International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 3
Number 3
September 2009
327
1 INTRODUCTION
Forming of a model of environment is one of major
tasks of the control systems. This model must ade-
quately reflect an environment, to provide the high
level of understanding of situations and serve as a
substantial auxiliary mean at the search of decisions.
Choosing one such model of environment for differ-
ent situations of vessels interaction is difficult, be-
cause belonging of elements of environment and
properties of operating ship to the categories «sub-
stantial», «unimportant» changes in them. It is also
difficult to get the universal method of decision for
preventing collisions. It is better to determine the
environment model and methods of decisions as it
applies to different situations. Then the choice of
strategies of conduct will be simpler, and they
more precise. Therefore the local problem of devel-
opment mode for presentation situation of vessels in-
teraction and choosing an effective B-manoeuvre for
collision avoidance and passing at a safe distance of
targets was set.
2 FORBIDDEN DOMAIN FOR B-MANOEUVRE
FORMING
It is accepted, that the alterations of course of oper-
ating ship are instantaneous. At such condition a B-
manoeuvre looks like shown on a Figure 1, where K
planned course of operating ship; θ angle of it
alteration; Y lateral distance from initial line of
way to the operating ship at the end of deviation; S
length of deviation segment; C
H
и C
K
points of
course alteration. Course for deviation to starboard
(K+θ) is designated K
S
, to port (K-θ) − as K
P
. An an-
gle θ for collisions avoidance can undertake from
20
0
to 150
0
, and for returning to the initial line of
way after passing vessels − from 10
0
to 45
0
.
Figure 1. Parameters of B-manoeuvre
Current positions of operating ship and scanned
vessel (target) is shown below on Figure 2 by points
C and Z. Taking into account presents of navigation-
al hazards and necessity to determine only dander
targets within navigable area the zone of manoeu-
vres and motion (ZMM) of operating ship is set
(maximum allowable track margin for current leg).
It is determined by width (Y
DS
, Y
DP
) of starboard
and port lanes for shifting of operating ship at B-
manoeuvres.
Beginning of lane of possible shifting to star-
board forms a segment CQ on the course K
S
=K+θ
S
The Display Mode for Choosing the Manoeuvre
for Collision Avoidance
L. Vagushchenko & A. Vagushchenko
Odessa National Maritime Academy, Odessa, Ukraine
ABSTRACT: The display mode is intended for facilitation of building strategies for collision avoidance by
so-called B-manoeuvres. It can be used in ECDIS, ARPA and the simulator systems. B-manoeuvre includes
the segment of deviation at a certain angle from the initial course and at the end of it the segment parallel to
the initial way’s line (planned route). The offered mode is based on the use of forbidden domains for B-
manoeuvres. These domains allow choosing parameters and beginning moment of B-manoeuvre for collision
avoidance with one or a few vessels. The account of presence of navigation hazards at the choice of B-
manoeuvre is produced by setting the borders of maximum lateral shifting from planned route. The offered
mode enables visual drafting of strategies for collision avoidance with vessels by successive B-manoeuvres. It
is possible to use this mode as basis of computer search of strategies for collisions avoidance with a few tar-
gets.
328
(Fig. 2), where θ
S
= set alteration of initial course
for B-manoeuvres to starboard. The butt end seg-
ment of port lane is directed parallel a course K
P
=K-
θ
P
(θ
P
= set alteration of initial course to port). The
values of θ
S
and θ
P
can be both identical and differ-
ent. The current position C of operating ship is con-
sidered as the appointed element of both lanes.
Figure 2. Principle of construction of forbidden domain
Principle of construction of forbidden domain
(FD) is characterized in starboard lane on a Figure 2
(Vagushchenko, A.L. 2008), where
K, V = planned course and speed of operating
ship;
K
Z
, V
Z
= course and speed of target;
и ,
S
и
S
= course and speed of operat-
ing ship in relation to a target at true courses K, K
S
of operating ship;
D
Z
= safe limit of distance between ships;
A
1
, A
2
= points of turn from a course K to the
course K
S
for passing a target at distance D
Z
;
B
1
, B
2
= points of returning from a course K
S
to
the former course K for passing a target at distance
D
Z
;
mnpqer = forbidden domain;
O, A
0
, B
0
= the FD center and points of turn from
a course K to the course K
S
and returning from a
course K
S
to the former course K for CPA=0;
0
,
1
,
2
and
0
,
1
,
2
= points on the lines
of relative motion of operating ship, proper to the
points A
0
, A
1
, A
2
and B
0
, B
1
, B
2
;
Δ
Y
- interval of lateral deviations from the
planned way which provide close-quarters situation
with a target at B-manoeuvres.
Distances S
AJ
and S
BJ
(J=0, 1, 2) from a current
place C of operating ship to the points A
0
, A
1
, A
2
and
B
0
, B
1
, B
2
are determined on intervals of time t
AJ
and t
BJ
for arrival in these points. These intervals
are calculated by values of
AJ
and
BJ
(C
0
, CA΄
1
,
CA΄
2
and CB΄
0
, CB΄
1
, CB΄
2
) and ,
S
:
V/St
AJAJ
=
SBJBJ
V/St
=
AJAJ
tVS =
BJBJ
tVS =
.
3 USE THE DISPLAY MODE FOR CHOOSING
MANOEUVRES FOR COLLISION
AVOIDANCE
The category of targets is determined on the loca-
tion FD in relation to the ZMM borders (Fig. 3). If a
target by transponder AIS reported the way points of
the route or informed about the set manoeuvre, then
an operating ship gets FD of this target taking into
account accepted information (target 5, Fig. 3). The
probability of possible maneuvering of danger or ob-
stacle vessels can be determined by the expert sys-
tem (not presented in this paper). In this case the
mode of situation can be added with the second FD
for this target, proper to possible new course (target
1, Fig. 3). These two FD of target 1 allow forming
the incorporated forbidden domain taking into ac-
count a possible manoeuvre of target.
Fig. 3. Situation presentation scheme
The B-manoeuvre for collision avoidance is de-
termined visually on the reflection situation on the
screen. The B-manoeuvre is set by pointing the cur-
sor, for example, on point C
K
. The trajectory of fu-
ture motion of operating ship would not cross the
forbidden domains. Point C
E
marked the end of B-
manoeuvre, after which a dangerous ship can be
considered finally passed. By a criterion for the
choice of B-manoeuvre it is possible to take mini-
mum distance of shifting (Y) from the planned line
on condition that the degree of risk of collision with
all targets will not exceed the legitimate value at the
point C
E
and manoeuvre will not conflict with
329
ColRegs.
The next action is then planned. Depending on
the circumstances one of three actions of operating
vessel gets out after the first B-manoeuvre: motion
along a new line parallel to the planned line (Fig.
4,a); returning on the planned line by B-manoeuvre
(Fig. 4,b); proceeding by the course to next way
point (Fig. 4,c). The borders of ZMM can be cor-
rected accordingly, if necessary.
Figure 4. Variants of conduct after the first B-manoeuvre
After this the point C
E1
is undertaken as ap-
pointted element for new ZMM. In this ZMM for-
bidden domains are determined on the prognosis of
motion of operating ship and targets. Similar to