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Citation: He, Y.; Du, Z.; Huang, L.;
Yu, D.; Liu, X. Maneuver Decision-
Making Method for Ship Collision
Avoidance in Chengshantou Traffic
Separation Scheme Waters. Appl. Sci.
2023,13, 8437. https://doi.org/
10.3390/app13148437
Academic Editor: Mirco Peron
Received: 22 June 2023
Revised: 19 July 2023
Accepted: 19 July 2023
Published: 21 July 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
applied
sciences
Article
Maneuver Decision-Making Method for Ship Collision
Avoidance in Chengshantou Traffic Separation Scheme Waters
Yixiong He 1,2, Zijun Du 1, Liwen Huang 1,2, Deqing Yu 1,* and Xiao Liu 1 ,*
1School of Navigation, Wuhan University of Technology, Wuhan 430063, China;
heyixiong7@whut.edu.cn (Y.H.); destan@163.com (Z.D.); lwhuang@whut.edu.cn (L.H.)
2Hubei Key Laboratory of Inland Shipping Technology, Wuhan 430063, China
*Correspondence: yude@whut.edu.cn (D.Y.); lxiao@whut.edu.cn (X.L.)
Abstract:
A maneuvering decision-making model based on time series rolling and feedback com-
pensation methods is proposed to solve the problem of high traffic risk in Chengshantou traffic
separation scheme (TSS) waters. Firstly, a digital traffic environment model suitable for the TSS
waters is proposed. Secondly, a navigation risk identification method in these waters is constructed
based on the digitized traffic environment and situation identification model in the Chengshantou
TSS waters. Thirdly, considering the requirements of the rules and good seamanship, minimum
course altering is obtained by combining the collision avoidance mechanism. Lastly, a maneuvering
decision-making model in the TSS waters based on time series rolling and feedback compensation
methods is developed. The simulation results show that the ship can correctly identify the collision
risk and appropriately obtain maneuvering decisions, and can resume the planned route under the
premise of ensuring safety. When the target ships alter course or change speed, the ship can also
make adaptive maneuvering decisions. In summary, the proposed method meets the requirement
of safe navigation in Chengshantou waters and provides a theoretical basis for the realization of
intelligent navigation in waters similar to TSS.
Keywords: maneuver decision-making; traffic separation scheme; collision avoidance mechanism
1. Introduction
Maritime transportation provides a guarantee for the spatial movement of goods
worldwide due to its advantages, such as large transport capacity and low cost. As one of
the main modes of transportation in international trade, maritime transport undertakes
more than 90% of the global trade volume [
1
]. As global commerce continues to grow, water
traffic, especially in coastal waters, has become increasingly busy and complex in recent
years. The prosperity of waterway transportation has also increased the probability of
water traffic accidents. To simplify traffic flow patterns in convergence areas and enhance
navigational safety, ship routing is widely used [
2
]. The traffic separation scheme (TSS) is a
specific type of ship routing that separates opposing traffic flows by employing appropriate
methods and establishing traffic lanes. TSS has been widely developed around the world,
and it has played a significant role in decreasing ship collision accidents and improving
navigation safety.
Chengshantou waters, a critical hub for China’s north–south marine transportation,
experience heavy ship traffic and occasional collision accidents. The implementation of a
TSS in Chengshantou waters has improved navigational safety and navigational efficiency.
However, despite the benefits of the TSS, collision accidents still occur due to navigators’
failure to correctly understand and execute the International Regulations for Preventing
Collisions at Sea, 1972 (COLREGs) [3].
The optimal solution to human error is to improve the level of ship intelligence, which is
also the hotspot and challenge of current related research [
4
]. In terms of current research, there
Appl. Sci. 2023,13, 8437. https://doi.org/10.3390/app13148437 https://www.mdpi.com/journal/applsci
Appl. Sci. 2023,13, 8437 2 of 22
is still a long way to go until fully autonomous navigation in restricted water and manual
ship manipulation continues to be the primary method of ship manipulation. Intelligent
maneuver decision-making, which complies with COLREGs and good seamanship [
5
–
7
], is
currently the most promising strategy to reduce navigational risk. This approach also provides
decision-making suggestions to navigators. The risks faced by ships during navigation, such
as collisions, groundings, and rocks, as well as violations of TSS rules, are referred to as
navigation risks in this study. Navigation risk warning and collision avoidance decision-
making are the primary components of intelligent navigation [
8
]. Related research can reduce
collision occurrences and lay the groundwork for intelligent navigation.
Various methods, including collision avoidance mechanism [
9
,
10
], four-stage the-
ory [
11
–
13
], collision risk index (CRI) [
12
], velocity obstacle (VO) [
14
–
17
], etc., have been
widely applied in collision avoidance research. What is more, some academic research
used deep reinforcement learning algorithms for ship collision avoidance decision-making,
followed by intense training to obtain a basic collision avoidance model [
18
,
19
]. Artificial
potential fields [
20
,
21
], ant colony algorithms [
22
], genetic algorithms [
23
], neural net-
works [
24
], and other intelligent algorithms also have significant influence when they are
used to solve the collision avoidance path planning problem.
At present, most of the research on special waters, such as ship routing waters, is to
analyze the traffic characteristics [
25
] and optimize [
26
] the ship’s routing scheme. For
example, Sunaryo et al. [
27
] analyzed the impact of the TSS in the Sunda Strait in preventing
ship accidents. He believed that the potential collision between ships could be minimized
by using TSS to separate ships’ traffic flow in the opposite direction. Liu et al. [
28
] analyzed
the ship routing system, navigation environment, and traffic flow in the Bohai Strait,
optimized the shipping route in this water area, and proposed a recommended scheme to
connect the existing routing system in this water area. Zbigniew et al. [
29
,
30
] defined the
ship domain within the precautionary area of TSS and investigated the law of traffic flow
and ship behavior in the real environment.
Many experts and scholars have also studied the collision avoidance warning system.
Huang et al. [
14
,
31
] constructed a collision avoidance system based on the generalized
velocity obstacle algorithm, which was applied to manned and unmanned in this study. Du
et al. [
11
,
32
] quantified the liability clauses of stand-on vessels in the COLREGs and divided
the severity of conflicts into nine categories based on the ship’s intention prediction and
conflict evolution. Then, combined with the four stages of ship encounters, they proposed a
collision early warning system. based on the perspective of a stand-on vessel. By evaluating
the dynamic characteristics of the ship’s navigation process, Wu et al. [
33
] proposed an
intelligent decision-making approach based on fuzzy logic for the inland-water TSS.
While the above research has contributed to the development of ship collision avoid-
ance, very few studies focus on specific waters, such as the Chengshantou TSS, Gibraltar
TSS, Malacca Strait TSS, etc. Some scholars have studied the traffic situation in the above-
mentioned area and completed revision studies on the TSS, but few have investigated
collision avoidance warning and maneuver decision-making.
Therefore, implementing ship collision avoidance early warning and maneuver decision-
making TSS waters has both practical and theoretical value for enhancing navigation safety
and efficiency, as well as ship autonomization.
Regarding the ship collision avoidance warning and maneuver decision-making in
unique types of water environments, such as TSS, there are still many issues worthy of
in-depth study on the basis of previous research. These issues are listed as follows.
(1)
The digital model of the traffic environment suitable for special water areas, such as
Chengshantou, is established;
(2)
The collision avoidance mechanism is applicable to special waters, such as TSS;
(3)
Rule 10 of the COLREGs and good seamanship requirements are incorporated into
the decision-making method;
In this work, we construct a static digital traffic environment based on the Chengshan-
tou TSS’s components, taking into account the need for risk identification and collision
Appl. Sci. 2023,13, 8437 3 of 22
avoidance decision-making. Secondly, the ship domain and a method for estimating ship
position based on ship behavior in TSS are introduced to achieve risk identification. Thirdly,
the encounter situation identification model is built, and corresponding avoidance ap-
proaches are provided. Fourthly, the collision avoidance mechanism of ships under the
constraints of the TSS is studied by analyzing the COLREG rules. Finally, a decision-making
method based on time-series rolling is proposed for multi-vessel encounter maneuvers in
TSS waters.
The rest of the contents of the paper are organized as follows: Section 2presents the
method for constructing a digital traffic environment. Section 3introduces the methods of
risk identification during navigation. The method of collision avoidance decision-making
is shown in Section 4, and the simulation results are implemented in Section 5. Finally,
conclusions are drawn in Section 6.
2. Digital Traffic Environment
The digital traffic environment is the key to ship situational awareness. This part
proposes the digital traffic environment model and the digital traffic environment modeling
of Chengshantou waters is carried out. By digitizing the traffic environment and perceiving
and acquiring dynamic and static environment information, it can provide data support for
ship maneuvering decisions.
2.1. Coordinate Systems
In this work, we adopt the coordinate system depicted in Figure 1. The geodetic
fixed coordinate system XOY is established with
(λ0,ϕ0)
as the origin coordinates. The
positive directions of the X and Y axes point to the true east and true north, respectively.
The coordinate system XOY fixed to the own ship (OS) is established. The center of gravity
of the OS is set as the origin, and the positive directions of the x and y axes point to the
starboard abeam and bow of the OS, respectively. True course (
TC
) of OS is the angle
between the
Y
and
y
axes, true bearing (
TB
) of target ship (TS) is the angle from
Y
-axis to
the bearing line, and relative bearing (
Q
) is the angle from OS heading line to the bearing
line. The relationship between T B,Q, and TC is shown in Equation (1).
(TB =Q+TC)(1)
Appl. Sci. 2023, 13, x FOR PEER REVIEW 3 of 23
In this work, we construct a static digital traffic environment based on the
Chengshantou TSS’s components, taking into account the need for risk identification and
collision avoidance decision-making. Secondly, the ship domain and a method for esti-
mating ship position based on ship behavior in TSS are introduced to achieve risk identi-
fication. Thirdly, the encounter situation identification model is built, and corresponding
avoidance approaches are provided. Fourthly, the collision avoidance mechanism of ships
under the constraints of the TSS is studied by analyzing the COLREG rules. Finally, a
decision-making method based on time-series rolling is proposed for multi-vessel encoun-
ter maneuvers in TSS waters.
The rest of the contents of the paper are organized as follows: Section 2 presents the
method for constructing a digital traffic environment. Section 3 introduces the methods of
risk identification during navigation. The method of collision avoidance decision-making
is shown in Section 4, and the simulation results are implemented in Section 5. Finally,
conclusions are drawn in Section 6.
2. Digital Traffic Environment
The digital traffic environment is the key to ship situational awareness. This part pro-
poses the digital traffic environment model and the digital traffic environment modeling
of Chengshantou waters is carried out. By digitizing the traffic environment and perceiv-
ing and acquiring dynamic and static environment information, it can provide data sup-
port for ship maneuvering decisions.
2.1. Coordinate Systems
In this work, we adopt the coordinate system depicted in Figure 1. The geodetic fixed
coordinate system XOY is established with (𝜆,𝜑) as the origin coordinates. The positive
directions of the X and Y axes point to the true east and true north, respectively. The co-
ordinate system XOY fixed to the own ship (OS) is established. The center of gravity of
the OS is set as the origin, and the positive directions of the x and y axes point to the
starboard abeam and bow of the OS, respectively. True course (𝑇𝐶) of OS is the angle
between the Y and y axes, true bearing (𝑇𝐵) of target ship (TS) is the angle from Y-axis to
the bearing line, and relative bearing (𝑄) is the angle from OS heading line to the bearing
line. The relationship between 𝑇𝐵, 𝑄, and 𝑇𝐶 is shown in Equation (1).
(𝑇𝐵=𝑄+𝑇𝐶) (1)
Figure 1. Coordinate systems transformation (Coordinate system XOY and xoy).
The transformation equation of the coordinate system from x-o-y to XOY is shown in
Equation (2).
Figure 1. Coordinate systems transformation (Coordinate system XOY and xoy).
The transformation equation of the coordinate system from x-o-y to XOY is shown in
Equation (2).
(X,Y)=(x,y)×B+(λo,ϕo)(2)
Appl. Sci. 2023,13, 8437 4 of 22
where B is the transformation matrix, as shown in Equation (3).
B=cos (TC)−sin (TC)
sin (TC)cos (TC)(3)
The coordinates of the ship in the XOY coordinate system can be obtained by trans-
forming its longitude and latitude ( λ,ϕ)through Equation (4).
X=R∗arcoshcos2ϕ0∗cos (λ−λ0)+sin2ϕ0i
Y=R∗arcos[cos ϕ∗cos ϕ0+sin ϕ0](4)
where Ris the radius of the Earth.
2.2. Ship Domain
The ship domain is considered a safe area that ensures navigation safety [
15
], which
prevents other ships and stationary objects from entering a certain range around the OS. It
has been half a century since the concept was proposed [
34
]. In the process of continuous
improvement and development [
30
], the boundary smoothing model shown in Figure 2is
widely accepted.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 4 of 23
(𝑋,𝑌)=(𝑥,𝑦)×𝐵+(𝜆,𝜑) (2)
where B is the transformation matrix, as shown in Equation (3).
𝐵=𝑐𝑜𝑠 (𝑇𝐶) −𝑠𝑖𝑛 (𝑇𝐶)
𝑠𝑖𝑛 (𝑇𝐶) 𝑐𝑜𝑠 (𝑇𝐶) (3)
The coordinates of the ship in the XOY coordinate system can be obtained by trans-
forming its longitude and latitude (𝜆,𝜑) through Equation (4).
𝑋=𝑅∗𝑎𝑟𝑐𝑜𝑠[𝑐𝑜𝑠2𝜑0∗𝑐𝑜𝑠(𝜆−𝜆0)+𝑠𝑖𝑛2𝜑0]
𝑌=𝑅∗𝑎𝑟𝑐𝑜𝑠𝑐𝑜𝑠𝜑∗𝑐𝑜𝑠𝜑0+𝑠𝑖𝑛𝜑0 (4)
where 𝑅 is the radius of the Earth.
2.2. Ship Domain
The ship domain is considered a safe area that ensures navigation safety [15], which
prevents other ships and stationary objects from entering a certain range around the OS.
It has been half a century since the concept was proposed [34]. In the process of continuous
improvement and development [30], the boundary smoothing model shown in Figure 2
is widely accepted.
Figure 2. The boundary smoothing ship domain model.
The aim of this study is to provide a collision avoidance decision-making method for
ships navigating in the TSS waters. When the OS sails in TSS, if there is a collision risk
with the TS, most of them are crossing situations. Therefore, the safety distance required
for the port and starboard side is basically the same. However, the distances required for
the fore and aft of the vessel are obviously different. When the collision risk comes from
the aft, the other ship generally overtakes the OS, and the OS is a stand-on vessel. When
the risk comes from the fore, there are many different encounter situations, and the avoid-
ance requirements are more complicated correspondingly. Therefore, the safety distance
of the fore should be greater than that of the aft. On the other hand, when the OS is moving
ahead, the distance variation of the fore or aft is greater than that of the port and starboard
sides. Therefore, the required safety distance of the fore and aft should also be greater
than that of both sides.
Based on the previous description, a symmetrical elliptical ship domain model with
an offset center is adopted in this study. The imaginary ship is located at the center of the
ellipse and at a distance of a*k before the OS. The model parameters are selected with the
length of the OS (L) as the reference unit. The long and short axis of the ellipse field is set
Figure 2. The boundary smoothing ship domain model.
The aim of this study is to provide a collision avoidance decision-making method for
ships navigating in the TSS waters. When the OS sails in TSS, if there is a collision risk with
the TS, most of them are crossing situations. Therefore, the safety distance required for
the port and starboard side is basically the same. However, the distances required for the
fore and aft of the vessel are obviously different. When the collision risk comes from the
aft, the other ship generally overtakes the OS, and the OS is a stand-on vessel. When the
risk comes from the fore, there are many different encounter situations, and the avoidance
requirements are more complicated correspondingly. Therefore, the safety distance of the
fore should be greater than that of the aft. On the other hand, when the OS is moving
ahead, the distance variation of the fore or aft is greater than that of the port and starboard
sides. Therefore, the required safety distance of the fore and aft should also be greater than
that of both sides.
Based on the previous description, a symmetrical elliptical ship domain model with
an offset center is adopted in this study. The imaginary ship is located at the center of
the ellipse and at a distance of a*k before the OS. The model parameters are selected with
the length of the OS (L) as the reference unit. The long and short axis of the ellipse field
Appl. Sci. 2023,13, 8437 5 of 22
is set as a = 5 L and b = 2 L, respectively. The eccentricity coefficient k is 0.7. In future
practical applications, the size of the parameters in the model can be adjusted by the captain
according to the navigation environment and the ship’s maneuverability.
2.3. Digitization of TSS
In order to provide proper collision avoidance decisions and suggestions to the naviga-
tor, the first step is to extract the static environment information from each part of the TSS.
The dynamic information of the ships sailing in TSS, such as position, course, speed, etc., is
extracted as well. These are then converted into digital information that can be recognized
by computer programs.
2.3.1. Static Environment
The static data of TSS is the static environment information that can be obtained from
the chart and will not change in a short time. The Chengshantou ship’s routing includes
three TSSs, two precautionary areas, and five traffic separation zones, as displayed in
Figure 3.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 5 of 23
as a = 5 L and b = 2 L, respectively. The eccentricity coefficient k is 0.7. In future practical
applications, the size of the parameters in the model can be adjusted by the captain ac-
cording to the navigation environment and the ship’s maneuverability.
2.3. Digitization of TSS
In order to provide proper collision avoidance decisions and suggestions to the nav-
igator, the first step is to extract the static environment information from each part of the
TSS. The dynamic information of the ships sailing in TSS, such as position, course, speed,
etc., is extracted as well. These are then converted into digital information that can be
recognized by computer programs.
2.3.1. Static Environment
The static data of TSS is the static environment information that can be obtained from the
chart and will not change in a short time. The Chengshantou ship’s routing includes three
TSSs, two precautionary areas, and five traffic separation zones, as displayed in Figure 3.
Figure 3. Digitalization traffic environment of Chengshantou TSS.
In Figure 3, each TSS features two traffic lanes and four boundary lines (numbered
from east to west as 1, 2, 3…), with n points (numbered from north to south as 1, 2, 3…)
on each boundary line. 𝑇𝑠 denotes the 𝑛-th point on the 𝑚-th boundary line of the 𝑠-
th TSS in this study. The traffic lanes are further divided into 16 segments based on distinct
traffic flow directions and the places from where they occupy. The TSS does not prescribe
a course in the precautionary area. According to COLREGs, when a vessel joins or leaves
from either side, it must do so at the smallest possible angle to the general direction of
Figure 3. Digitalization traffic environment of Chengshantou TSS.
In Figure 3, each TSS features two traffic lanes and four boundary lines (numbered
from east to west as 1, 2, 3
. . .
), with npoints (numbered from north to south as 1, 2, 3
. . .
)
on each boundary line.
Tsm
n
denotes the
n
-th point on the
m
-th boundary line of the
s
-th TSS
in this study. The traffic lanes are further divided into 16 segments based on distinct traffic
flow directions and the places from where they occupy. The TSS does not prescribe a course
in the precautionary area. According to COLREGs, when a vessel joins or leaves from
Appl. Sci. 2023,13, 8437 6 of 22
either side, it must do so at the smallest possible angle to the general direction of traffic
flow. In this study, we set up a virtual traffic lane in the precautionary area
A1
, and set
the centerline of the traffic lane as the planned route based on the author’s real navigation
experience and cluster analysis of the historical trajectories of ships in the study area [35].
1. Traffic Lane
The i-th traffic lane of the s-th TSS is represented by Lsi.
Lsi =
hareaTs2i−1
1,Ts2i−1
4,Ts2i
4,Ts2i
1is=1
hareaTs2i−1
1,Ts2i−1
3,Ts2i−1
5,Ts2i
5,Ts2i
3,Ts2i
1is=2
hareaTs2i−1
1,Ts2i−1
2,Ts2i−1
3,Ts2i
3,Ts2i
2,Ts2i
1is=3
(5)
2. Planned Route
Rsi
shows the planned route on the
s
-th TSS’s
i
-th traffic lane. The midpoint of the line
between points Tsm
nand Tsm−1
nis represented by Tsm
n+Tsm−1
n/2.
Rsi =
hlineTs2i−1
1+Ts2i
1/2, Ts2i−1
4+Ts2i
4/2i,s=1
hlineTs2i−1
1+Ts2i
1/2, Ts2i−1
3+Ts2i
3/2, Ts2i−1
5+Ts2i
5/2i,s=2
hlineTs2i−1
1+Ts2i
1/2, Ts2i−1
3+Ts2i
3/2, Ts2i−1
5+Ts2i
5/2i,s=3
(6)
3. Segment
Equation (7) can be used to represent the segment Os.
Os=OTsm
n=hareaTsm
n,Tsm
n+1,Tsm+1
n+1,Tsm+1
ni(7)
Table 1shows the main traffic flow direction of each segment as well as the segment
area corresponding to Os.
Table 1. Information about the static environment.
Segment Number O1O2O3O4O5O6O7O8
Segment Area OT33
1OT33
2OT31
1OT31
2OT13
1or OT23
1OT23
4OT11
1or OT21
1OT21
4
General Direction of
traffic flow 150◦180◦330◦000◦120◦180◦300◦000◦
Segment Number O9O10 O11 O12 O13 O14 O15 O16
Segment Area OT13
3OT11
3OT11
2OT13
2OT11
2or OT21
2OT21
3OT13
2or OT23
2OT13
1
General Direction of
traffic flow 120◦300◦300◦120◦300◦000◦120◦180◦
4. Precautionary Area
Equation (8) can be used to represent the precautionary area As.
As=
hareaT11
2,T11
3,T14
3,T24
4,T14
2i,s=1
[area|(X1+cosα,Y1+R0sinα)],s=2(8)
where
α∈[0, θ1]∪[2π−θ2, 2π]
,
(X1,Y1)
,
R0
represent the center and radius of the precau-
tionary area, respectively.
5. Traffic Separation Zone
Appl. Sci. 2023,13, 8437 7 of 22
Equation (9) can be used to represent the traffic separation zone Zs.
Zs=
hareaT12
2s−1,T12
2s,T13
2s,T13
2s−1i,s<3
areaT12
s+1,T12
s+2,T13
s+2,T13
s+1,s=3
areaT21
4,T24
2,T24
4,T24
5,T31
3,T31
2,T31
1,P,s=4
areaT32
1,T32
2,T32
3,T33
3,T33
2,T33
1,s=5
(9)
2.3.2. Dynamic Environment
The dynamic environment mainly contains a variety of ship information. Based on
this information, all ships are divided into special ships, ships sailing along the general
direction of the traffic flow, and ships not sailing in the general direction of the traffic flow.
According to rules 10, 12, and 18 of COLREGs [
36
], when the special ship and OS pose a
collision risk, the OS should take collision avoidance action.
Ships sailing in the general direction of traffic flow of the channel refer to ships sailing
following a traffic lane, and their course is basically consistent with the general direction of
traffic flow. When ships are navigating normally in the traffic lane, they often encounter
other ships that do not follow the traffic lane because they cross or leave the traffic lane or
take action to avoid a collision.
3. Risk Identification during Navigation
During the actual sea voyage, the navigator calculates the position of the TS based on
the current velocity vector of the TS to judge whether it poses a collision risk to the OS.
Then the navigator continuously observes the intention of the TS. Once the TS changes the
current motion state, a reevaluation is made to draw new conclusions.
This study refers to the navigator’s judgment method in navigation practice, draws
the conclusion of collision avoidance warning, and produces collision avoidance maneuver
decision-making. These conclusions are made according to the current speed vector and
position of the TS to estimate the ship’s position after a period of time (e.g., 30 min).
At the next calculation moment, re-import the dynamic information of TSs for cyclic
calculation. The calculation frequency of the computer program system will be higher than
the frequency of manual judgment of the ship navigators in practice, so the early warning
and collision avoidance decision-making provided will be timelier and more accurate.
3.1. Ship’s Position Dead Reckoning
When the ship enters the next segment of the traffic lane in TSS waters, the general
direction of traffic flow changes and the ship will continue to sail in the general direction of
traffic flow in the following segment.
Ships often travel at sea speed in the Chengshantou TSS due to the broader navigable
waters and fewer obstacles. Sea speed denotes that the revolution speed of the main engine
is constant and cannot be changed in a short time. As a result, this paper assumes that the
weather is fine, and the ship is sailing at sea speed. Dead reckoning of the OS’s and TS’s
positions is carried out based on the OS’s and TSs’ present information. Rapid data updates
and cyclic calculations are used to correct ship position dead reckoning errors and achieve
a self-adaptive judgment. The course-altering process when performing ship position dead
reckoning is, therefore, ignored.
When the TS’s course is nearly identical to the recommended traffic flow direction of
the traffic lane to which it belongs, the TS’s position is determined using the traffic flow
direction and the TS’s speed. The specific implementation method is as follows.
1. Determine the ship’s position in the channel.
For any convex quadrilateral segment
abcd
, if the sum of the triangle areas
S1
,
S2
,
S3
,
S4
formed by the line connecting the ship’s center of gravity to the four vertices of the convex
Appl. Sci. 2023,13, 8437 8 of 22
quadrilateral abcd is equal to the area
(Sabcd)
of the quadrilateral abcd, the ship can be
judged to be within the convex quadrilateral segment. The illustration is as per Figure 4.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 8 of 23
Figure 4. Schematic diagram of judging the section of the ship.
2. Check whether the ship is sailing in the general direction of traffic flow.
If the difference between the course and the recommended traffic flow direction of a
segment is less than 10°, it is assumed that the ship is sailing along the channel, as shown
in Equation (10). If the course difference is greater than 10°, it is assumed that the ship is
not sailing along the general direction of traffic flow, as shown in Equation (11).
𝑋,𝑌∈𝑂&|𝑇𝐶−𝜑|<10° (10)
(𝑋,𝑌)∉∑𝑂
||𝑋,𝑌∈𝑂&|𝑇𝐶−𝜑|≥10° (11)
where 𝜑 indicates the recommended traffic flow direction for the segment where the
ship is positioned, 𝜑 represents the recommended traffic flow direction for the next
segment, 𝑋,𝑌 is the coordinate of the 𝑗-th TS at the moment 𝑡, 𝑇𝐶 is the course of
the 𝑗-th TS, and 𝑇𝐶 is the course of the OS.
3. The method for dead reckoning the ship’s position in different situations
Based on the judgment conclusions in steps 1 and 2, the ship’s current speed, course,
and position, the ship’s positions after a period of time can be calculated. The ship’s posi-
tion when the OS and TSs proceed in the appropriate traffic lane in the general direction
of traffic flow for that lane is dead reckoning through Equation (12). The positions of OS
or TSs, which are in the traffic lane but not along the general direction of traffic flow, can
be dead reckoned by Equations (13) and (14), respectively. The ship’s position when the
ship is not in the TSS traffic lane is dead reckoned through Equation (14).
⎩
⎪
⎨
⎪
⎧
𝑋=𝑋+𝑣∗𝑡∗sin𝑇𝐶,𝑡∈[0,𝑇]
𝑌=𝑌+𝑣∗𝑡∗cos𝑇𝐶,𝑡∈[0,𝑇]
𝑋=𝑥+𝑣∗(𝑡−𝑇)∗sin(𝜑),𝑡∈[𝑇,1800]
𝑌=𝑦+𝑣∗(𝑡−𝑇)∗cos(𝜑),𝑡∈[𝑇,1800] (12)
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
𝑋=𝑋+𝑣∗𝑡∗sin𝑇𝐶,𝑡∈[0,𝑇]
𝑌=𝑌+𝑣∗𝑡∗cos𝑇𝐶,𝑡∈[0,𝑇]
𝑋=𝑥+𝑣∗(𝑡−𝑇)∗sin(𝜑),𝑡∈[𝑇,𝑇]
𝑌=𝑦+𝑣∗(𝑡−𝑇)∗cos(𝜑),𝑡∈[𝑇,𝑇]
𝑋=𝑥+𝑣∗(𝑡−𝑇)∗sin(𝜑),𝑡∈[𝑇,1800]
𝑌=𝑦+𝑣∗(𝑡−𝑇)∗cos(𝜑),𝑡∈[𝑇,1800]
(13)
Figure 4. Schematic diagram of judging the section of the ship.
2. Check whether the ship is sailing in the general direction of traffic flow.
If the difference between the course and the recommended traffic flow direction of a
segment is less than 10
◦
, it is assumed that the ship is sailing along the channel, as shown
in Equation (10). If the course difference is greater than 10
◦
, it is assumed that the ship is
not sailing along the general direction of traffic flow, as shown in Equation (11).
Xj
t,Yj
t∈Os&|TCj−ϕs|<10◦(10)
{(Xj
t,Yj
t)/∈∑16
s=1Os}||{(Xj
t,Yj
t)∈Os&|TCj−ϕs| ≥ 10◦}(11)
where
ϕs
indicates the recommended traffic flow direction for the segment where the ship
is positioned,
ϕs+1
represents the recommended traffic flow direction for the next segment,
Xj
t,Yj
t
is the coordinate of the
j
-th TS at the moment
t
,
TCj
is the course of the
j
-th TS,
and TCois the course of the OS.
3. The method for dead reckoning the ship’s position in different situations
Based on the judgment conclusions in steps 1 and 2, the ship’s current speed, course,
and position, the ship’s positions after a period of time can be calculated. The ship’s position
when the OS and TSs proceed in the appropriate traffic lane in the general direction of
traffic flow for that lane is dead reckoning through Equation (12). The positions of OS or
TSs, which are in the traffic lane but not along the general direction of traffic flow, can be
dead reckoned by Equations (13) and (14), respectively. The ship’s position when the ship
is not in the TSS traffic lane is dead reckoned through Equation (14).
(Xj
t=Xj
o+vj∗t∗sin TCj,t∈[0, T]
Yj
t=Yk
o+vj∗t∗cos TCj,t∈[0, T]
(Xj
t=xT+vj∗(t−T)∗sin (ϕs+1),t∈[T, 1800]
Yj
t=yT+vj∗(t−T)∗cos (ϕs+1),t∈[T, 1800]
(12)
(Xj
t=Xj
o+vj∗t∗sin TCj,t∈[0, T1]
Yj
t=Yk
o+vj∗t∗cos TCj,t∈[0, T1]
(Xj
t=xT1+vj∗(t−T1)∗sin (ϕs),t∈[T1,T2]
Yj
t=yT1+vj∗(t−T1)∗cos (ϕs),t∈[T1,T2]
(Xj
t=xT2+vj∗(t−T2)∗sin (ϕs+1),t∈[T2, 1800]
Yj
t=yT2+vj∗(t−T2)∗cos (ϕs+1),t∈[T2, 1800]
(13)
Appl. Sci. 2023,13, 8437 9 of 22
(Xj
t=Xj
o+vj∗t∗sin TCj,t∈[0, 1800]
Yj
t=Yj
o+vj∗t∗cos TCj,t∈[0, 1800](14)
where
vj
is the speed of the j-th TS,
v0
is the speed of the OS,
(xT,yT)
is the coordinate of
the next segment’s starting point,
T
is the time when the ship reaches the next segment,
(xT1,yT1
, and
T1
are the coordinates and time when the ship reaches the current segment’s
track control boundary line, respectively. The position and time when the ship reaches the
track control boundary line of the next segment are (xT2,yT2a and T2, respectively.
3.2. Collision Risk Judgment Method
If the OS and the TS maintain their course and speed, ultimately, the TS will eventually
enter the OS’s ship domain, and a potential collision risk (PCR) is thought to exist. In this
study, the term “keep course and speed” also means that ships in the TSS consistently
follow the channel’s general direction of traffic flow. The time threshold for entering the
OS’s ship domain, as well as the PCR between OS and TS, are utilized to assess if a collision
risk exists in the TSS waters. The threshold value (
Ts1
) can be modified by the master based
on the ship’s actual sailing conditions. In this study, it is set as 1800 s.
The collision risk index (CRI) is a physical quantity determined by the relationship
between the maneuvering features, locations, and motions of the two ships to indicate the
risk of collision and the necessity of implementing anti-collision actions. It is separated into
a two categories-time collision risk index (TCRI) and a space collision risk index (SCRI).
TCRI and SCRI are combined to describe CRI. Equation (15) illustrates it:
CR =CRt·CRs(15)
where
CR
is the CRI value,
CRt
is the TCRI value, and
Rs
is the SCRI value. When
CR >
0,
it shows the collision threat is arising, and a collision danger alert can be issued to remind
the ship navigators.
1. TCRI
When there is a PCR exited, CRI is defined as the urgency with which one of the two
ships in an encountering situation approaches the latest steering point [
12
]. The value of
TCRI (CRt) is calculated by Equation (16).
CRt=
1TTs ≤0
(1−TTS
Ts2)3.03
0TTS ≥Ts1
0<TTS <Ts1(16)
2. 2SCRI
The SCRI is used to determine whether or not there is a potential collision risk between
ships and the possibility of anti-collision actions that need to be taken. There are only two
outcomes—PCR exists or not—which corresponds to a SCRI score of 1 or 0. The value of
SCRI CRsis calculated as Equation (17).
CRs=
1∃t∈[0, Ts2],(Xj
t,Yj
t∈Domt
0@t∈[0, Ts2],(Xj
t,Yj
t∈Domt
(17)
(Xj
t,Yj
t
represents the
j
-th TS’s position of the time at
t=k×∆t
,where
∆t
means
the calculating time step.
Domt
indicates that the point set in the field of the OS’s ship
domain at time
t
.
Ts2
is the calculation time threshold, which can be adjusted by the captain
according to the traffic environment. In this paper, it is set as 2400
s
. If the TS is too far away
and the time (
TTS
) from now to entering the ship domain is greater than
Ts2
, the TS will not
Appl. Sci. 2023,13, 8437 10 of 22
be included in the computation. The aim of it is to prevent frequent steering decisions by
the system caused by the targets very far away for which no collision avoidance actions are
actually needed.
3.3. Ship Position Monitoring Method
Ships shall navigate on the centerline as much as possible when navigating within the
channel of TSS to avoid navigation risks, such as grounding, hitting rocks, and sailing out
of the traffic lane due to anti-collision or human negligence. As a result, the track control
boundary line is established in the traffic lane as the ship’s safe navigation zone in this
study. A yaw warning is delivered when the ship departs the region, reminding the ship
navigators to alter the course in a timely manner.
Set
DIS
as the distance from the track control boundary line to the real traffic lane
boundary line. Because the traffic lane in the Chengshantou TSS waters is very wide and
the ship in the study is large,
DIS =
2
L
is used in the study. Figure 5displays the ship
location monitoring method.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 10 of 23
3.3. Ship Position Monitoring Method
Ships shall navigate on the centerline as much as possible when navigating within
the channel of TSS to avoid navigation risks, such as grounding, hiing rocks, and sailing
out of the traffic lane due to anti-collision or human negligence. As a result, the track con-
trol boundary line is established in the traffic lane as the ship’s safe navigation zone in this
study. A yaw warning is delivered when the ship departs the region, reminding the ship
navigators to alter the course in a timely manner.
Set 𝐷𝐼𝑆 as the distance from the track control boundary line to the real traffic lane
boundary line. Because the traffic lane in the Chengshantou TSS waters is very wide and
the ship in the study is large, 𝐷𝐼𝑆=2𝐿 is used in the study. Figure 5 displays the ship
location monitoring method.
Figure 5. Ship position monitoring schematic diagram.
When 𝐷𝐼𝑆 < 𝐷𝐼𝑆 or 𝐷𝐼𝑆 < 𝐷𝐼𝑆, a yaw warning will be issued to remind the nav-
igator to adjust the course. Equation (18) shows the 𝐷𝐼𝑆 and 𝐷𝐼𝑆 computation method-
ology.
𝐷𝐼𝑆=|
|
𝐷𝐼𝑆=|
|
(18)
where 𝑝 is the slope of the traffic lane boundary.
4. Collision Avoidance Decision-Making Method
Ships will encounter many unknown factors during navigation which are also ex-
tremely difficult to forecast, such as TSs’ uncoordinated collision avoidance maneuvers,
which makes research on ship maneuvering decision-making approaches extremely diffi-
cult. To deal with the TS’s unpredictable maneuvering, this research developed a maneu-
vering decision method based on time series rolling calculation and produced adaptive
decisions by rapidly updating input data.
4.1. Encounter Situation Recognition Model
The encounter situation of the two ships, as well as whether the ship being a give-
way ship, can be determined using the encounter situation identification model based on
the comparison of ship angles described in the previous study [15].
The condition of the collision risk of ships existing is that there is a PCR and 𝐶𝑅,
which is the value of CRI is greater than 0. Figure 6 depicts the model for judging the
different types of encounter situations that can occur in the TSS waters.
Figure 5. Ship position monitoring schematic diagram.
When
DISS<DIS
or
DISP<DIS
, a yaw warning will be issued to remind the naviga-
tor to adjust the course. Equation (18) shows the
DISS
and
DISP
computation methodology.
DISS=|px−y+YTsm
n−pXTsm
n|
√1+p2
DISP=|px−y+YTsm+1
n−pXTsm+1
n|
√1+p2
(18)
where pis the slope of the traffic lane boundary.
4. Collision Avoidance Decision-Making Method
Ships will encounter many unknown factors during navigation which are also ex-
tremely difficult to forecast, such as TSs’ uncoordinated collision avoidance maneuvers,
which makes research on ship maneuvering decision-making approaches extremely diffi-
cult. To deal with the TS’s unpredictable maneuvering, this research developed a maneu-
vering decision method based on time series rolling calculation and produced adaptive
decisions by rapidly updating input data.
4.1. Encounter Situation Recognition Model
The encounter situation of the two ships, as well as whether the ship being a give-way
ship, can be determined using the encounter situation identification model based on the
comparison of ship angles described in the previous study [15].
Appl. Sci. 2023,13, 8437 11 of 22
The condition of the collision risk of ships existing is that there is a PCR and
CR
, which
is the value of CRI is greater than 0. Figure 6depicts the model for judging the different
types of encounter situations that can occur in the TSS waters.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 11 of 23
Figure 6. Encounter Situation Recognition Model.
4.2. Collision Avoidance and Manoeuvre Principle
1. Collision avoidance principle
The OS in this work is an ordinary power-driven vessel sailing in the Chengshantou
TSS. While the OS sails in the recommended traffic flow direction, all TSs are classified as
ordinary power-driven vessels and special ships described in Table 2. What is more, ordi-
nary power-driven vessels are classified as whether they sail along recommended traffic
flow direction.
Table 2. Classification of special ships.
Category Vessel Engaged
in Fishing
Vessel Restricted in Her
Ability
to Maneuver
Not under Command Vessel Non-Powered Vessel
Characteristics
A vessel is small in size and
engaged in fishing, and a large
safety distance needs to be
maintained
The vessel is restricted in
her ability to maneuver
and cannot give way to
another vessel
A vessel whose main engine,
steering gear, etc., is out of
control and cannot give way
to another vessel
Vessels that do not
use propeller sailing
Figure 6. Encounter Situation Recognition Model.
Appl. Sci. 2023,13, 8437 12 of 22
4.2. Collision Avoidance and Manoeuvre Principle
1. Collision avoidance principle
The OS in this work is an ordinary power-driven vessel sailing in the Chengshantou
TSS. While the OS sails in the recommended traffic flow direction, all TSs are classified
as ordinary power-driven vessels and special ships described in Table 2. What is more,
ordinary power-driven vessels are classified as whether they sail along recommended
traffic flow direction.
Table 2. Classification of special ships.
Category Vessel Engaged
in Fishing
Vessel Restricted in
Her Ability
to Maneuver
Not under
Command Vessel Non-Powered Vessel
Characteristics
A vessel is small in size
and engaged in fishing,
and a large safety distance
needs to be maintained
The vessel is restricted in her
ability to maneuver and
cannot give way to
another vessel
A vessel whose main
engine, steering gear, etc.,
is out of control and
cannot give way to
another vessel
Vessels that do not use
propeller sailing
The responsibility of taking avoidance actions of OS can be identified as per “COL-
REGs” when the TS poses a risk of collision. Although certain target vessels have the
obligation of not impeding, when the OS and special ships pose a risk of collision, the OS
remains a give-way ship. For ordinary power-driven vessels, it can be determined by the
encounter situation identification model.
When the OS is unable to sail in the general direction of traffic flow for any reason,
she should resume sailing in that direction as quickly as practical.
2. The principle of collision avoidance
On condition that the OS is running at sea speed in the Chengshantou TSS, a head-on
situation may appear if the TS violates the ship’s routing provisions and sails in the opposite
direction. The OS shall normally alter course to the starboard side and pass from the TS’s
port side.
If the minimum distance between the OS and the TSS boundary line is very small, a
violation of the ship’s routing may therefore occur after the OS alters course to starboard and
invades the boundary line, and the collision avoidance action may be different. When the TS
is far away, and there is no risk of collision (but PCR exists), altering the course to the port
side can also be accepted. However, when a collision risk exists, the OS can only alter course
to the starboard side, according to the COLREGs and the requirements of good seamanship.
When the OS is a give-way vessel in an overtaking situation, she should stay out of
the way of the overtaken vessel and can choose to overtake in a direction with a smaller
diversion. In a crossing situation, the OS can only alter course to starboard by a large
margin and avoid crossing the fore of the stand-on vessel.
In the early stages of a developed collision risk, while the OS is a stand-on vessel,
she should keep course and speed. If the give-way vessel does not behave according to
the COLREGs until
CR >
0.2, the OS will alter course to starboard to avoid collision in a
crossing situation. In an overtaking situation, the OS can choose an anti-collision action
with a smaller course alteration amplitude. The master can set the parameter
CR
to match
the actual situation, and the system will execute it automatically. Collision avoidance
details can refer to the previous research [7].
Appl. Sci. 2023,13, 8437 13 of 22
4.3. Collision Avoidance Mechanism
The collision avoidance mechanism is defined as a rule between the ship motion vector
and the collision avoidance effect [
20
]. It refers to the relationship between the OS’s velocity
vector and collision avoidance results under the limits of ships routing in TSS waters and
be shown through the following steps.
Step 1: If a TS enters the OS’s ship domain within the time
Ts2
, the time of the TS
from the current time to enter the OS’s ship domain (TESD) is obtained from Figure 7. In
addition, the TS’s CRI is obtained via Section 3.2, and the TS’s details, as well as the CRI’s
value
CR
are logged. Furthermore, it is important to keep a record of how many TSs
(N)
of this type there are.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 13 of 23
Figure 7. Flowchart for TESD (𝑇) computation
Step 2: If 𝑁≠0, use the TS information saved in Step 1 to find the TS with the highest
CRI value. This is the most dangerous TS, and the CRI value of which ship is logged as 𝐶𝑅.
Step 3: Determine the direction of the OS’s course altering based on the most danger-
ous TS, as indicated in Figure 8.
Figure 8. The judgment of direction of course alteration.
Step 4: Increase the course alteration angle at 1° intervals based on the results of the
third step’s judgment. Furthermore, judge whether the OS can clear all of the TSs, and
obtain the minimal course alteration angle that can clear all TSs. As indicated in Figure 9.
The OS’s course-altering angle should not be too large due to the high traffic flow in the
seas of the TSS and the traffic lane limits. In this study, when the OS’s course altering angle
(𝛽) reaches 45° to the port or starboard side, it is still impossible to clear all TSs, which
shows no acceptable maneuvering scheme can be obtained.
Figure 7. Flowchart for TESD (TTs ) computation.
Step 2: If
N6=
0, use the TS information saved in Step 1 to find the TS with the highest
CRI value. This is the most dangerous TS, and the CRI value of which ship is logged as
CRmax
.
Step 3: Determine the direction of the OS’s course altering based on the most dangerous
TS, as indicated in Figure 8.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 13 of 23
Figure 7. Flowchart for TESD (𝑇) computation
Step 2: If 𝑁≠0, use the TS information saved in Step 1 to find the TS with the highest
CRI value. This is the most dangerous TS, and the CRI value of which ship is logged as 𝐶𝑅.
Step 3: Determine the direction of the OS’s course altering based on the most danger-
ous TS, as indicated in Figure 8.
Figure 8. The judgment of direction of course alteration.
Step 4: Increase the course alteration angle at 1° intervals based on the results of the
third step’s judgment. Furthermore, judge whether the OS can clear all of the TSs, and
obtain the minimal course alteration angle that can clear all TSs. As indicated in Figure 9.
The OS’s course-altering angle should not be too large due to the high traffic flow in the
seas of the TSS and the traffic lane limits. In this study, when the OS’s course altering angle
(𝛽) reaches 45° to the port or starboard side, it is still impossible to clear all TSs, which
shows no acceptable maneuvering scheme can be obtained.
Figure 8. The judgment of direction of course alteration.
Appl. Sci. 2023,13, 8437 14 of 22
Step 4: Increase the course alteration angle at 1
◦
intervals based on the results of the
third step’s judgment. Furthermore, judge whether the OS can clear all of the TSs, and
obtain the minimal course alteration angle that can clear all TSs. As indicated in Figure 9.
The OS’s course-altering angle should not be too large due to the high traffic flow in the
seas of the TSS and the traffic lane limits. In this study, when the OS’s course altering angle
(
β
) reaches 45
◦
to the port or starboard side, it is still impossible to clear all TSs, which
shows no acceptable maneuvering scheme can be obtained.
Step 5: Start the collision avoidance maneuver if a feasible course-altering angle is
determined in Step 4. Determine whether the distance between the OS and the fairway’s
boundary line is smaller than DIS during the diversion process. If it is less than
DIS
, the
OS plans to sail along the fairway’s boundary in the general direction of traffic flow to
avoid leaving the traffic lane.
Appl. Sci. 2023, 13, x FOR PEER REVIEW 14 of 23
Figure 9. Flowchart of feasible course altering angle obtaining.
Step 5: Start the collision avoidance maneuver if a feasible course-altering angle is
determined in Step 4. Determine whether the distance between the OS and the fairway’s
boundary line is smaller than DIS during the diversion process. If it is less than 𝐷𝐼𝑆, the
OS plans to sail along the fairway’s boundary in the general direction of traffic flow to
avoid leaving the traffic lane.
4.4. Method of Resuming the Original Route
When the OS is sailing in the general direction of the traffic flow in the traffic lane,
the course and position may deviate from the planning route due to anti-collision with
obstacles. After passing and then keeping clear of the obstacles, OS will try to return to
the planned route and follow the recommended traffic flow direction sailing. This process
of sailing is called “resume sailing”. When resuming sailing, the target point is the inter-
section of the planned route of the current segment and the line between this segment and
the next segment of the traffic lane.
Figure 10 shows a schematic diagram of the resume sailing method, with 𝑁 point-
ing to true north, WPT2 representing the target point of the OS’s resume sailing, 𝐶,
representing the current segment’s planned route direction (the course from waypoint
WPT1 to waypoint WPT2), and 𝑇𝐵 representing the true bearing of the OS relative to the
target point.
1. Target course of resume sailing
To ensure that the OS returns and sails following the planned route, the target course
𝐶 should be determined based on the relative position of OS and the planned route.
Equation (19) demonstrates this.
𝐶=
𝑓
𝑇𝐵−𝐶,+𝐶, (19)
where 𝑓 is the approach coefficient, which has a value greater than 1. The approaching
speed to the planned route will be too slow if the value of m is too lile. If the 𝑓 is too
great, the difference between the ship’s course and the general direction of traffic flow will
be too large, and the voyage will be squandered, which will prevent the resume sailing
procedure from being completed. This research argues that taking 𝑓=1.5 is more ac-
ceptable based on several experiments [15].
Figure 9. Flowchart of feasible course altering angle obtaining.
4.4. Method of Resuming the Original Route
When the OS is sailing in the general direction of the traffic flow in the traffic lane,
the course and position may deviate from the planning route due to anti-collision with
obstacles. After passing and then keeping clear of the obstacles, OS will try to return to the
planned route and follow the recommended traffic flow direction sailing. This process of
sailing is called “resume sailing”. When resuming sailing, the target point is the intersection
of the planned route of the current segment and the line between this segment and the next
segment of the traffic lane.
Figure 10 shows a schematic diagram of the resume sailing method, with
NT
pointing
to true north,
WPT
2 representing the target point of the OS’s resume sailing,
Cw,w+1
representing the current segment’s planned route direction (the course from waypoint
WPT
1 to waypoint
WPT
2), and
TB
representing the true bearing of the OS relative to the
target point.
Appl. Sci. 2023,13, 8437 15 of 22
Appl. Sci. 2023, 13, x FOR PEER REVIEW 15 of 23
Figure 10. Schematic diagram of the resume sailing.
2. Resume sailing time
When the OS alters her course to avoid the TS, whether she can resume sailing will
be assessed in the next time step. The discrete method can be used to nd the earliest
resume time. The diagram of Figure 11 depicts the specic calculating procedure.
Figure 11. The procedure of resuming sailing.
This work develops the maneuvering decision-making method, as shown in Figure
12. The collision avoidance system continually cycles the process at 5 s intervals through-
out the operation, based on the above research.
Figure 10. Schematic diagram of the resume sailing.
1. Target course of resume sailing
To ensure that the OS returns and sails following the planned route, the target course
CT
should be determined based on the relative position of OS and the planned route.
Equation (19) demonstrates this.
CT=f(TB −Cw,w+1)+Cw,w+1(19)
where
f
is the approach coefficient, which has a value greater than 1. The approaching
speed to the planned route will be too slow if the value of m is too little. If the
f
is too great,
the difference between the ship’s course and the general direction of traffic flow will be too
large, and the voyage will be squandered, which will prevent the resume sailing procedure
from being completed. This research argues that taking
f=
1.5 is more acceptable based
on several experiments [15].
2. Resume sailing time
When the OS alters her course to avoid the TS, whether she can resume sailing will be
assessed in the next time step. The discrete method can be used to find the earliest resume
time. The diagram of Figure 11 depicts the specific calculating procedure.
This work develops the maneuvering decision-making method, as shown in Figure 12.
The collision avoidance system continually cycles the process at 5 s intervals throughout
the operation, based on the above research.
Appl. Sci. 2023,13, 8437 16 of 22
Appl. Sci. 2023, 13, x FOR PEER REVIEW 15 of 23
Figure 10. Schematic diagram of the resume sailing.
2. Resume sailing time
When the OS alters her course to avoid the TS, whether she can resume sailing will
be assessed in the next time step. The discrete method can be used to find the earliest
resume time. The diagram of Figure 11 depicts the specific calculating procedure.
Figure 11. The procedure of resuming sailing.
This work develops the maneuvering decision-making method, as shown in Figure
12. The collision avoidance