Ship automatic track keeping at low speed

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Ship Automatic Track keeping At Low Speed
MSc. Thanh-Dat Le1, Prof. Nam-kyun Im2, PhD. Van-Luong Tran3
1. Vietnam Maritime University, lethanhdat@vimaru.edu.vn
2. Mokpo National Maritime University, namkyun.im@mmu.ac.kr
3. Vietnam Maritime University, tranvanluong@vimaru.edu.vn
Abstract: There are lots of ship’s situations when operating from port to port such as with full speed
sailing, reducing speed inside traffic scheme, stopping at a certain area and berthing operation with
designed heading angle. However, the previous studies on ship automatic track -keeping controllers
have not been designed properly as they considered that the ship speed is stable and in constant value.
It seems improperly situation in practical maneuverings, especially when the ship entering to ports.
In this paper, the authors focus on studying on the activities of the ship inside traffic scheme until ship
is stopped at certain area before berthing. We considered ship operation at low speed and reducing speed
situation under disturbance effect. However, in low speed and disturbance’s influence, ship’s Track-
keeping is not easy. Extra auxiliary devices such as tug-boats, ship’s bow and side thrusters, etc. are also
needed. Without these assistances, other methods should be needed in order to help the ship that called
“Boosting effect”. “Boosting effect” study will be introduced in this paper and numerical simulations
for this effect were carried out to perform the ship auto track-keeping inside traffic scheme at low speed
under disturbance influence. The results of simulations showed good performance and this designed
control can be adapted in near future.
Keywords: Simulation; Track-keeping; Nonlinear expression; Wind effect; Boosting Effect.
1. Introduction
In the field of maritime safety system, various reports have been given on the research of ship automatic
Track-keeping control and ship automatic berthing control over a long time but they are distinct from
each other. Until the late 1970s, marine control studies were focused on the design of different
autopilots. While the classical proportional-integral-derivative (PID) autopilots perform reasonably well
in a specified performance envelope, their overall operational effectiveness is limited; this is due to the
fact that classical PID autopilots require manual adjustments to compensate for changes in environment
(wind and sea state) and in the dynamics of the ship. With the advent of accurate marine positioning
system installed on board, Track-keeping control for ships has been studied extensively during the
1980s.
Hasegawa, K. (1987) introduced an adaptive track keeping subsystem for automatic collision avoidance
system using fuzzy control which is described quite similar to human behaviors and easily linkable to
an expert system. Kallstrom (1999) suggested PID automatic track keeping algorithm for high speed
craft. Hwang, C. (2002) suggested a H∞-autopilots using PID-type controllers for collision avoidance.
His autopilots subsystem considered the worst case disturbances. Velagic, J. (2005) developed a
standard fuzzy ship autopilot to an adaptive fuzzy autopilot for track keeping. Furthermore, Xue,
Y.(2011) also introduced simulation result of PID heading control for automatic collision avoidance for
ships navigating in waterway. However, they have considered in common just nearly constant speed,
which could not be assured of in berthing circumstance. To be confirmed berthing in advance, a ship is
required to reduce its own speed and to stop at a certain area with designed heading angle.
The automatic berthing control of ships has been a relatively new development beginning in earnest in
the 1990s. In a marine context, the berthing maneuver is a complicated procedure in which both human
experience and intensive control operations are involved. Ship berthing needs for handling multiple
input and output parameters with the inclusion of data from environmental disturbances. Due to the slow
speed of the berthing ship the controllability of the ship is significantly reduced, whereas the
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disturbances from wind and current can become relatively large; intensive rudder/propeller adjustments
and large lateral movement of the ship can intensify the non-linear aspects of the ship dynamics, making
the behavior of the ship rather unpredictable; ship motion at low advance speed is difficult to represent
using differential equations, there by negating most control methods which are dependent upon the
mathematical model of the dynamics of the ship; the shallow water and bank effects will add further
adverse influence upon the ship handling.
Hasegawa, K. and Im, N (2002) introduced comparison method in which wind forces and moment were
compared with rudder and thrusters forces and moment respectively when ship maneuvers in port. More
recently, Tran, V (2012) used nonlinear mathematical expression and equilibrium equation to calculated
critical wind velocity in automatic berthing. These researches was successful as the effects of the wind
to ship maneuvering were clearly verified. Although considering low speed situation and disturbances,
those previous researches on automatic berthing control have been carried out in very short
circumstances with few steps to finish the operation. And even they suggested auxiliary devices, it still
did not make a perfectly benefit for whole auto-berthing system for ship from port to port.
Usually, the ship that manned carries out three stages to be berthed at a quay;
 Stage 1, the ship departs from previous port, takes manoeuvring through open sea, then
approaches the entrance of port of arrival. She often operates at normal speed or full speed.
Previous researches on auto-Track-keeping are in this stage;
 Stage 2, she navigates inside traffic scheme route leading to a certain area with reducing speed.
She stops at that area with desired heading angle;
 Stage 3, ... No.5 to waypoint No. 8 the ship’s speed will be reduced to about 2 knots
as real Track-keeping of T/S SAE NURI conducted by human. Then ship’s speed will be continuously
reduced its own speed until approximately 0 knots for safe approaching to anchorage place at waypoint
No. 10. In case of the speed is too high even the engine stopped (i.e. n=0) and the ship has a risk of
passing out the anchorage point, the astern thruster force should be made to reduce that inertial motion.
Hence, if ship’s berthing procedure is to conduct, it will be carried out by automatic berthing controller
or by assistant of tug boats, etc. as usual.
Boosting Effect method
The environment to carry out this reseach can be explained by following figure;
 At stage 1, ships in open sea usually use full speed or normal speed to manoeuvre.
 At stage 2, ships in port domain usually reduce their speed for safely manoeuvring. They have
to stop at a certain area with desired heading angle.
 At stage 3, ships take berthing to wharf with the assistants of tug-boats, side-thrusters, port
mooring equipments
Figure 4 Operation of ship until berthing
Previous researches have been carried out in stage 1 or stage 3. That is the reason we suggested the stage
2 to be our environment of research to adapt with auto-berthing system for ship from port to port.
Usually, keeping heading angle at low speed is difficult. Previous researches related to ship’s auto-
berthing suggested tugboats, side-thrusters,  in this situation for short moment. Meanwhile, previous
researches that related to ship’s auto-track keeping have not been mentioned this situation. Ship
movement in low speed also occurred difficult to keep her own heading angle. In that case, rudder is not
as effective as in high speed situation. It can be explained that at low speed situation, ship’s turn rate is
not change even its rudder reached the limit effective angle (i.e. 35º-40º both sides).
Figure 5 Diagram of turning characteristic is used to correct rudder’s effect
Stage 1 Stage 3Stage 2
5º 10º 15º 20º 25º 30º
35º
35º 30º 25º 20º 15º
10º 5º
Port
Starboard
r
δ
Normal
speedLow speed
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The diagram in Fig. 5 shows how ship’s turning characteristic depends on ship’s speed. As normal as
ship’s high speed, ship’s turn rate increases as fast as rudder angle increases for each side of turn. But
at low speed, ship’s turn rate is not effective as slow changing of turn rate or even unchanging. Due to
the effect of disturbances, this problem will lead the ship off the designed track as soon as possible.
According to Fig. 5, ship’s turn-rate at normal speed (above 10 knots) changes to high value as fast as
rudder angle is increased. While at low speed, it changes slowly and only can reach low value. That
shows rudder effect is small at low speed.
To solve these problems, “boosting effect” was suggested as the advance solutions. “Boosting effect”
has been used often in ship’s berthing procedure. The ship’s engine was ordered to “boost” for short
time by the Pilot or ship’s Captain to aid the turning when ship’s speed is too low. “Boosting effect” has
a character as a pulse signal, when applied, it won’t increase ship’s speed as much as normal speed but
also increase ship’s turn rate. Therefore, “boosting effect” is applied when ship’s turn rate (yaw rate - r)
has not changed big enough to aid the ship’s turning while maximum effective rudder angle was also
used for such moment. When this happened, ship’s thruster is being boosted until yaw rate reaches a
value for good enough ship’s turning.
The diagram below describes how the system responses for each time of facing this problem;
Figure 6 Block diagram of heading angle control
The diagram in Fig. 8 shows exact process of using engine for heading control. Speed of ship is reduced
base on current waypoint Pi, some waypoints Pn-k1, Pn-k2,.. are marks for ship to keep her rpm at certain
values. Engine is boosted only when the ship has problem on keeping heading angle, even the rudder
reaches maximum effective angle 35º. Otherwise, astern force is used only to remove forward inertial
force in order to stop the ship at certain area safely.
The engine control is stopped when ship stay near stopping point with no speed. The desired heading
angle will continuously be kept until the stop of ship.
4. Simulation results
For a start of simulation, when no wind model was applied, the ship’s trajectory under no wind’s
influence left small off-track errors. The ship kept close to the track inside traffic scheme and stayed
firm in way-point No. 10 anchorage point. This would prove that without disturbance, this control is
reliable for Track-keeping inside port domain with reduced speed. With the increased wind speed’s
affection from 0 to 5 knots, more errors have been seen in Fig. 7 below.
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Figure 7 Ship’s trajectory with the assistant of “Boosting effect”
under the affection of wind (from N to S, 5 kts)
More errors have been found when the ship at the very end of keeping track from way-point No. 9 to
No. 10 when ship’s speed was very low under 1.2 knots. However, the ship could keep stable as former
situation. The ship reached the final point, kept staying at last waypoint. For outcome history data, the
control seems to be reliable when keeping ship’s track under small disturbance’s influence.
When wind’s speed was 10 knots high, it seems that the control finally completed the Track-keeping
procedure with great effort. Fig. 8 shows the ship’s Track-keeping trajectory with the assistant of
“Boosting effect”. In this circumstance, the last schedule of Track-keeping this trajectory is the most
error trajectory among the last shown 3 results, under the wind’s conditions of 0 kts upped to 10 kts.
The ship drifted out of track from way-point No.6 to No.10.
In fact that this problem lead us to reconsider to improve the effort of the control. However, we should
pay attention to the disturbance’s affection to review this controller’s effort. Wind speed in this
circumstance was about 10 knots high meanwhile the ship’s speed was very low at the end of the
operation as about 1.0 knots when she had just passed waypoint No.9 and even equal to 0 knots when
she reached way-point No. 10.
Figure 8 Ship’s trajectory with the assistant of “Boosting effect”
under the affection of wind (from N to S, 10 knots)
Fig. 9 shows how the ship’s Track-keeping without the assistant of “Boosting effect” under the same
characteristic with the last condition shown above;
-50 -40 -30 -20 -10 0 10 20 30
-40
-30
-20
-10
0
10
L
L
Wind: N to S, 5 kts
Time interval 150(s)
-50 -40 -30 -20 -10 0 10 20 30
-40
-30
-20
-10
0
10
L
L
Wind: N to S, ~ 10 kts
Time interval 150(s)
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Figure 9 Ship’s trajectory without the assistant of “Boosting effect”
under the affection of wind ( from N to S, 10 knots)
According to Fig. 9, ship’s Track-keeping under wind effect without using “Boosting effect” left so
many errors. The ship did not only drift out of designed track from waypoint No. 6 to waypoint No. 8
but also could not reach the anchorage point.
To find out more details of the assistant of “Boosting effect”, the comparison between the controllers of
each situation with or without “Boosting effect” under wind’s influence has been made by following
figures;
Figure 10 Comparison between controllers with “B.E” and without B.E” by
time history of parameters: Deviation, Remain distance to waypoint
Time history parameter “Remain distance to waypoint” in Fig. 10 shows how the ship passed each way-
point. It was shown as the distance to previous way-point had been reduced to minimum value and
distance to current way-point has been raised up to maximum value. The last distance should be the
distance from the ship to the wharf. In this case, the controller without “Boosting effect” did not move
the ship to way-point No.9, even drifted far off the track. Whilst the controller with “Boosting effect”
has done it also brought the ship to way-point No.10.
While time history of parameter “Deviation” shows how the ship kept close to the designed track. The
maximum deviation off-track of the ship using controller with “Boosting effect” is 160 meters, about
1.7 ship’s length, according to the segment between waypoint No. 9 and waypoint No. 10. This deviation
value was accepted because of this segment was inside anchorage place, and there are no obstacles of
water level or passing ships. The others deviation value was also accepted because the traffic scheme’s
breadth was 6 to 7 times of ship’s length and the ship’s motion was inside the half safe of traffic scheme’s
route. The thicker line stands for engine process with “Boosting effect”, the rest stands for engine
process without “Boosting effect”.
-50 -40 -30 -20 -10 0 10 20 30
-40
-30
-20
-10
0
10
L
L
Wind: N to S, 5 kts
Time interval 150(s)
0 1000 2000 3000 4000 5000 60000
0.5
1
1.5
2
t [s]
De
via
tion
 [m
/L]
0 1000 2000 3000 4000 5000 60000
5
10
15
20
25
30
35
t [s]
Re
ma
in d
ista
nce
 to
 wa
ypo
int 
[m/
L] with B.E
without B.E
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Figure 11 Comparison between controllers with “B.E” and without B.E” by
time history of parameters: Error, Used Rudder Angle
According to Fig. 11, the controllers with “Boosting effect” totally helped the ship to reduce the heading
error. At the end of simulation, controllers with “Boosting effect” was turned to port because of strong
wind effect. This could be acceptable because the ship would conduct berthing procedure after finish
Track-keeping. The controllers’ simulation result was accepted in using rudder angle. Rudder angle was
used without breaking the limitation (|δ| ≤ 35º).
Figure 12 Comparison between controllers with “B.E” and without B.E” by time history
of parameters: Change of turn rate, Propeller index and ship’s speed
Fig. 12 shows how ship’s engine control the ship’s speed. Because of no “Boosting effect” was used,
propeller history (rpm) of the controller without “Boosting effect” was reduced step-by-step to reduce
ship’s speed. At the end of simulation, ship’s speed is equal to 0.5 knots that could not help the ship to
return its track.
Otherwise, controller with “Boosting effect” using propeller index for both increasing and decreasing
ship’s speed. The speed was increased a little bit by “Boosting” of ship’s engine when ship’s turn rate
was not being changed big enough. At that time, propeller index was increased up. When the ship’s
speed was too high to slow down, propeller was also used to astern thrust the ship. At the end of
simulation, ship’s speed was equal to 0.005 knots. This is safe enough as the ship stopped near the last
waypoint. The criteria was met.
5. Conclusion
After reviewing the simulation results, this study proved that:
0 1000 2000 3000 4000 5000 6000-100
-50
0
50
100
150
t [s]
Erro
r [d
eg]
0 1000 2000 3000 4000 5000 6000-40
-20
0
20
40
t [s]
Rud
der
 An
gle 
[de
g]
0 1000 2000 3000 4000 5000 6000
-100
0
100
t [s]
Pr
op
ell
er 
[rp
m]
0 1000 2000 3000 4000 5000 6000
0
5
10
t [s]
Sp
ee
d [
kts
]
0 1000 2000 3000 4000 5000 6000
-0.5
0
0.5
t [s]
Tu
rn 
rat
e [
%]
with B.E
without B.E
with B.E
without B.E
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 The ship can use this controller for specific purpose of automatic Track-keeping at the specified
moment as when finished ocean navigating and before berthing to a quay; in the specified place
as Track-keeping insides traffic scheme that is leading to the wharf; and with difficulties are
low speed, reducing speed and disturbance effect.
 Heading angle at low speed was controlled with the assistant of “Boosting effect” which is
unfamiliar with other previous researches. “Boosting effect” was proved as a vital characteristic
of this controller to aid the ship at low speed, under the strong wind and without any help of
extra auxiliary devices.
Acknowledgement
This research was a part of the project titled “Development of Ship-handling and Passenger Evacuation
Support System” funded by the Ministry of Oceans and Fisheries (South Korea - MOF).
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