can be modeled as the discrete set of altering course and changing
speed. So we can imagine the maneuvering space such as the horizontal axis is a course,
the longitudinal axis is a speed and the evaluated value of each maneuver is extended
perpendicularly upward. When a navigator selects a certain way of maneuver X i,j that
includes keeping course and speed, he prefers the minimum of loss and risk of collision.
In this case, a preference relation can be expressed as followings by
using a cardinal utility function as follows.
A navigation without any collision avoidance maneuver has the minimum
load and is the most preferable for the navigators. On the other hand, they don't prefer a
drastic change in the course or speed. Such a preference order about the maneuvers to
prevent a collision may be depended on a lots of items related to a navigation and it is
difficult to fix the only one model at present time. However, considering a practical
maneuver of the navigators, it seems that they don't accurately estimate the physical
losses like a distance but they select a better way by preference order based on their
experience. Thus a preference is better than the physical losses to express a internal
process of a navigator. At the present time, equations and coefficients were assumed as
follows.
where, Pb(X i,j) is degree of preference of maneuver X i,j ; Δ Co is
degree of altering course, Δ V is a ratio of changing speed, ac and av are the
coefficient to simulate the preference order. When a preference order like above was
obtained, it enable us to estimate a mental loss of a navigator and to define the utility
function as follows.
The second term of a right side means that the maximum risk value of
targets in encounter situation to the number of p and the α is a coefficient to adjust
the relation between a preference and a risk. (α was assumed to 1.0 at present time.)
According to the definitions mentioned above, as a trial calculation, a
distribution chart of the risk and a utility of each maneuver were shown in Fig.8 (a) and
(b). The encounter situation using this trial has two target vessels: both targets have
one nautical mile in distance from an own vessel, equally separated 300 meters in left and
right side from an own vessel, and have the opposite course to the own one as shown in
Fig.8 (c).
Figure (a) and (b) directly show the fact that altering course to
starboard or port is highly obstructed and keeping a present course is most preferable.
