collision risk assessment for ships
TRANSCRIPT
ORIGINAL ARTICLE
Collision risk assessment for ships
CheeKuang Tam • Richard Bucknall
Received: 27 May 2009 / Accepted: 26 March 2010 / Published online: 23 April 2010
� JASNAOE 2010
Abstract Efficient maritime navigation through dynamic
obstructions at close range is still a serious issue faced by
mariners. There have been studies focusing on collision
risk assessment in the past, but the majority were based on
the first person perspective, with area-based ship domain
concepts that are defined around either the ownship or the
obstacle. Such methods are acceptable for encounters
where the ownship is required to manoeuvre according to
the collision regulations (COLREGs), but they will not
work correctly if the ownship is the stay-on party. This
article presents an alternative method of assessing the
collision risk for surface ships in close-range encounters
that is compliant with the COLREGs as well as other ships
from different perspectives.
Keywords Collision risk � Collision avoidance �Evasive manoeuvre
1 Motivation
Efficient maritime navigation through dynamic obstacles at
close range is still one of the many problems faced by
mariners, especially in terms of determining the manoeu-
vres necessary to avoid a potential collision that is com-
pliant with the collision regulations (COLREGs). In the
past, studies have been conducted to assess the collision
risk using parameters based on the properties related to the
closest point of approach (CPA), such as the time (TCPA)
and distance (DCPA); however, such approaches only
provide one-dimensional information on the traffic situa-
tion. A two-dimensional assessment of the collision risk,
the ship domain concept, was introduced by Fujii et al. [1]
and Goodwin [2], using an area around either the OS or
TS1 to indicate the risk of collision, which is easily visu-
alised in 2-D space. There are numerous subsequent studies
[3–5] that have focused on collision risk assessment using
such area-based concepts, but which employ a modified
model or different methodologies to generate the boundary
of the safety area (i.e. fuzzy logic or artificial neural net-
works); these studies have been reviewed and discussed in
Tam et al. [6] and Thomas et al. [7].
Overall, the majority of these studies are based on the
ship domain concept and define a safety area around either
the OS or TS which represents the region where other ships
should not enter so as to avoid the need to make evasive
manoeuvres. These studies have not incorporated the
COLREGs explicitly in such a way that all obstacles have
areas that the OS should not enter, or an area around the OS
that all other obstacles should keep out of. The effects of
COLREGs were partially realised by employing a specially
constructed geometry of the safety area, i.e. the approaches
of Smierzchalski [8] and Davis et al. [4], where the safety
area is enlarged on the starboard side so that a longer
distance is needed if the navigation path is around the
starboard side. This makes navigation around the port side
a more favourable manoeuvre, mimicking the effect of the
COLREGs in certain types of encounter. Such methods are
acceptable for encounters where the OS is legally obliged
C. Tam (&) � R. Bucknall
Department of Mechanical Engineering,
University College London,
Torrington Place, London WC1E 7JE, UK
e-mail: [email protected]
1 In this article, a ship that is in direct control is referred as an
ownship (OS), while any other ship besides an OS is referred as the
target ship (TS) or obstacle.
123
J Mar Sci Technol (2010) 15:257–270
DOI 10.1007/s00773-010-0089-7
to give way to the TS, but will not interpret the traffic
scenario correctly otherwise.
Other studies, which have used other techniques such as
reinforced learning [9] or fuzzy logic based [10] collision
risk assessments, usually contain explicit requirements of
the COLREGs based on evaluating the direction of
approach of the TS. However, such approaches are gen-
erally not suitable for path-planning algorithms, as they
solely determine the safest manoeuvre for a single obstacle
at a particular instance—typically the obstacle with the
highest risk of collision without considering other obstacles
with a lower risk of collision. This way of assessing the
collision risk could lead the OS into an unfavourable sit-
uation at a later stage, as it is not considering the overall
picture of the traffic scenario.
In addition, most studies have taken the first person
view, where the OS is the only manoeuvring party while
the other object remains at the detected bearing; hence, the
resulting safety area would not be compatible if the colli-
sion risk is evaluated from different perspectives. The
result of such an approach is that the OS would avoid all
other obstacles even though the OS is not legally obliged to
give way. This article reports a novel method of assessing
the risk of collision for ships, which was developed spe-
cifically for close-range encounters that address the short-
comings identified above.
This article is structured into three main sections: Sect. 2
explains the concept as well as the assumptions of the
proposed method in assessing the risk of collision, which is
determined based on two major conditions—the encounter
type (Sect. 2.2) and the dimensions of the safety area (Sect.
2.3). Simulation results are presented in Sect. 3; they are
grouped according to type of encounter. The results are
followed by a discussion in Sect. 4. Section 5 is a con-
clusion that focuses on the main findings and explains
aspects of the next publication on an extension to this
study.
2 Concept
2.1 Simplification
In order to reduce the computational complexity and
resources, all ships (including the OS and all TS) are
reduced to point objects, since the ratio of the distance
traversed across the water to the ship’s dimensions is
normally large, even in close-range encounters.
Due to the fact that there are no explicit guidelines or
regulations on safe distances, there are bound to be dis-
agreements regarding the ‘‘appropriate’’ dimensions of the
safety area among navigators due to different interpreta-
tions of the traffic scenario; hence, the safety area is
designed to be as general as possible while maintaining the
flexibility to be customised to different ship dynamic
properties.
Furthermore, it is worth emphasising that this study is
not intended to recommend a specific dimension of the
safety area, as this topic has been well documented by
some recent studies [11, 12]. In addition, the method used
in the generation of a navigation path that is COLREGs
compliant will not be discussed in this article, but will be
the subject of the next publication from us.
2.2 Overview
Figure 1 shows the overall concept and processes involved
in assessing the risk of collision. It is assessed based on the
discretised navigation path of the OS, where the type of
instantaneous encounter and the risk of collision are eval-
uated. The assessment process involves computing the
dimensions and shape of the safety area, which is consid-
ered the region where ships should not normally enter, as
the relative distance between the ships is too low to allow
safe operation in this area; this is similar to the concept
proposed by Goodwin [2]. The risk of collision is assessed
in two main steps (italics in Fig. 1): determining the type of
encounter and determining the dimensions of the safety
area, which is explained in Sects. 2.3 and 2.4 respectively.
The collision risk assessment process effectively works in a
loop in such a way that it evaluates all of the discretised
points along the navigation path for risk of collision;
however, as mentioned in Sect. 2.1, it only indicates the
suitability of the navigation path for the traffic scenario; it
does not provide suggestions regarding the best evasive
manoeuvre.
2.3 Encounter type for each obstacle
The safety area developed in this study will be located
only on selected obstacles that the OS is mandated to give
way to according to the COLREGs. There is no safety area
on the OS; the benefits of this approach are discussed in
Sect. 3.
In this study, the collision risk between the OS and the
obstacle is assessed by an area-based method similar to that
of Davis et al. [4]. However, the safety area will be located
on the obstacle, and the dimensions and geometry of the
safety area are determined using a different principle. The
safety area will be computed at a fixed temporal interval
for all obstacles. The overall approach can be explained in
two steps: the first step involves determining the type of
encounter with the obstacle of concern; the second step
involves calculating the dimensions of the safety area as
necessary.
258 J Mar Sci Technol (2010) 15:257–270
123
The need for a safety area around an obstacle is deter-
mined by the type of encounter associated with it; each
obstacle is categorised into a particular encounter type
based on its direction of approach as well as its relative
bearing with respect to the heading of the OS (OS_hs). The
obstacle is first categorised based on its instantaneous
position with respect to the heading and position of the OS
according to the regions defined in Fig. 2. The regions R1
to R6 are arbitrary regions created using data from the
COLREGs, where:
fHO1;HO2;OT1;OT2g ¼ fp=8; 15=8p; 5=8p; 11=8pg:
The values of OT1 and OT2 are based on Rule 13 of the
COLREGs, which defines an overtaking encounter. How-
ever, there is no explicit guideline in Rule 14 of the
COLREGs that defines a head-on encounter, except when
discussing the visibility of the masthead light and side-
lights; sidelight visibility is defined in Annex I 9(a) of the
COLREGs to be small (1–3�). In this study, instead of
the recommended values, the HO1 and HO2 values were
increased (to angles of p/8 radians), and they will be dis-
cussed later.
The obstacle is also further categorised based on its
relative heading with respect to the heading of the OS,
based on the same principle used to categorise the instan-
taneous position. The categorising regions TSR1 to TSR6
are again arbitrary regions, as shown in Fig. 3.
Finally, the encounter type will be determined based on
the combination of the instantaneous categorisation of the
obstacle’s relative position and its heading with respect to
the position and heading of the OS. The overall idea is
illustrated in Fig. 4, where categories of relative TS
heading are placed on top of categories of relative TS
position with respect to the position and heading of the OS.
Short descriptions of each possible encounter type are lis-
ted in Table 1; the difference between a ‘‘stay-on’’ and a
‘‘safe’’ encounter is that, in a ‘‘stay-on’’ encounter, the OS
is within the collision range of the obstacle, and the
obstacle is expected to avoid such encounters by initiating
an evasive manoeuvre according to the rules of the
If needed
Else
Yes No
Collision risk assessment
Navigation path of OS
Discretised at fixed intervals At each point
Determinine
the instantaneous
position and heading
All TS
Based on projection
of initial velocity vector
Determine the type of
encounter for all TS
Determinethe dimensions
of the safety area
No risk of collision
Check whether OS is in safety area?
Risk of collision exists
Next time step
Fig. 1 Flow chart of the
collision risk assessment
process
OS_ s
R1
R4
R2
R3
R6
R5
HO1HO2
2
3
2
OT1OT2
Fig. 2 Regions used to categorise the position of the obstacle; the OS
is located at the centre
J Mar Sci Technol (2010) 15:257–270 259
123
COLREGs; on the other hand, in a ‘‘safe’’ encounter, there
is no close range contact, and hence the obstacle can be
safely disregarded so long as both the OS and the obstacle
maintain the initial heading.
As mentioned earlier, the HO1 and HO2 values are larger
(angles of p/8 radians) than those recommended, as it has
OS_ s
TSR1
TSR4
TSR2
TSR3
TSR6
TSR5
HO1HO2
2
3
2
OT1OT2
Fig. 3 Regions used to categorise the heading of the obstacle
R1
R4
R2
R3
R6
R5
OT
HO
SO
SO
SF
SF
OT
HO
SF
SF
GW
GW
OT
HO
SO
SO
GW
GW
OT
SF
SF
SF
GW
GW
OT
SF
SO
SO
SF
SF
OT
SF
SO
SF
GW
SF
OS_ s
Fig. 4 Chart used to determine
the encounter type. An obstacle
is associated with a different
encounter type depending on its
bearing and position relative to
the OS. For example, if the
obstacle is located in the region
R2, and the heading of the
obstacle is in the zone TSR1,
the resulting encounter type for
the obstacle will be an
overtaking (OT) encounter,
according to the label
Table 1 Abbreviations for and brief descriptions of encounter types
for obstacles
Abbreviation Description
HO Head-on encounter
OT Overtaking encounter
SO Stay-on encounter
SF Safe encounter
GW Give-way encounter
ST Static obstacle
260 J Mar Sci Technol (2010) 15:257–270
123
been found from simulations that the algorithm behaves
better with increased angles. With small angles, the
encounter type changed from HO to either GW or SO
rather sensitively upon small changes in the OS heading.
This is because the region R1 was too narrow. Note that
there is a drastic difference between HO and GW or SO in
term of legal status: only one of the ships needs to perform
the evasive manoeuvre in a GW or SO while the other
maintains its course, whereas both ships must perform
evasive manoeuvres in an HO. On the other hand, the
enlarged R1 also provides an additional buffer against
uncertainties when deciding upon the type of encounter
occurring; as stated in Rule 14 (c), ‘‘when a vessel is in any
doubt as to whether such a situation exists she shall assume
that it does exist and act accordingly’’. Therefore, the
approach adopted in this study is biased towards the safe
and conservative side; it considers marginal HO and GW
encounters to be HO encounters, where both ships should
perform evasive manoeuvres.
2.4 Dimensions of the safety area
Collision risk assessment is based on safety areas around
each obstacle, as this is the most computationally practical
and popular method. The dimensions and shape of the
safety area depend on the type of encounter as well as the
relative speeds of the OS and the obstacle of concern, as
shown in Table 2.
StaticRadius is the minimum safe relative distance
between the OS and a static obstacle, while TS_U and
OS_U are the speeds of the TS and OS, respectively. CSA
is a function that computes the dimensions of a circular
safety domain in an encounter in which the OS overtakes
the TS, and is defined as follows:
where OTScaling (= 1.0 min) is the safety area scaling
factor for a specific overtaking encounter, which is intro-
duced as a way to customise the shape and dimensions of
the safety area. MinSAD is the minimum safe distance that
must be maintained between OS and TS for safety pur-
poses. It is defined as 0.25 nmi, computed based on the
distance covered by a TS travelling at 30 kn in 30 s, which
is considered sufficient for most evasive manoeuvres. The
geometry of the safety area for such an encounter is
deemed to be circular, because such a shape maintains the
safe distance at the stern section of the TS, while also
ensuring that the safe distance from the side of the TS is
maintained if the TS fails to notice the OS overtaking from
stern. The safety area at the bow section of the TS is
insignificant for two reasons; first, since TS_U B OS_U, a
circular safety area with a radius proportional to TS_U is
considered sufficient to ensure safety. Second, once the OS
has successfully overtaken the TS, the encounter type
changes and hence the circular safety area alters according
to the new traffic configuration, meaning that its role is not
as significant under such conditions.
For HO and GW encounters, the safety area is half-
elliptical, and it is different from previously published
studies in such a way that the safety area at the fore section
of the TS is elliptical while that at the aft section is circular.
The dimensions of this half-elliptical area are computed by
two common functions, namely ESAA and ESAF, which
determine the radii for the aft and fore sections of the
safety area, respectively. The reason for dividing the
elliptical domain into fore and aft sections is to reduce
complexity when modelling the geometry of the safety
area. ESAA is defined as follows:
Table 2 Dimensions of the safety area for different encounter types
Dimensions (shape) Condition
0 Encounter type = SO OR SF
CSA (circular) Encounter type = OT AND TS_U B OS_U
ESA (half-elliptical) Encounter type = HO
0 Encounter type = OT AND TS_U [ OS_U
ESA (half-elliptical) Encounter type = GW
StaticRadius (circular) Encounter type = ST
StaticRadius is the minimum safe relative distance between the OS
and a static obstacle, CSA refers to a circular safety domain, ESArefers to a half-elliptical safety domain, while TS_U and OS_U are the
speeds of the TS and OS, respectively
CSA ¼ TS U� OTScaling if TS U� OTScaling�MinSAD;MinSAD otherwise;
�
ESAA ¼ RadiusAþ DTScaling if RadiusA�MinSAD�MinSAD;MinSAD otherwise;
�
J Mar Sci Technol (2010) 15:257–270 261
123
where DTScaling = ||Dt|| 9 DTScale (in min) is the function
that relates ||Dt|| (the size of the time step, Dt) to the dimen-
sions of the safety area, such that a large ||Dt|| will give a
slightly larger safety area in order to prevent tunnelling.
DTScale (= 0.5) is the predefined dimensionless scaling factor
for the magnitude of the time step, and RadiusA computes the
safety area’s aft-section radius, defined as follows:
where SAScaling (= 1.0 min for ESAA and 1.5 min for ESAF)
is the generic scaling variable of the safety area, which
depends on the type of encounter (HO or GW). SASLimit
(*0.7 nmi) is a predefined scalar property that limits the
maximum allowable safety area radius on the side and stern
sections; it depends on the manoeuvrability of the TS and will
be explained in detail later. Similar to OTScaling, the
parameters DTScale, DTScaling, SAScaling and RadiusA are
introduced to the process in order to act as customising
parameters; the values used in this study are based on educated
guesses for the performance of a typical 10 t ship. The changes
in the magnitudes of the radii at the aft and fore sections are
collectively shown in Fig. 5; the dotted line represents the
output of the ESAA function, which starts with a constant
value of MinSAD when RadiusA is lower than MinSAD, so
that a minimum clearance distance is maintained between the
OS and TS. Once RadiusA is greater than MinSAD, it grows
linearly with TS_U, reaching a peak at SASLimit; then it
decreases linearly before settling at MinSAD, the minimum
allowable size of the safety area.The function that determines
the safety area’s fore section (ESAF) is defined as:
Referring to Fig. 5, ESAF returns a similar output to
ESAA at low speeds (up to the speed where the size of the
safety area reaches SASLimit); at high speeds, ESAA is
capped and gradually reduces to MinSAD, while ESAF
increases in proportion to TS_U, as more emphasis is
placed on the fore section of the safety area or the direction
of travel of the TS at high TS_U.
The combined outputs of ESAA and ESAF are depicted
in Fig. 6. At low TS_U, the safety area is circular;
assuming that the ship has high manoeuvrability and low
inertia at low speed, the TS can easily turn in any direction,
so the probability of existence is evenly distributed around
the TS. As TS_U increases, the safety area gets larger
while maintaining a circular shape up to a certain TS_U
value (the peak of the dotted line, TS_U & 0.5), which is
referred as SASLimit. Practically speaking, the value of
TS_U at which SASLimit occurs should be specific to each
TS, as different ships have different characteristics and
manoeuvrability; however, for simplicity, all ships were
assumed to have the same dynamic properties in this study
(i.e. a 10 t displacement vessel).
When TS_U [ 0.5, the output of the ESAA function
reduces while the output of ESAF increases, such that the
fore section of the safety area becomes elliptical while the
aft section remains circular but diminishes in radius. Such a
change in geometry is designed to emulate the behaviour
and manoeuvrability of a typical displacement ship. When
it is travelling above a certain speed, its manoeuvrability
deteriorates and hence the ship is more likely to travel in
the direction of the initial velocity vector, so the safety area
has an elliptical shape that follows its velocity vector, with
a higher probability of the OS existing directly in front of
its velocity vector. Also note that the minor axis of the
safety area has a radius similar to that of the aft section, so
that the safety area always has a continuous boundary.
The radius of the safety area at the aft section reduces as
an indication of TS diminishing probability of existence at
its side and aft sections. This trend persists until ESAA
reaches MinSAD, where ESAF continues to increase
according to the magnitude of TS_U while ESAA remains
at MinSAD, thus ensuring that, regardless of the magnitude
0.2 0.4 0.6 0.8 1.0 1.2 1.4TS_U, kn
0.5
MinSAD
SASLimit
1.
1.5
Safety area outputs, nm
ESAF
ESAA
Fig. 5 Safety area outputs for increasing TS_U. The dotted linerepresents the output for the aft section, while the dashed linerepresents the fore section of the TS
RadiusA ¼ TS U� SAScaling TS U� SAScaling\SASLimit;2 SASLimit� ðTS U� SAScalingÞ otherwise;
�
ESAF ¼ ðTS U� SAScalingÞ þ DTScaling if ðTS U� SAScalingÞ þ DTScaling�MinSAD;MinSAD otherwise;
�
262 J Mar Sci Technol (2010) 15:257–270
123
of TS_U, a minimum clearance between OS and TS is
maintained at the instantaneous positions at all times. As
explained earlier, the OT encounter type has a circular
safety area because, in an overtaking encounter, the OS
approaches the TS from aft, so a safety area with a
diminishing aft section is not suitable for such an
encounter.
As mentioned earlier, the safety area is a concept with
no established geometrical or dimensional standards in
collision risk assessment; it is open to alternate interpre-
tations in terms of the traffic scenario, and different people
may be prepared to perform riskier manoeuvres. For
this reason, all of the parameters (OTScaling, DTScale,
SAScaling, SASLimit and MinSAD) can be altered to
accommodate the effects of changes in manoeuvrability
due to changes in speed, different ship types, or to account
for different personal judgements.
In addition, the dimensions and geometry of the safety
area can be further enhanced by using data on the ship’s
length, manoeuvrability and dynamic characteristics.
Since this study focuses on close-range encounters, we
can also increase the size of MinSAD in order to maintain
a healthy distance from the TS during a close-range
encounter, thus preventing the performance of the OS
from being dynamically affected by the pressure field of
the TS.
3 Simulations
The proposed method of collision risk assessment was
tested with a range of typical traffic scenarios that were
constructed specifically to emulate different types of
encounter, and which can be grouped according to the
initial position and heading of the obstacle. These simu-
lations were setup to study the variation in the safety area
over time, as both the OS and obstacles move according to
the navigation path. As mentioned earlier, the method used
to generate the navigation path, which is COLREGs
compliant, will not be discussed here.
0.2 nm min , 12. kn
0.37 aft, 0.37 fore
2 1 0 1 22
1
0
1
2
0.45 nm min , 27. kn
0.62 aft, 0.62 fore
2 1 0 1 22
1
0
1
2
0.7 nm min , 42. kn
0.47 aft, 0.87 fore
2 1 0 1 22
1
0
1
2
0.95 nm min , 57. kn
0.25 aft, 1.1 fore
2 1 0 1 22
1
0
1
2
1.2 nm min , 72. kn
0.25 aft, 1.4 fore
2 1 0 1 22
1
0
1
2
1.45 nm min , 87. kn
0.25 aft, 1.6 fore
2 1 0 1 22
1
0
1
2
Fig. 6 The changes in the shape of the combined outputs of ESAA
and ESAF (i.e. the safety area) as TS_U is increased. Note that a
scaling factor of 1 was used. The black arrows indicate the magnitude
and direction of TS_U. The top row of numerical values in each figure
indicate the speed of the TS in different units (nm/min and kn), while
the bottom row of numerical values shows the dimensions of the
safety areas for the aft and fore sections, respectively. The values on
the X and Y axes are in nmi
J Mar Sci Technol (2010) 15:257–270 263
123
3.1 Crossing encounters
The first test cases were crossing encounters where the TS
approached the OS to port, and where both the OS and TS
had the same initial speeds. These crossing encounters
allowed us to evaluate the conceptual risk assessment
method’s interpretation of Rule 15 of the COLREGs for a
crossing situation.
A motion simulation of this scenario is shown in Fig. 7.
According to Rule 15 of the COLREGs, in such a traffic
scenario the OS is the passive party and is not required to
alter course in a stay-on (SO) encounter, whereas the TS is
the active party that has the responsibility to alter course,
crossing the OS at the stern. This explains why there is no
safety area for the TS in the figures. Figure 7 only shows
the traffic from the OS’s perspective; the TS’s interpreta-
tion will be explained next, and it is the combination of
the navigation paths from the OS and TS perspectives
that will resolve the potential collision shown in Fig. 7 at
t = 3.0 min.
The second crossing scenario was similar to the first,
except that the roles of the OS and TS were reversed, such
that the TS approaches from the OS’s starboard while the
other properties remain unchanged. This is essentially the
previous crossing test case but considered from the TS’s
perspective. A motion simulation of this test case is shown
in Fig. 8, and the aim of this test was similar to the aim of
the first test, but the OS is now the manoeuvring party and
is therefore required to avoid the TS by passing it on the
stern side while the TS stays on, in accordance with the
COLREGs.
The starboard manoeuvre is a better option since it is
shorter in length; a port manoeuvre involves a longer path
to avoid the larger fore section of the TS’s safety area. The
safety area is rendered in dark grey in the figure in order to
distinguish it from the safety area of HO, which is shown in
red in Fig. 10. The safety area exists at the initial step
(t = [0.0, 1.5]) because the TS has an encounter of type
GW (give way) according to the conditions shown in
Fig. 4. Once the TS has crossed the path of the OS, this
42.
0.000
TS
4 2 0 2 4
4
2
0
2
442.
1.500
OS
4 2 0 2 4
4
2
0
2
442.
3.000
4 2 0 2 4
4
2
0
2
4
42.
4.500
4 2 0 2 4
4
2
0
2
442.
6.000
4 2 0 2 4
4
2
0
2
442.
7.500
4 2 0 2 4
4
2
0
2
4
Fig. 7 Motion simulation of a port-crossing encounter at selected
times. There is no safety area for the TS (in gold; the arrow indicates
its velocity vector) since the OS (in red) is the stay-on party in this
traffic scenario. The numerical value in the top left corner of each
figure is the instantaneous speed of the OS in kn, and the numericalvalue in the lower left corner shows the instantaneous time in min
corresponding to that particular figure. The green circle represents the
initial position while the blue circle shows the final position of the
OS, and the yellow line is the navigation path of the OS. The values
on the axes are given in nmi, which is also true of all other figures in
this article unless otherwise stated
264 J Mar Sci Technol (2010) 15:257–270
123
changes to safe (SF) because both the OS and the TS are
moving away from each other.
These two crossing scenarios were constructed specifi-
cally to verify the consistency of the proposed collision risk
assessment method, since they essentially reverse the roles
of the OS and the TS under the same traffic scenario.
Figure 9 shows the combined navigation paths from these
crossing scenarios. It shows that the interpretations of the
traffic scenario from different perspectives are compatible
with the proposed collision risk assessment, where both
parties perform manoeuvres that are compliant with Rule
15 of the COLREGs, i.e. that a ship that has a ship
approaching from its starboard side should manoeuvre and
avoid passing ahead of the other party. If we had used
previously proposed methods where a safety area exists for
all encounter types, there would be a safety area on the TS,
and the OS in the first test case would need to manoeuvre to
port to avoid the TS even though it is not legally obliged to,
so the combination of navigation paths viewed from the
perspectives of the OS and the TS would be impractical.
3.2 Head-on encounter
The second test scenario was a head-on encounter with the
TS approaching the OS head-on. The objective of this test
was to evaluate the collision risk assessment concept in
42.
0.000
TS
4 2 0 2 4
4
2
0
2
439.7832
1.500
OS
4 2 0 2 4
4
2
0
2
442.
3.000
4 2 0 2 4
4
2
0
2
4
31.3504
4.500
4 2 0 2 4
4
2
0
2
434.3204
6.000
4 2 0 2 4
4
2
0
2
437.2904
7.500
4 2 0 2 4
4
2
0
2
4
Fig. 8 Motion simulation of the starboard crossing at selected times.
There is a safety area around the TS initially because the TS is in the
R2 and TSR5 regions, which results in a GW encounter type. The OS
is required to alter its heading to starboard, otherwise it would enter
the safety area of the TS. From t = 3.33 onwards, the encounter type
changes to safe SF according to the conditions shown in Fig. 3. The
changes in the speed of the OS at t = 1.50 and 4.50 are due to losses
of momentum by the OS after it changes heading
Positions of OS
Positions of TS
-4 -2 0 2 4-1
0
1
2
3
4
5
Fig. 9 Comparison of the navigation paths (circles represent ship
positions at different times) from the two crossing scenarios. The
straight line from right to left is the navigation path from port
crossing, while the curved path from centre to top is the starboard
crossing. The ship positions are colour coded according to the scaleon the right, where each number represents a time step
J Mar Sci Technol (2010) 15:257–270 265
123
interpreting Rule 14 of the COLREGs, which dictates that
the ships should pass each other port to port. Figure 10
shows a motion simulation of the OS performing a star-
board manoeuvre in order to pass the TS on its port side.
Similar to previous simulations, the TS is not manoeuvring
in the simulation because we are viewing the scenario from
the OS’s perspective. The method used to ensure the star-
board manoeuvre will be discussed in a subsequent publi-
cation from the authors.
Since the initial traffic conditions are the same from
either the OS’s or the TS’s perspective, given that the
initial headings of both ships cause them to be directly
head-on, observing the navigation path from the OS’s
perspective alone is sufficient to investigate the interpre-
tation of the COLREGs from a different perspective, since
the TS’s perspective of the traffic is simply a mirror image
of the OS’s perspective, as shown in Fig. 11. In the figure,
both ships are manoeuvring according to Rule 14 of the
COLREGs, such that both ships pass each other port to port
in a head-on encounter. The relative distance between the
two ships may be excessive for such a head-on encounter
because the navigation paths were generated by assuming
that the other party was maintaining course. However,
other parameters such as the magnitude of MinSAD or
42.
0.000
4 2 0 2 4
4
2
0
2
438.624
1.500
OS
TS
4 2 0 2 4
4
2
0
2
441.594
3.000
4 2 0 2 4
4
2
0
2
4
28.2489
4.500
4 2 0 2 4
4
2
0
2
431.2189
6.000
4 2 0 2 4
4
2
0
2
434.1889
7.500
4 2 0 2 4
4
2
0
2
4
Fig. 10 Motion simulation of a head-on encounter at selected times.
From t = 0.00 to t = 4.50 there is a safety area on the TS because the
encounter is of type HO according to the conditions in Fig. 4. Once
the OS has passed the TS at t = 6.00, the safety area vanishes because
the encounter changes to type SF, as both ships are moving away from
each other. The safety area is shown in red in order to differentiate it
from GW, which is shown in dark grey
Positions of OS
Positions of TS
-4 -2 0 2 4-1
0
1
2
3
4
5
Fig. 11 Ship positions based on the navigation paths during a head-
on encounter viewed from different perspectives. The navigation pathfrom centre to top refers to the OS’s perspective, while the other path
is based on the TS’s perspective. The positions of the ships are also
colour coded according to the scale on the right, where each number
represents a time step
266 J Mar Sci Technol (2010) 15:257–270
123
SAScaling can be adjusted to reduce the safety margin
between the ships, hence producing a more realistic and
practical navigation path.
3.3 Overtaking encounter
The third test scenario was an overtaking scenario where
the OS approaches the TS from TS’s stern. The aim of this
test case was to evaluate the method’s interpretation of
Rule 13 of the COLREGs. A motion simulation of this
traffic scenario is shown in Figs. 12 and 13 from the
perspectives of the OS and the TS, respectively. In
Fig. 12, which evaluates the situation from the OS’s per-
spective, there is a safety area around the TS because its
encounter type is OT (overtaking), meaning that the OS
needs to manoeuvre to either port or starboard to avoid
entering this safety area. Since the velocity of the OS is
greater than that of the TS throughout the simulation, the
safety area remains in place well after the OS has over-
taken the TS, because the encounter type of the OS
remains OT according to the conditions defined in Fig. 4
and Table 2.
Figure 13 shows a motion simulation for the same sce-
nario from the TS’s point of view. There is no safety area
around the OS in this encounter because the velocity of the
OS is greater than that of the TS throughout the encounter,
so the TS should maintain course while the OS manoeuvres
according to Rule 13 of the COLREGs.
Figure 14 shows the combined navigation paths from
the perspectives of the OS and the TS, where both ships
manoeuvre as dictated by Rule 13 of the COLREGs, i.e.
the overtaking (or faster) ship keeps a safe distance away
from the slower TS.
4 Discussion
Two important assumptions were adopted as the basis of
collision risk assessment, namely the availability of navi-
gational information on all obstacles and universal adher-
ence to COLREGs. The availability of navigational
information on all obstacles can be justified by noting
the increasingly widespread implementation of ARPA
and AIS, which provide this positional information. The
42.
0.000
TS
4 2 0 2 4
4
2
0
2
442.
1.500
OS
4 2 0 2 4
4
2
0
2
442.
3.000
4 2 0 2 4
4
2
0
2
4
39.2842
4.500
4 2 0 2 4
4
2
0
2
442.
6.000
4 2 0 2 4
4
2
0
2
442.
7.500
4 2 0 2 4
4
2
0
2
4
Fig. 12 Motion simulation of the overtaking encounter at selected
times from the OS’s perspective. There is a safety area around the TS
(shown in light brown; the velocity vector of the TS is too small to be
visible) throughout the simulation because the encounter type of the
OS remains OT according to the conditions defined in Fig. 4 and
Table 2
J Mar Sci Technol (2010) 15:257–270 267
123
COLREGs are effectively the framework that dictates
movements during all surface ship encounters, and have
therefore been widely adopted. Thus, it would be unwise to
manoeuvre against the established regulations and expect
others to harmonise (unless, of course, when the navigation
is centrally controlled). The proposed collision risk
assessment method will only work if all ships follow the
COLREGs or are collaborating such that all ships are
aware of each others’ intents.
One of the main differences between the proposed
collision risk assessment method and others [2, 8] is that
the collision risk is continuously assessed at fixed time
intervals in the proposed method, rather than solely based
on the initial configuration. Unlike a sweep volume-based
method, the proposed approach creates a temporary safety
area on a particular TS that is deemed necessary
according to the COLREGs, based on the relative
instantaneous positions and velocities of the OS and the
TS in question. The benefits of such an approach are that
the safety area can easily be computed at each time step,
and the safety area is designed to automatically switch on
or off depending on the ship’s instantaneous legal status
(whether to stay on or give way) according to the COL-
REGs. This means that the COLREGs are interpreted on
the fly for a particular navigation path. Such properties
are useful for a path-planning algorithm for close-range
15.
3.000
4 2 0 2 4
4
2
0
2
415.
6.000
TS
OS
4 2 0 2 4
4
2
0
2
415.
9.000
4 2 0 2 4
4
2
0
2
4
15.
12.000
4 2 0 2 4
4
2
0
2
415.
15.000
4 2 0 2 4
4
2
0
2
415.
18.000
4 2 0 2 4
4
2
0
2
4
Fig. 13 Motion simulation of the overtaking encounter at selected times from the TS’s perspective. There are no safety areas for the OS in this
encounter because OS_U [ TS_U, so the TS must maintain course while the OS manoeuvres according to Rule 13 of the COLREGs
Positions of OS
Positions of TS
-4 -2 0 2 4-2
-1
0
1
2
3
4
5
Fig. 14 Ship positions based on the navigation paths during an
overtaking encounter viewed from different perspectives. The straightnavigation path is based on the TS’s perspective, while the other is
based on the OS’s perspective. The positions of the ships are also
colour coded according to the scale on the right, where each number
represents a time step
268 J Mar Sci Technol (2010) 15:257–270
123
manoeuvres, because unnecessary manoeuvres can be
eliminated since it is the responsibility of the TS to ini-
tiate the evasive manoeuvres shown in the crossing and
overtaking simulations when the legal status of the OS is
‘‘stay on’’.
In contrast to ‘‘traditional methods’’ [3, 4], there is no
need to offset the safety area (to port or starboard) in order
to mimic the effect of the COLREGs in the proposed
method, as it is built into the assessment process such that
there is no safety area if the ship is on a COLREGs-com-
pliant path. A number of scaling parameters have been
introduced when modelling the safety area so that the
dimensions and shape of the safety area can be customised,
thus making it easy to add supplementary properties such
as changes in ship manoeuvrability in different environ-
ments to the model. In addition, the safety area generated
was consistent from different perspectives as well as
COLREGs compliant in the simulations.
On the other hand, such an interpretation of traffic may
create a risky situation for the stay-on ship, as, according to
Rule 17 (b) of the COLREGs, ‘‘when, from any cause, the
vessel required to keep her course and speed finds herself
so close that collision cannot be avoided by the action of
the give-way vessel alone, she shall take such action will
best aid to avoid collision’’. As mentioned earlier, one of
the main objectives of this study was to produce a collision
risk assessment method that eliminates ‘‘unnecessary’’
manoeuvres if the ship has stay-on status, as it is the
responsibility of the ship that gives way to initiate an
avoidance manoeuvre and avoid any risk of collision.
However, one could always set up a special reactive con-
dition to initiate an emergency avoidance manoeuvre by
the stay-on ship if the ship that gives way passes too close
to the stay-on ship. While this is outside the scope of this
study, it will be addressed in future studies.
Since the collision risk is assessed based on the rela-
tive instantaneous positions of the ships, it is only as
good as the accuracy of the detected bearing or possible
future course deviations (if known), because the method
is based on linear time projection of the velocity vector.
The elliptical shape of the safety area, on the other hand,
includes the probability of existence, as shown in Fig. 6,
in order to reduce the uncertainty over ship positional
information. This effectively incorporates statistical
properties of the TS by varying the safety area according
to the magnitude and direction of TS_U from its pre-
dicted instantaneous position, which constrains the num-
ber of possible practical manoeuvres available to the TS.
As the future positions of the TS are computed based on
linear projection of its velocity vector at discrete time
steps, it is also possible to incorporate known future
changes in the TS velocity vector into the collision risk
assessment.
On the other hand, there are additional benefits of the
proposed method that have not been addressed in this
article, but will be discussed in our next publication. For
example, it is easier to compute the variation in OS_U
under the influence of environmental force fields (i.e. wind
or current flow) with a discretised path by computing the
OS_U at each time step. In addition, since the encounter
type is examined for each obstacle at each time step, we are
not limited to assessing the collision risk for a single
obstacle; we can examine the overall traffic scenario. The
safety area was placed around the point of the TS instead of
using the more common CPA because the collision risk
assessment was developed in association with a path-
planning algorithm that utilises another parameter for the
TS which generates a vector field where the direction of
rotation is determined by the COLREGs. It is therefore
more computationally convenient for the safety area to be
located around the TS, since it allows the ‘‘cost’’ of a
particular OS manoeuvre with respect to the COLREGs
vector field to be calculated more easily.
5 Conclusion
A conceptual collision risk assessment for ships in close-
range encounters has been presented and discussed. The
risk of collision is assessed based on a safety area assigned
to any obstacle that the OS is legally obliged to give way
to. The safety area is generated based on the COLREGs
using the instantaneous properties of the traffic configura-
tion. Compared with previous methods, the proposed
method is more precise in interpreting the COLREGs,
capable of generating safety areas around obstacles
whenever appropriate (as deemed by the COLREGs), and
consistent from different perspectives (meaning that the
navigation paths of all ships involved are compatible).
In addition, the geometry of the safety area does not
require offsets like those used in most previous methods to
mimic the effects of the COLREGs, because these are
incorporated into the collision risk assessment process. The
shape of the safety area also depends on the obstacle’s
velocity vector, which provides the probability of existence
for the obstacle in question, therefore reducing positional
uncertainties. In the next publication, we will discuss how
this collision risk assessment method can be used in a path-
planning algorithm for ships in close-range encounters.
Acknowledgments The authors would like to express their grati-
tude for financial support from the ACCeSS group. The Atlantic
Centre for the Innovative Design and Control of Small Ships
(ACCeSS) is an ONR-NNRNE programme with grant number
N0014-03-0160; the group consists of universities and industrial
partners that perform small-ship-related research. The authors also
wish to thank Alistair Greig for his comments.
J Mar Sci Technol (2010) 15:257–270 269
123
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