- Email: [email protected]
Safety Measures for a Ships Passing Track in the Multiagent Framework
Copyright @ IF AC Manoeuvring and Control of Marine Craft. Aalborg. Denmark. 2000
SAFETY MEASURES FOR A SHIPS PASSING TRACK IN THE MULTIAGENT FRAMEWORK Dmitriev S.P., Kolesov N.V., Osipov A.V. St Petersburg, Russia, State Research Center of Russia - Central Scientific & Research Institute Elektropribor Malaya Posadskaya, 30, 197046, Saint-Petersburg, Russia Fax: (7-812) 232 33 76, Phone: (7-812) 238 78-90, E-mail: [email protected]
Abstract: The paper considers the problem of assessing safety of a previously generated ship track for passing with other vessels (OV) and navigational hazards (NH). The safety measure for the passing track (PT) allows different recommended tracks to be compared with the aim to select one suited to the operation. The probability of lack of OS collision with all OV and NH is considered as a safety measure. The model of a passing process is considered as a multiagent system. Each passing OV is shown up as an intelligent agent that is guided by the COLREGS, on the one hand, and by the knowledge of the operational conditions and the performance criteria, on the other hand. Copyright @2000 fFAC Keywords: safety, artificial intelligence, trajectory planning, traffic control
conditions entered by the mariner, this module synthesizes a set of alternative passing tracks that minimize the OS deviation from the programmed track. The set of tracks is plotted on the display. Among these tracks the mariner chooses the best one suited to the operation. The passing track is represented as a linearly broken curve of several legs.
INTRODUCfION At present the problem of ships passing is solved with the use of the Automatic Radar Plotting Aids (ARPA) whose potentialities reduce to computation of sectors dangerous for OS. As the ARPA information does not include any recommendations about the assessment of the situation or the choice of the passing track, it does not seem to meet the present-day requirements for safety at sea.
To be able to follow the changes in the surrounding conditions, the approach provides for the current analysis of the present situation with a certain prescribed interval, for instance, one each minute. If all synthesized tracks seem to be unacceptable for the mariner, he can assign his own track. In this case the program module only checks the safety of the track.
The approach proposed in this paper provides automatic synthesis of the passing track for OS with all OV and NH (Dmitriev et al. 1997, 1999) over a certain prediction interval that takes into account the radar scale. This approach made the basis for the Mariner's Intelligence Support Aids designed as a part of the Electronic Chart Display and Information System (ECDIS). Using the data from the ARPA and ECDIS and the data about the operational
Figure I illustrates one of the solutions of the ships passing problem, with the program track of OV
373
motion shown as a dotted line and a set of synthesized passing tracks as solid lines. The other vessels are shown as their speed vectors.
L, then the probability P( C) of the lack of collision on the fixed PT is expressed by the probabilities P(Cd(i = 1,2 , .. . ,L) of the lack of collision with each ~V :
I I
L
I I
P( C)
I
OV-2'
cf)V-3 -~
I
OV-4
-----g~~~:1
i=l
_J
~
, OV-)
= n P( Ci )
In its turn, the probability P( Ci) is related to a set of situations E ij (j
in the case when OS
is passing clear of the i-th OV . This set of situations forms a complete group of events, thus the probability P(C i ) takes the form:
PT3
PT) PT 2 PT 3
=1,2, . . . , M i)
Safety PT P = 0.95-0.99 P = 0.80-0.85 P = 0.84-0.90
Mj P(C) =
L
P(CiIEij)P(Eij)'
j=1
Fig.1 Plotting of passing process where P(Eij) - the probability of the situation Eij ,
The problem of ships passing is not easy to formalize, that is why it should be characterized as an intelligence problem. It was not long ago that it could only be solved by a man. The important feature of the discussed solution is that the Mariner's Intelligence Support Aid is intended to operate not simply in the real time, but in "rigid" real time as well. This means extremely small time resource for solving the problem (of about I-tO seconds). Consequently, in spite of the evident intelligence attributes of the problem under consideration (symbolic models and reasoning, fuzzy rules and criteria), the program module designed provides for its algorithmic realization with elements of knowledge base, aids of logical reasoning, explanation interface and so on. I.
P( C i I Eij) - the conditional probability of lack of
collision in the situation Eij Thus, in order to calculate safety assessment for a specific passing track, it is necessary to define a set of possible situations {Eij j and then to determine both the probability
P(Eij)
and corresponding
probability P( C i I Eij) of lack of collision for each situation Eij' The situations Eij consider possible actions of the i - th OV in compliance and non-compliance with the Rules . Probabilities of the situations Eij take into account the beliefs to different OV actions.
SAFETY ASSESSMENT
In the adopted conception the belief assessment for the same actions turns out to be different for different ranges to OV. In this conception the larger is the range, the less is the belief. The validity of this approach for belief assessment is supposed to be obvious for the following reason. If the range to OV is large, then the probability of changes in the surrounding conditions is also large because of OV manoeuvring and new other vessels that can enter the zone of the radar range. For this reason the probability of reviewing the prediction derived before is high. The mathematical methods used to take into account this feature may be different. For example, the belief function that was first proposed by Shafer (1976) may be used. In this case the uncertainty is described not only by probability but also by upper and lower bounds, and for such probability intervals special mathematical techniques such as Dempster rules of combination (Dempster, 1967) are used. This approach is illustrated by the following example.
The track safety measure is defined here as a probability of lack of own ship collision with all OV and NH. The procedures of track safety assessment were considered in many papers [Imazu 1997, Finkelstein 1998]. However, the approach proposed differs in principle from the known ones, as it takes into account possible actions of all dangerous OV and considers each OV as an intelligent agent (Green 1997). The problem is formulated as follows. Using the current values of the motion parameters of all OV and properties of the passing track to be assessed, it is necessary to calculate the probability of lack of own ship collision with all OV that are found in the prediction zone of own ship. The problem of track safety assessment considered here can be stated as follows. If the number of OV that belong to the OS prediction domain is equal to
374
Suppose that in OS passing with some OV, the own ship predicts different OV actions and one of them is a manoeuvre M av . Let us assess the probability of p(M av)
events. The graph has an initial node (or initial nodes) and a set of terminal nodes. The initial point plays an auxiliary role, being the origin of predicting reasoning. Any terminal node relates with only one of two possible results of ships passing - collision and non-collision. Any situation may be expressed as a product of compatible and dependent events.
for this action. Assume that in track
planning the radar observes a zone within a distance D with the center at the point of the current OS position (usually D = 12 -16 nmi). In this case OV is separated from the boundary of the manoeuvring zone by the distance till that will be passed by her over the time t. Introduce the following notations: p probability of non-appearance of a new OV in the observation zone within the time t; a - probability of this OV manoeuvring under the condition of nonappearance of a new OV in the observation zone within the time t, b - probability of this OV manoeuvring under the condition of appearance of a new OV in the observation zone within the time t. Then we have p(M av ) =ap
Here, the value
The development of the event's graph for OS safety assessment is based on the model of OV mariners' actions. It must be sufficiently detailed to provide for assessment of different situations, but at the same time it must be rather simple to guarantee the model support with well-grounded initial data. The approach suggested for OV mariner's actions model is based on the principles of multiagent systems. In this model each OV is presented as an equal in rights and independent agent. It is impossible to take into account and assess all variants of the events for the ships passing. For this reason the hypothesis of proximity of OS and OV goals is used to reflect their intentions about safety passing. The main thesis for developing a subjective OV model is an assumption that the OV mariner is guided by approximately the same rules as the OS mariner (the principle of RAOlogic (Shi, 1997».
+ b(l - p) .
may be represented by the
p
relation D- till p=--D
The prerequisite for the multiagent approach is the fact {hat due to the fuzzy character of the COLREGS and possible subjective interpretation, the participants of the passing process do not have precise knowledge about intentions of the other participants.
different values of a stored in the data base depend on the situation and are detennined by seamanship. But it is obvious probability of value Taking into account interval (0,1), the
that the assessment of the b is not available, in principle. that the value b belongs to the following inequality may be
For this reason two possible variants of events is always to be considered: in one of them OS and OV assess the situation in the same way, in the other - in different ways. The ships actions are coordinated in the first case and noncoordinated in the second case. The significance of each of these variants for the resulting safety assessment depends on the properties of the track considered.
derived: ap < p(M av ) < ap
+ (1 -
p) .
This means that if the OV considered is not far from the manoeuvring zone (till« D) , then the interval of
possible
concentrated
p(M av )
at one
values
point,
and
is
In the first case OS and OV are assumed to pass clear of each other at a safety distance that is of a minimum value if it is determined by OV and a rather large value if it is determined by OS. The known statistical data is used to assess the probability of noncoordinated actions.
practically
p(M av ) =a .
Otherwise, when the OV is far from the manoeuvring zone the width of the interval for p(M av) has a large value (it is equal to 1- p ), and this results in the effect of small belief to the event under consideration. 2.
When making a prediction for a specific OV in the domain that separates her from OS, in a general case it is possible to distinguish three typical domains: - the analysis domain where OV moves on the program track and makes a decision about the risk of collision and if it does exist - a decision about a future action aimed at clear passing; - the manoeuvring domain where OV keeps out of the way as a give-way vessel;
A GRAPH OF EVENTS FOR THE PASSING PROCESS
The purpose of the graph is to present the structure of the mariner's decision making and thus calculate probabilities of the ships passing events. The events graph is a directional noncyclic tree whose nodes are related to possible events of ships passing and the arcs represent the dependence on the preceding
375
mathematical technique used to calculate probability intervals and it permits reasoning when local actions are in a 'soft' conflict with each other and also determining the belief to the event of coordinated actions of OV with the fixed program track of OS.
- the close-quarter situation where the stand-on vessel and give-way vessels act independently to avoid collision. It is clear that the set of events in the specific case depends on the domain where OV is situated Consider a set of events that form the matter of prediction when OV is in the analysis domain . Here the following events can be introduced: "Risk of collision" ( RC ) and an alternative event (RC ). The event RC corresponds to the prediction that the closest point of approach is smaller than the accepted safety distance. The following events are introduced for the manoeuvring domain: "Manoeuvre" M av
3. CALCULATION OF PROBABILITIES OF EVENTS FOR SHIPS PASSING The approach used to calculate probabilities of different events is illustrated here by the example of the event "risk of collision". As mentioned above, the decision that the risk of collision does exist is adopted when the calculated CPA dcpa.i for the OS passing with the i - th OV is
and M av . In the first domain the type of passing situation (crossing, overtaking, reciprocal course) is identified in order to assess the safety measure for these events. If in the manoeuvring domain both ships performed non-coordinated actions, then in the close-quarter situation they shall take the manoeuvre of the last minute and the corresponding events will be - MLM and MLM. For the closest point of approach, only two events are possible as a result of ships passing - "Collision" (Ci ) and "Non -
smaller than a certain threshold level
Dmin,i'
The
value dcpa,i is a random variable due to the errors in the measurements of coordinates and motion parameters of the OS and OV. Its distribution function may be assumed as the normal function $0 with the mean d i corresponding to the CPA for the programmed track and the variance CTi that depends on the time of prediction. Then the probability event RCi is given by
collision" (C i). All the events described above represent future OV actions. A fragment of a graph for a crossing situation with OV as the give-way vessel is shown in Figure 2.
P(RCi ) = P{!dcpa,i! < Dmin,i}=
- 1
=~ Dmi~j-di l-~ Dmi~j+di
Domain of
The value of the safety passing distance is determined by fuzzy rules in accordance with the motion conditions.
analysis
Domain of manoeuvring
This relation is approximate not only because of its insufficient adequacy but also mainly because of uncertainty of the predicted values of d j and CTi •
Close·quarter situation
Close point of approach
4.
RESULTS
Many real passing situations have been simulated to study the performance of the program module. The module has been positively assessed by experts. Let us consider the results of the track safety assessment for the case of the ships P. Vasev and Admiral Nakhimov collision on 31 .08.1986. It was studied in detail by Olshamovsky et al. (1993). The circumstances were as follows. The ship Admiral Nakhimov was moving on a crossing course with respect to the ship P. Vasev. In compliance with the Rules she should have kept her course and speed. The ship P. Vasev was acting in non-compliance with the Rules and did not give way assuming that there was no risk of collision. Besides, in the c1osequarter situation both ships made non-effective and non-substantial manoeuvres of the last minute that
Fig.2 Graph of passing events Attention should be drawn to the fact that this graph represents all classes of similar situations, but it does not represent the properties of the OS track analyzed. The properties are manifested in the values of the probabilities for the events under consideration. For the case when OS passes with a few OV the analysis of events and the graph are more complicated. The graph has several nodes (corresponding to the number of OV) and reflects the mutual influence of actions of OS and all other vessels. The belief calculation based on this graph is performed by means of basic probability assignment introduced by Shafer (1976). This function is a
376
Finkelstein, M.S . (1998). A Point-Process Stochastic Model with Application to Safety at Sea. Reliability and System Safety . .60, .227-233. Green , S., I.Hurst and B.Nangle (1997). Software Agents; a Review. May 27. /!http//www.cs.tcd.ie/research groups/iag/pubreview. Imazu, H. (1997) An Ability of Collision A voidance by Own Ship. C)'h World Congress Int. Ass. Of Inst. Of Navigation . November 18-21, Amsterdam. Olshamovsky, S.B., G.N . Fedchenko and V.V. Mordvinov (1993). Investigation of causes of collision of the steamer Admiral Nakhimov with the motor ship P. Vase v Sudovozhdeniye. svyaz i bezopasnost moreplavaniya. Issue 8 pp .. I -43. OJlhlllaMOBcKHH, C .n. r .H.e.ll'ieHKO H B.B.Mop.llBHHOB (1993) I1ccJle.lloBaHHe npH'iHH CTOJlKHOBeHHlI napoxo.lla" A.llMHpaJI HaxHMOB" c TenJlOXO.llOM "IlBaceB" 3Kcnpecc-uHfjJopMal/UR .. MOpCKOU mpaHcnopm Cep. Cyo080:>ICOeHue. C8R3b U 6e30nacHocmb Mopenna8aHUR . BhIn 8.crp. 1-43 (In Russian). Shafer, G. (1976) A Mathematical Theory of Evidence .Princeton University Press. Shi, Z., Q.Tian and Y.Li (1997). RAO Logic for Multiagent Framework. Proc. of the Int. Workshop DAlMAS-97. June 15-18, St. Petersburg.
resulted in the collision at 23.11 (1Lll p.m.). In our analysis the ship Admiral Nakhimov was adopted as OS. The results of the analysis of her track safety are shown in the Table below that includes both the values P(C) and P(RC) . These values are given for different instants of time t and distances r between the ships. If the ships had had the suggested program module at their disposal, the watchkeeper on P. Vasev would have decided that the risk of collision did exist and would have taken actions to avoid the collision. In the close-quarter situation the values P(RC ) and P(C) would have been interpreted in such a way that it was necessary for them to make substantial manoeuvres of the last minute at a distance of 3.5 nmi . The assessed probabilities of the events RC and C are in compliance with the quality conclusions of the commission (Olshamovsky, et aI., 1993). Table 1. Probability assessment of the passing events
H .
t
r, nmi
P(RC)
P(C)
22.47
7.2
0.68-0.84
0.01-0.07
22.53
5.3
0.77-0.89
0.03-0.09
22.59
3.5
0.88-0.94
0.07-0.12
23.05
1.7
0.99-1.0
0.11-0.15
CONCLUSION In this paper we have formulated a definition of safety of the passing track and proposed a method for its determination. This method takes into account possible actions of other vessels both in compliance and non-compliance with the COLREGS. The method considers each dangerous other vessel as an intelligent agent, which is realized in the own ship' s software as a block of the expert system. REFERENCES Dempster, A. (1967). Upper and lower probabilities induced by a multi valued mapping. Annals of Mathematical Statistics , 38, 325-330. Dmitriev, S.P., N.V.Kolesov and A.V .Osipov (1997). Artificial Intelligence Technology Implementation in the Ships Collision Avoidance. 4th Saint Petersburg International Conference of Integrated Navigation Systems. May 26-28. Dmitriev, S.P., N.V.Kolesov, A.V .Osipov and G.N.Romanycheva (1999). System of Intelligence Support for Collision Avoidance at Sea. 55th Annual Meeting Institute of Navigation . June 28-30, Cambridge, MA.
377
SAFETY MEASURES FOR A SHIPS PASSING TRACK IN THE MULTIAGENT FRAMEWORK Dmitriev S.P., Kolesov N.V., Osipov A.V. St Petersburg, Russia, State Research Center of Russia - Central Scientific & Research Institute Elektropribor Malaya Posadskaya, 30, 197046, Saint-Petersburg, Russia Fax: (7-812) 232 33 76, Phone: (7-812) 238 78-90, E-mail: [email protected]
Abstract: The paper considers the problem of assessing safety of a previously generated ship track for passing with other vessels (OV) and navigational hazards (NH). The safety measure for the passing track (PT) allows different recommended tracks to be compared with the aim to select one suited to the operation. The probability of lack of OS collision with all OV and NH is considered as a safety measure. The model of a passing process is considered as a multiagent system. Each passing OV is shown up as an intelligent agent that is guided by the COLREGS, on the one hand, and by the knowledge of the operational conditions and the performance criteria, on the other hand. Copyright @2000 fFAC Keywords: safety, artificial intelligence, trajectory planning, traffic control
conditions entered by the mariner, this module synthesizes a set of alternative passing tracks that minimize the OS deviation from the programmed track. The set of tracks is plotted on the display. Among these tracks the mariner chooses the best one suited to the operation. The passing track is represented as a linearly broken curve of several legs.
INTRODUCfION At present the problem of ships passing is solved with the use of the Automatic Radar Plotting Aids (ARPA) whose potentialities reduce to computation of sectors dangerous for OS. As the ARPA information does not include any recommendations about the assessment of the situation or the choice of the passing track, it does not seem to meet the present-day requirements for safety at sea.
To be able to follow the changes in the surrounding conditions, the approach provides for the current analysis of the present situation with a certain prescribed interval, for instance, one each minute. If all synthesized tracks seem to be unacceptable for the mariner, he can assign his own track. In this case the program module only checks the safety of the track.
The approach proposed in this paper provides automatic synthesis of the passing track for OS with all OV and NH (Dmitriev et al. 1997, 1999) over a certain prediction interval that takes into account the radar scale. This approach made the basis for the Mariner's Intelligence Support Aids designed as a part of the Electronic Chart Display and Information System (ECDIS). Using the data from the ARPA and ECDIS and the data about the operational
Figure I illustrates one of the solutions of the ships passing problem, with the program track of OV
373
motion shown as a dotted line and a set of synthesized passing tracks as solid lines. The other vessels are shown as their speed vectors.
L, then the probability P( C) of the lack of collision on the fixed PT is expressed by the probabilities P(Cd(i = 1,2 , .. . ,L) of the lack of collision with each ~V :
I I
L
I I
P( C)
I
OV-2'
cf)V-3 -~
I
OV-4
-----g~~~:1
i=l
_J
~
, OV-)
= n P( Ci )
In its turn, the probability P( Ci) is related to a set of situations E ij (j
in the case when OS
is passing clear of the i-th OV . This set of situations forms a complete group of events, thus the probability P(C i ) takes the form:
PT3
PT) PT 2 PT 3
=1,2, . . . , M i)
Safety PT P = 0.95-0.99 P = 0.80-0.85 P = 0.84-0.90
Mj P(C) =
L
P(CiIEij)P(Eij)'
j=1
Fig.1 Plotting of passing process where P(Eij) - the probability of the situation Eij ,
The problem of ships passing is not easy to formalize, that is why it should be characterized as an intelligence problem. It was not long ago that it could only be solved by a man. The important feature of the discussed solution is that the Mariner's Intelligence Support Aid is intended to operate not simply in the real time, but in "rigid" real time as well. This means extremely small time resource for solving the problem (of about I-tO seconds). Consequently, in spite of the evident intelligence attributes of the problem under consideration (symbolic models and reasoning, fuzzy rules and criteria), the program module designed provides for its algorithmic realization with elements of knowledge base, aids of logical reasoning, explanation interface and so on. I.
P( C i I Eij) - the conditional probability of lack of
collision in the situation Eij Thus, in order to calculate safety assessment for a specific passing track, it is necessary to define a set of possible situations {Eij j and then to determine both the probability
P(Eij)
and corresponding
probability P( C i I Eij) of lack of collision for each situation Eij' The situations Eij consider possible actions of the i - th OV in compliance and non-compliance with the Rules . Probabilities of the situations Eij take into account the beliefs to different OV actions.
SAFETY ASSESSMENT
In the adopted conception the belief assessment for the same actions turns out to be different for different ranges to OV. In this conception the larger is the range, the less is the belief. The validity of this approach for belief assessment is supposed to be obvious for the following reason. If the range to OV is large, then the probability of changes in the surrounding conditions is also large because of OV manoeuvring and new other vessels that can enter the zone of the radar range. For this reason the probability of reviewing the prediction derived before is high. The mathematical methods used to take into account this feature may be different. For example, the belief function that was first proposed by Shafer (1976) may be used. In this case the uncertainty is described not only by probability but also by upper and lower bounds, and for such probability intervals special mathematical techniques such as Dempster rules of combination (Dempster, 1967) are used. This approach is illustrated by the following example.
The track safety measure is defined here as a probability of lack of own ship collision with all OV and NH. The procedures of track safety assessment were considered in many papers [Imazu 1997, Finkelstein 1998]. However, the approach proposed differs in principle from the known ones, as it takes into account possible actions of all dangerous OV and considers each OV as an intelligent agent (Green 1997). The problem is formulated as follows. Using the current values of the motion parameters of all OV and properties of the passing track to be assessed, it is necessary to calculate the probability of lack of own ship collision with all OV that are found in the prediction zone of own ship. The problem of track safety assessment considered here can be stated as follows. If the number of OV that belong to the OS prediction domain is equal to
374
Suppose that in OS passing with some OV, the own ship predicts different OV actions and one of them is a manoeuvre M av . Let us assess the probability of p(M av)
events. The graph has an initial node (or initial nodes) and a set of terminal nodes. The initial point plays an auxiliary role, being the origin of predicting reasoning. Any terminal node relates with only one of two possible results of ships passing - collision and non-collision. Any situation may be expressed as a product of compatible and dependent events.
for this action. Assume that in track
planning the radar observes a zone within a distance D with the center at the point of the current OS position (usually D = 12 -16 nmi). In this case OV is separated from the boundary of the manoeuvring zone by the distance till that will be passed by her over the time t. Introduce the following notations: p probability of non-appearance of a new OV in the observation zone within the time t; a - probability of this OV manoeuvring under the condition of nonappearance of a new OV in the observation zone within the time t, b - probability of this OV manoeuvring under the condition of appearance of a new OV in the observation zone within the time t. Then we have p(M av ) =ap
Here, the value
The development of the event's graph for OS safety assessment is based on the model of OV mariners' actions. It must be sufficiently detailed to provide for assessment of different situations, but at the same time it must be rather simple to guarantee the model support with well-grounded initial data. The approach suggested for OV mariner's actions model is based on the principles of multiagent systems. In this model each OV is presented as an equal in rights and independent agent. It is impossible to take into account and assess all variants of the events for the ships passing. For this reason the hypothesis of proximity of OS and OV goals is used to reflect their intentions about safety passing. The main thesis for developing a subjective OV model is an assumption that the OV mariner is guided by approximately the same rules as the OS mariner (the principle of RAOlogic (Shi, 1997».
+ b(l - p) .
may be represented by the
p
relation D- till p=--D
The prerequisite for the multiagent approach is the fact {hat due to the fuzzy character of the COLREGS and possible subjective interpretation, the participants of the passing process do not have precise knowledge about intentions of the other participants.
different values of a stored in the data base depend on the situation and are detennined by seamanship. But it is obvious probability of value Taking into account interval (0,1), the
that the assessment of the b is not available, in principle. that the value b belongs to the following inequality may be
For this reason two possible variants of events is always to be considered: in one of them OS and OV assess the situation in the same way, in the other - in different ways. The ships actions are coordinated in the first case and noncoordinated in the second case. The significance of each of these variants for the resulting safety assessment depends on the properties of the track considered.
derived: ap < p(M av ) < ap
+ (1 -
p) .
This means that if the OV considered is not far from the manoeuvring zone (till« D) , then the interval of
possible
concentrated
p(M av )
at one
values
point,
and
is
In the first case OS and OV are assumed to pass clear of each other at a safety distance that is of a minimum value if it is determined by OV and a rather large value if it is determined by OS. The known statistical data is used to assess the probability of noncoordinated actions.
practically
p(M av ) =a .
Otherwise, when the OV is far from the manoeuvring zone the width of the interval for p(M av) has a large value (it is equal to 1- p ), and this results in the effect of small belief to the event under consideration. 2.
When making a prediction for a specific OV in the domain that separates her from OS, in a general case it is possible to distinguish three typical domains: - the analysis domain where OV moves on the program track and makes a decision about the risk of collision and if it does exist - a decision about a future action aimed at clear passing; - the manoeuvring domain where OV keeps out of the way as a give-way vessel;
A GRAPH OF EVENTS FOR THE PASSING PROCESS
The purpose of the graph is to present the structure of the mariner's decision making and thus calculate probabilities of the ships passing events. The events graph is a directional noncyclic tree whose nodes are related to possible events of ships passing and the arcs represent the dependence on the preceding
375
mathematical technique used to calculate probability intervals and it permits reasoning when local actions are in a 'soft' conflict with each other and also determining the belief to the event of coordinated actions of OV with the fixed program track of OS.
- the close-quarter situation where the stand-on vessel and give-way vessels act independently to avoid collision. It is clear that the set of events in the specific case depends on the domain where OV is situated Consider a set of events that form the matter of prediction when OV is in the analysis domain . Here the following events can be introduced: "Risk of collision" ( RC ) and an alternative event (RC ). The event RC corresponds to the prediction that the closest point of approach is smaller than the accepted safety distance. The following events are introduced for the manoeuvring domain: "Manoeuvre" M av
3. CALCULATION OF PROBABILITIES OF EVENTS FOR SHIPS PASSING The approach used to calculate probabilities of different events is illustrated here by the example of the event "risk of collision". As mentioned above, the decision that the risk of collision does exist is adopted when the calculated CPA dcpa.i for the OS passing with the i - th OV is
and M av . In the first domain the type of passing situation (crossing, overtaking, reciprocal course) is identified in order to assess the safety measure for these events. If in the manoeuvring domain both ships performed non-coordinated actions, then in the close-quarter situation they shall take the manoeuvre of the last minute and the corresponding events will be - MLM and MLM. For the closest point of approach, only two events are possible as a result of ships passing - "Collision" (Ci ) and "Non -
smaller than a certain threshold level
Dmin,i'
The
value dcpa,i is a random variable due to the errors in the measurements of coordinates and motion parameters of the OS and OV. Its distribution function may be assumed as the normal function $0 with the mean d i corresponding to the CPA for the programmed track and the variance CTi that depends on the time of prediction. Then the probability event RCi is given by
collision" (C i). All the events described above represent future OV actions. A fragment of a graph for a crossing situation with OV as the give-way vessel is shown in Figure 2.
P(RCi ) = P{!dcpa,i! < Dmin,i}=
- 1
=~ Dmi~j-di l-~ Dmi~j+di
Domain of
The value of the safety passing distance is determined by fuzzy rules in accordance with the motion conditions.
analysis
Domain of manoeuvring
This relation is approximate not only because of its insufficient adequacy but also mainly because of uncertainty of the predicted values of d j and CTi •
Close·quarter situation
Close point of approach
4.
RESULTS
Many real passing situations have been simulated to study the performance of the program module. The module has been positively assessed by experts. Let us consider the results of the track safety assessment for the case of the ships P. Vasev and Admiral Nakhimov collision on 31 .08.1986. It was studied in detail by Olshamovsky et al. (1993). The circumstances were as follows. The ship Admiral Nakhimov was moving on a crossing course with respect to the ship P. Vasev. In compliance with the Rules she should have kept her course and speed. The ship P. Vasev was acting in non-compliance with the Rules and did not give way assuming that there was no risk of collision. Besides, in the c1osequarter situation both ships made non-effective and non-substantial manoeuvres of the last minute that
Fig.2 Graph of passing events Attention should be drawn to the fact that this graph represents all classes of similar situations, but it does not represent the properties of the OS track analyzed. The properties are manifested in the values of the probabilities for the events under consideration. For the case when OS passes with a few OV the analysis of events and the graph are more complicated. The graph has several nodes (corresponding to the number of OV) and reflects the mutual influence of actions of OS and all other vessels. The belief calculation based on this graph is performed by means of basic probability assignment introduced by Shafer (1976). This function is a
376
Finkelstein, M.S . (1998). A Point-Process Stochastic Model with Application to Safety at Sea. Reliability and System Safety . .60, .227-233. Green , S., I.Hurst and B.Nangle (1997). Software Agents; a Review. May 27. /!http//www.cs.tcd.ie/research groups/iag/pubreview. Imazu, H. (1997) An Ability of Collision A voidance by Own Ship. C)'h World Congress Int. Ass. Of Inst. Of Navigation . November 18-21, Amsterdam. Olshamovsky, S.B., G.N . Fedchenko and V.V. Mordvinov (1993). Investigation of causes of collision of the steamer Admiral Nakhimov with the motor ship P. Vase v Sudovozhdeniye. svyaz i bezopasnost moreplavaniya. Issue 8 pp .. I -43. OJlhlllaMOBcKHH, C .n. r .H.
resulted in the collision at 23.11 (1Lll p.m.). In our analysis the ship Admiral Nakhimov was adopted as OS. The results of the analysis of her track safety are shown in the Table below that includes both the values P(C) and P(RC) . These values are given for different instants of time t and distances r between the ships. If the ships had had the suggested program module at their disposal, the watchkeeper on P. Vasev would have decided that the risk of collision did exist and would have taken actions to avoid the collision. In the close-quarter situation the values P(RC ) and P(C) would have been interpreted in such a way that it was necessary for them to make substantial manoeuvres of the last minute at a distance of 3.5 nmi . The assessed probabilities of the events RC and C are in compliance with the quality conclusions of the commission (Olshamovsky, et aI., 1993). Table 1. Probability assessment of the passing events
H .
t
r, nmi
P(RC)
P(C)
22.47
7.2
0.68-0.84
0.01-0.07
22.53
5.3
0.77-0.89
0.03-0.09
22.59
3.5
0.88-0.94
0.07-0.12
23.05
1.7
0.99-1.0
0.11-0.15
CONCLUSION In this paper we have formulated a definition of safety of the passing track and proposed a method for its determination. This method takes into account possible actions of other vessels both in compliance and non-compliance with the COLREGS. The method considers each dangerous other vessel as an intelligent agent, which is realized in the own ship' s software as a block of the expert system. REFERENCES Dempster, A. (1967). Upper and lower probabilities induced by a multi valued mapping. Annals of Mathematical Statistics , 38, 325-330. Dmitriev, S.P., N.V.Kolesov and A.V .Osipov (1997). Artificial Intelligence Technology Implementation in the Ships Collision Avoidance. 4th Saint Petersburg International Conference of Integrated Navigation Systems. May 26-28. Dmitriev, S.P., N.V.Kolesov, A.V .Osipov and G.N.Romanycheva (1999). System of Intelligence Support for Collision Avoidance at Sea. 55th Annual Meeting Institute of Navigation . June 28-30, Cambridge, MA.
377