
manoeuvring mode. After that, the Positioning regu-
lator immediately set the main engine to full astern
mode to stop the vessel quickly (see Fig. 11).
The Figures 8-11 show the recorded parameters
of the four experiments. The vessel was stopped at
the waypoint B with position deviation less than 0.5
m and the heading drift in these slowdown manoeu-
vres was less than 2
o
.
5.2 Experiment using scaled model Blue Lady
The next experiment was performed with the Blue
Lady model on the lake. In this experiment, the ves-
sel was running from waypoint A(75273, 71480) to
waypoint B(74952, 71754) with the engine mode
slow ahead (r.p.m = 240 ∼ V = 0.6 m/s). The task of
the autopilot was to reduce the vessel speed to the
manoeuvring speed at waypoint B. At waypoint B,
the vessel was turned to the heading of 150
o
and
then moved to waypoint C(74978, 71780).
At the speed of 0.6 m/s, the braking distance was
72 m (using formula 3). When the distance from the
vessel to waypoint B was less than 72 m, the autopi-
lot changed the control mode to the transitional
mode. The Processing block controlled the braking
force by the main engine r.p.m., while the Position-
ing regulator and Trajectory regulator controlled the
heading by the two thrusters and the rudder.
At the moment t
2
, when the model was within the
manoeuvring range of the waypoint B, the autopilot
changed the control mode to the manoeuvring mode.
From t
3
to t
4
the vessel turned to the heading of 150
o
as required in the set path.
Table 3. Set path of experiment No. 5
___________________________________________________
Way X [m] Y [m] Set speed Set head- Control mode
-points [m/s] ing [
o
]
___________________________________________________
A 75273 71480
B 74952 71754 A→B: 0.6 A→B: 130 Trajectory&
at B: 150 Transitional
C 74978 71780 B→C: B→C: 150 Manoeuvring
not set
___________________________________________________
From t
4
to the end of the experiment, the vessel
moved translationally to waypoint C with the head-
ing of 150
o
.
-5
0
5
y err.
[m]
175
180
185
ψ
[
o
]
0
10
20
d
to
WP
[m]
0
1
2
u[m/s]
-1
0
1
b. thru
-1
0
1
s. thru
-500
0
500
r.p.m.
0
100
200
300
400
500
600
700
800
900
1000
-10
0
10
δ
[
o
]
ti me [ s]
-5
0
5
y err.
[m]
175
180
185
ψ
[
o
]
0
10
20
d
to
WP
[m]
0
1
2
u[m/s]
-1
0
1
b. thru
-1
0
1
s. thru
-500
0
500
r.p.m.
0
100
200
300
400
500
600
700
-10
0
10
δ
[
o
]
ti me [s]
t
1
t
2
-5
0
5
y err.
[m]
175
180
185
ψ
[
o
]
0
10
20
d
to
WP
[m]
0
1
2
u[m/s]
-1
0
1
b. thru
-1
0
1
s. thru
-500
0
500
r.p.m.
0
100
200
300
400
500
600
700
800
900
-10
0
10
δ
[
o
]
ti me [s]
156
Figure 12. Experiment No. 5 from second 1000
th
to 1825
th
. The
positions are marked every 60 s.
Figure 13. Recorded data of experiment No. 5 from second
1000
th
to 1825
th
.
The recorded data is shown in Figure 13. Com-
pared to the results obtained using computer simula-
tion, the thrusters were working harder. The reason
of this is that the simulator did not simulate well the
effect of a chaotic water flow. In the experiment on
the lake, the chaotic water flow had a very strong ef-
fect on the model. In many experiments, the thrust-
ers were not powerful enough to manage the model
while braking up it by full astern or half astern en-
gine. That is why the autopilot brakes up a vessel
only by dead slow astern engine.
6 CONCLUSIONS
In simulation experiments, the model was stopped
completely with the position deviation less than 0.5
m around the set waypoint. In the experiment on the
lake in windy conditions, the final position deviation
was about 2 m. Compared to the length of the model
(13.75 m), the deviations are acceptable in practical
manoeuvrings. The heading deviations of the model
in this manoeuvre were less than 5o in all experi-
ments.
When vessel runs at full speed, to stop it the pass-
ing distance is 192 m (about 15 lengths of the ves-
sel). It is also can be accepted in the practice naviga-
tion.
REFERENCES
Rak A., Nguyen Cong V., Pomirski J, Morwaski L. 2005. Sim-
ulation and real-time control of scale ship model in Matlab-
Simulink environment. 16th Conference HYDMAN’05,
Ostroda, Poland
Fosen T.I., 2002. Marine Control Systems. Marine Cybernet-
ics, Trondheim, Norway.
Gierusz W. 2005. Simulation model of the ship handling train-
ing boat “Blue Lady”
Morawski L., Nguyen Cong V., Rak A. 2008. Full-Mission
Marine Autopilot Based on Fuzzy Logic Techniques. Gdy-
nia. Poland
Nguyen Cong V. & Morawski L. 2006 Track keeping autopilot
with fuzzy logic controller. 6th ASIA CONFERENCE.
Haiphong Vietnam
Nguyen Cong V., 2007. The synthesis of trajectory regulator
using fuzzy logic theory in a marine vessel autopilot. Gdy-
nia. Poland
-5
0
5
y err. [m]
120
140
160
ψ
[
o
]
-0.5
0
0.5
ψ
[
o
]
-0.2
0
0.2
v[m/s]
-0.2
0
0.2
0.4
0.6
u[m/s]
-1
0
1
b. thru
-1
0
1
s. thru
-500
0
500
r.p.m.
-10
0
10
δ
[
o
]
0
100
200
300
400
500
600
700
800
0
10
20
30
wind[m/s]
time [s]
71640
71660
71680
71700
71720
71740
71760
71780
74940
74960
74980
75000
75020
75040
75060
75080
East [ m]
North [m]
A
B
130
o
B
Set path
A l l k
Zoom 3x
150
o
C
t
1
t
2
72 m
