CN109298712A - A kind of autonomous Decision of Collision Avoidance method of unmanned ship based on the study of adaptive sailing situation - Google Patents
A kind of autonomous Decision of Collision Avoidance method of unmanned ship based on the study of adaptive sailing situation Download PDFInfo
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Abstract
The invention discloses a kind of autonomous Decision of Collision Avoidance methods of unmanned ship based on the study of adaptive sailing situation.Step 1: analyzing and describes unmanned ship navigation state information, establishes the sailing situation estimation Ontological concept model of the entity class in navigation environment and marine areas attributes;Step 2: being determined as binary crelation for the relationship between unmanned ship and barrier, is divided into a variety of sailing situation sub-scenes to ontology model quantization in conjunction with International Regulations for Preventing Collisions at Sea;Step 3: the environmental state information that unmanned ship is current in sub-scene is obtained, the long memory network in short-term of building feeds back memory unit, it is interacted using the autonomous Decision of Collision Avoidance algorithm of ship with maritime environment, the optimal policy of autonomous collision prevention is calculated by the study of adaptive sailing situation.The present invention substantially increases decision feasibility and algorithm iteration speed to the sailing situation dimensionality reduction of Decision of Collision Avoidance adaptive learning, it is ensured that the real-time automatic obstacle avoiding of unmanned freighter and navigation safety.
Description
Technical field
The present invention relates to unmanned ship control field more particularly to it is a kind of based on adaptive sailing situation study
The unmanned autonomous Decision of Collision Avoidance method of ship.
Background technique
The outer research about the autonomous Decision of Collision Avoidance of unmanned ship of Current Domestic is less, mostly unmanned boat, nobody
The fields such as vehicle are slightly achieved, and application method has based on Models of Decision-making in Ship Collision Avoidance system, knowledge base, expert system, fuzzy logic, mind
Through the methods of network, evolutionary computation, colony intelligence and immune algorithm, but these above-mentioned methods usually require to assume complete ring
Border information, however for uncertain environment, is hardly formed complete knowledge base, largely with need nobody in environmental interaction
Driving ship has stronger adaptive ability, carries out on-line decision collision prevention by sensor real-time perception obstacle information.It is right
In unmanned transport freighter, autonomous Decision of Collision Avoidance research is less, using unconsummate, still faces ship autonomous navigation and complexity
The problem of the autonomous Decision of Collision Avoidance of waters ship.
Summary of the invention
According to problem of the existing technology, the invention discloses a kind of based on the study of adaptive sailing situation nobody
The autonomous Decision of Collision Avoidance method of ship is driven, unmanned ship can be made not have ambient enviroment priori to know in uncertain environment
By improving the autonomous Decision of Collision Avoidance of learning ability progress and Adaptive Planning avoidance path with interacting for environment in the case where knowledge.
The present invention discloses a kind of autonomous Decision of Collision Avoidance method of unmanned ship based on the study of adaptive sailing situation,
It is characterized by comprising following steps:
Step 1: analyzing and describes the operational configuration information of unmanned ship, by nautical chart information, ship and barrier
The navigation safeties information such as information is divided into entity class and attribute, constructs the sailing situation estimation ontology of unmanned ship
Model;
Step 2: building marine ships sailing situation ontology model attribute of a relation table, by unmanned ship and barrier
Between relationship be determined as binary crelation, in conjunction with International Regulations for Preventing Collisions at Sea to ontology model quantization be divided into a variety of navigation states
Gesture scene;
Step 3: in conjunction with environment priori knowledge known in nautical chart information, unmanned ship is originated into port to port of destination
Sea area sliding-model control is the two-dimensional grid unit with state space characteristic, by determining that seaway domain is built with barrier zone
Vertical maritime environment model;In environmental model, the information in the sub-scene after division is perceived, obtains unmanned ship
The current environmental state information of oceangoing ship;
Step 4: building for storage vessel collision prevention behaviour decision making length in short-term memory network feed back memory unit, utilize
The autonomous Decision of Collision Avoidance algorithm of ship (DQN-Collision Avoidance Decision-making, DQNCAD) and marine ring
Border interaction calculates the optimal policy of the unmanned autonomous collision prevention of ship by the study of adaptive sailing situation.
One complete maritime traffic system is exactly a closed loop feedback system as composed by " people-ship-sea-environment ".
Sailing situation entity is divided into four sub- entity class: sea chart entity, barrier entity class, nothing by ship's navigation feature after study
People drives ship entity class and environmental information.
Sea chart entity includes typical open waters, navigation channel, boundary, narrow channel, prohibited area and anchorage.Barrier entity is then
Including static-obstacle thing and dynamic barrier.Unmanned ship entity is to describe oneself state information.Environmental information includes
Sea disturbance, visibility and depth of water etc..
Semantic attribute of the Attribute class to description object, such as the Position class ... to describe point entity position
Attribute selective analysis barrier entity association attributes, to describe the position relation between barrier entity and unmanned boat entity
With sea area positional relationship.
Relationship between unmanned ship and barrier can be divided into binary crelation: unmanned boat and static-obstacle thing, nobody
Ship and dynamic barrier, are respectively as follows: Egoship-StaticObstacle, are abbreviated as ES; Egoship-
DynamicObstacle is abbreviated as ED, shipyard scape hasFront before being specifically divided into the sailing situation of unmanned ship,
Shipyard scape hasBehind, front left side scene hasFrontLeft, forward right side scene hasFrontRight, left rear side scene afterwards
HasBehindLeft, right lateral side scene hasBehindRight.
Quantization division is carried out to 6 scenes such as hasFront, hasBehind in step 2:
π/8 hasFrontED:15~π/8, included navigation scene have: HO, OT and CR;
π/8 hasBehindED:5~11 π/8, included navigation scene have: OT;
HasFrontLeftED:3 pi/2~15 π/8, included navigation scene have: CR and OT;
HasFrontRightED: π/8~pi/2, included navigation scene have: CR and OT;
π/8 hasBehindLeftED:11~3 pi/2s, included navigation scene have CR;
HasBehindRightED: pi/2~5 π/8, included navigation scene have CR;
Wherein HO indicates end-on scene (Head-on encounter);CR indicates to intersect the scene (Crossing that meets
encounter);OT expression overtakes scene (Overtaking encounter).
The current environmental state information of unmanned ship are as follows:
Wherein obstIndicate unmanned ship current ambient conditions information, vtIndicate the ship's speed of t moment,When indicating t
The course at quarter, δtIndicate the relative bearing of t moment unmanned ship and barrier, disU-PIndicate unmanned ship to mesh
Port distance, disU-OIndicate unmanned ship to barrier distance.
Duration T will be observedPIn obtain historic state information and current state information are stored in feedback memory unit,
The long memory network training pattern in short-term of building, shown in the following matrix of the environmental state information of acquisition:
And using LSTM as the Q value network of unmanned ship, setup parameter ω;Q (s, a, ω) ≈ Q π (s, a),
Wherein s indicates unmanned ship environment state space, and a indicates the unmanned autonomous Decision of Collision Avoidance behavior of ship, then multiple to keep away
The collection for touching decision behavior is combined into autonomous Decision of Collision Avoidance space A;
Loss function is defined using mean square deviation in Q value:
WhereinIndicate that desired value symbol, r indicate that unmanned ship is obtained by excitation function and environmental interaction
Excitation value, γ indicate decay factor;
Gradient of the calculating parameter ω about loss function:
Using stochastic gradient descent undated parameter ω, acquire in unmanned ship collision prevention behavior and ambient condition mapping
The accumulative maximum Q value of return, and then obtain optimal autonomous collision prevention behavior.
Excitation function R is by close to target point rdistanceWith avoidance safety rcollosionTwo parts composition, form are as follows:
Wherein λdistanceAnd λdistanceThe weighted value influenced close to target point and avoidance on total excitation function is respectively indicated,
(xt,yt) indicate coordinate points position of the unmanned ship t moment in environmental model, (xO,yO) indicate barrier in environment
Coordinate points position in model, (xP,yP) indicate coordinate points position of the destination in environmental model, NobsIndicate unmanned
Barrier quantity in need of consideration under ship current state;∨ is the "or" in logical language, and Z indicates navigation safety meeting
It meets distance and captain L is positively correlated.
By adopting the above-described technical solution, it is provided by the invention it is a kind of based on adaptive sailing situation study nobody
The autonomous Decision of Collision Avoidance method of ship is driven, by radar sensor model real-time perception environmental state information, by constructing length
When memory network establish feedback memory unit, using the environmental state information perceived as the input of the network, using ship from
Main Decision of Collision Avoidance algorithm (DQN-Collision Avoidance Decision-making, DQNCAD) interacts with navigation environment,
The optimal policy of the autonomous collision prevention of unmanned ship is obtained by training deep neural network.Its beneficial effect is nobody
The continuous storage sensors data of ship are driven, carry out on-line study evacuation barrier strategy simultaneously certainly by interacting with maritime environment
What is adapted to cooks up avoidance path, compared to by study of the convolutional neural networks to image, accelerates iteration speed, and keep away
The problems such as having exempted from the more difficult perception of image object under severe sea condition, especially in the case of poor visibility, sensing data effect
Amplification, and without establishing complete knowledge base and expert system, bound fraction environment priori knowledge and online adaptive study
Algorithm realizes autonomous Decision of Collision Avoidance efficiently, quickly, safe, has broad application prospects and greatly nobody has been pushed to drive
Sail the development of ship autonomous navigation technology.
Detailed description of the invention
In order to illustrate the technical solutions in the embodiments of the present application or in the prior art more clearly, below will to embodiment or
Attached drawing needed to be used in the description of the prior art is briefly described, it should be apparent that, the accompanying drawings in the following description is only
Some embodiments as described in this application, for those of ordinary skill in the art, in the premise not made the creative labor
Under, it is also possible to obtain other drawings based on these drawings.
Fig. 1 is a kind of autonomous Decision of Collision Avoidance algorithm of unmanned ship based on the study of adaptive sailing situation of the present invention
Schematic diagram;
Fig. 2 is ontology model concept figure in scene partitioning layer of the present invention;
Fig. 3 is ontology model attribute of a relation table in scene partitioning layer of the present invention;
Fig. 4 is that International Regulations for Preventing Collisions at Sea is combined to quantify schematic diagram to scene is divided in scene partitioning layer of the present invention;
Fig. 5 is a kind of autonomous Decision of Collision Avoidance method of unmanned ship based on the study of adaptive sailing situation of the present invention
In environmental model figure;
Fig. 6 is a kind of autonomous Decision of Collision Avoidance of unmanned ship based on the study of adaptive sailing situation of the present invention
Method flow diagram;
Specific embodiment
To keep technical solution of the present invention and advantage clearer, with reference to the attached drawing in the embodiment of the present invention, to this
Technical solution in inventive embodiments carries out clear and complete description:
A kind of autonomous Decision of Collision Avoidance method of unmanned ship based on the study of adaptive sailing situation as shown in Figure 1,
Specific steps are as follows:
Step 1: analyzing and describes the operational configuration information of unmanned ship, by nautical chart information, ship and barrier
The navigation safeties information such as information is divided into entity class and attribute, constructs the sailing situation estimation ontology of unmanned ship
Model, as shown in Figure 2;
Step 2: building marine ships sailing situation ontology model attribute of a relation table, as shown in Figure 3.By unmanned ship
Relationship between oceangoing ship and barrier is determined as binary crelation, is divided into conjunction with International Regulations for Preventing Collisions at Sea to ontology model quantization
A variety of sailing situation sub-scenes, as shown in Figure 4;
Step 3: in conjunction with environment priori knowledge known in nautical chart information, unmanned ship is originated into port to port of destination
Sea area sliding-model control is the two-dimensional grid unit with state space characteristic, by determining that seaway domain is built with barrier zone
Vertical maritime environment model, as shown in Figure 5;In environmental model, the information in the sub-scene after division is perceived, is obtained
The current environmental state information of unmanned ship;
Step 4: building for storage vessel collision prevention behaviour decision making length in short-term memory network feed back memory unit, utilize
The autonomous Decision of Collision Avoidance algorithm of ship (DQN-Collision Avoidance Decision-making, DQNCAD) and marine ring
Border interaction calculates the optimal policy of the unmanned autonomous collision prevention of ship by the study of adaptive sailing situation.
One complete maritime traffic system is exactly a closed loop feedback system as composed by " people-ship-sea-environment ".
Sailing situation entity is divided into four sub- entity class: sea chart entity, barrier entity class, nothing by ship's navigation feature after study
People drives ship entity class and environmental information.
Sea chart entity includes typical open waters, navigation channel, boundary, narrow channel, prohibited area and anchorage.Barrier entity is then
Including static-obstacle thing and dynamic barrier.Unmanned ship entity is to describe oneself state information.Environmental information includes
Sea disturbance, visibility and depth of water etc..
Semantic attribute of the Attribute class to description object, such as the Position class ... to describe point entity position
Attribute selective analysis barrier entity association attributes, to describe the position relation between barrier entity and unmanned boat entity
With sea area positional relationship.
Relationship between unmanned ship and barrier can be divided into binary crelation: unmanned boat and static-obstacle thing, nobody
Ship and dynamic barrier, are respectively as follows: Egoship-StaticObstacle, are abbreviated as ES; Egoship-
DynamicObstacle is abbreviated as ED, shipyard scape hasFront before being specifically divided into the sailing situation of unmanned ship,
Shipyard scape hasBehind, front left side scene hasFrontLeft, forward right side scene hasFrontRight, left rear side scene afterwards
HasBehindLeft, right lateral side scene hasBehindRight.
Quantization division is carried out to 6 scenes such as hasFront, hasBehind in step 2:
π/8 hasFrontED:15~π/8, included navigation scene have: HO, OT and CR;
π/8 hasBehindED:5~11 π/8, included navigation scene have: OT;
HasFrontLeftED:3 pi/2~15 π/8, included navigation scene have: CR and OT;
HasFrontRightED: π/8~pi/2, included navigation scene have: CR and OT;
π/8 hasBehindLeftED:11~3 pi/2s, included navigation scene have CR;
HasBehindRightED: pi/2~5 π/8, included navigation scene have CR;
Wherein HO indicates end-on scene (Head-on encounter);CR indicates to intersect the scene (Crossing that meets
encounter);OT expression overtakes scene (Overtaking encounter).
The current environmental state information of unmanned ship are as follows:
Wherein obstIndicate unmanned ship current ambient conditions information, vtIndicate the ship's speed of t moment,When indicating t
The course at quarter, δtIndicate the relative bearing of t moment unmanned ship and barrier, disU-PIndicate unmanned ship to mesh
Port distance, disU-OIndicate unmanned ship to barrier distance.
Duration T will be observedPIn obtain historic state information and current state information are stored in feedback memory unit,
The long memory network training pattern in short-term of building, shown in the following matrix of the environmental state information of acquisition:
And using LSTM as the Q value network of unmanned ship, setup parameter ω; Q(s,a,ω)≈Qπ(s, a),
Wherein s indicates unmanned ship environment state space, and a indicates the unmanned autonomous Decision of Collision Avoidance behavior of ship, then multiple to keep away
The collection for touching decision behavior is combined into autonomous Decision of Collision Avoidance space A;
Loss function is defined using mean square deviation in Q value:
WhereinIndicate that desired value symbol, r indicate that unmanned ship is obtained by excitation function and environmental interaction
Excitation value, γ indicate decay factor;
Gradient of the calculating parameter ω about loss function:
Using stochastic gradient descent undated parameter ω, acquire in unmanned ship collision prevention behavior and ambient condition mapping
The accumulative maximum Q value of return, and then obtain optimal autonomous collision prevention behavior.
Excitation function R is by close to target point rdistanceWith avoidance safety rcollosionTwo parts composition, form are as follows:
Wherein λdistanceAnd λdistanceThe weighted value influenced close to target point and avoidance on total excitation function is respectively indicated,
(xt,yt) indicate coordinate points position of the unmanned ship t moment in environmental model, (xO,yO) indicate barrier in environment
Coordinate points position in model, (xP,yP) indicate coordinate points position of the destination in environmental model, NobsIndicate unmanned
Barrier quantity in need of consideration under ship current state;∨ is the "or" in logical language, and Z indicates navigation safety meeting
It meets distance and captain L is positively correlated.
A kind of autonomous Decision of Collision Avoidance side of unmanned ship based on the study of adaptive sailing situation disclosed by the invention
Autonomous Decision of Collision Avoidance is divided into scene partitioning layer and decision-making level by method, this method, is innovated and is answered for the first time in unmanned ship domain
With ontology model scene partitioning, the environmental state information dimensionality reduction effectively inputted by the autonomous Decision of Collision Avoidance of unmanned ship,
Improve the high efficiency of Decision of Collision Avoidance.In scene partitioning layer, it is by the entity division in ambient condition locating for unmanned ship
Sea chart entity class, barrier entity class, unmanned ship entity class and environmental information class, wherein sea chart entity class and environment
Info class includes component environment priori knowledge, avoids the multiple trial and error of autonomous Decision of Collision Avoidance algorithm and local iteration.Utilize length
Short-term memory network accumulate experience to sensor perception driving environment status information on-line study, in conjunction with intensified learning and ring
Border interactive decision making collision prevention executes "front", "rear", "left", "right", " left front ", " left back ", " before right ", " after right " 8 kinds of movements, most
The autonomous Decision of Collision Avoidance of unmanned ship in the scene is completed eventually, and this method is suitable for a variety of uncertain scenes, especially right
There is stronger adaptive ability in marine environment complicated and changeable.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited to
This, anyone skilled in the art in the technical scope disclosed by the present invention, according to the technique and scheme of the present invention
And its inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (8)
1. a kind of autonomous Decision of Collision Avoidance method of unmanned ship based on the study of adaptive sailing situation, it is characterised in that: packet
Include following steps:
S1: analyzing and describes the operational configuration information of unmanned ship, by ships such as nautical chart information, ship and obstacle informations
Navigation safety information is divided into entity class and attribute, constructs the sailing situation estimation ontology model of unmanned ship;
S2: building marine ships sailing situation ontology model attribute of a relation table, by the pass between unmanned ship and barrier
System is determined as binary crelation, is divided into a variety of sailing situation sub-scenes to ontology model quantization in conjunction with International Regulations for Preventing Collisions at Sea;
S3: in conjunction with environment priori knowledge known in nautical chart information, unmanned ship starting port is discrete to port of destination sea area
Changing processing is the two-dimensional grid unit with state space characteristic, by determining that maritime environment is established in seaway domain and barrier zone
Model;In environmental model, the information in the sub-scene after division is perceived, obtains the current environment of unmanned ship
Status information;
S4: building for storage vessel collision prevention behaviour decision making length in short-term memory network feed back memory unit, it is autonomous using ship
Decision of Collision Avoidance algorithm is interacted with maritime environment, calculates the unmanned autonomous collision prevention of ship most by the study of adaptive sailing situation
Dominant strategy.
2. a kind of autonomous Decision of Collision Avoidance of unmanned ship based on the study of adaptive sailing situation according to claim 1
Method, which is characterized in that the analysis that entity and attribute are carried out to unmanned ship navigation state information in S1 are as follows:
One complete maritime traffic system is exactly a closed loop feedback system as composed by " people-ship-sea-environment ", is passed through
Ships navigate by water feature and sailing situation entity are divided into four sub- entity class: sea chart entity, barrier entity class, unmanned
Ship entity class and environmental information;
Sea chart entity includes that typical open waters, navigation channel, boundary, narrow channel, prohibited area and anchorage, barrier entity then include quiet
State barrier and dynamic barrier, unmanned ship entity are disturbed to describe oneself state information, environmental information including sea
Dynamic, visibility and the depth of water;
Semantic attribute of the Attribute class to description object, the Position generic attribute selective analysis to describe point entity position hinder
Hinder object entity association attributes, to describe position relation and sea area positional relationship between barrier entity and unmanned boat entity.
3. a kind of autonomous Decision of Collision Avoidance of unmanned ship based on the study of adaptive sailing situation according to claim 1
Method, which is characterized in that sailing situation estimation ontology model attribute of a relation table is established in the step S2 are as follows:
Relationship between unmanned ship and barrier can be divided into binary crelation: unmanned boat and static-obstacle thing, unmanned boat with
Dynamic barrier is respectively as follows: Egoship-StaticObstacle, is abbreviated as ES;Egoship-DynamicObstacle writes a Chinese character in simplified form
For ED, the sailing situation of unmanned ship is specifically divided into preceding shipyard scape hasFront, rear shipyard scape hasBehind, a left side
Front side scene hasFrontLeft, forward right side scene hasFrontRight, left rear side scene hasBehindLeft, right lateral side field
Scape hasBehindRight.
4. a kind of autonomous Decision of Collision Avoidance of unmanned ship based on the study of adaptive sailing situation according to claim 1
Method, which is characterized in that combine International Regulations for Preventing Collisions at Sea to the scene quantification treatment of division in the step S2 are as follows:
Quantization division is carried out to 6 scenes such as hasFront, hasBehind in step S2:
π/8 hasFrontED:15~π/8, included navigation scene have: HO, OT and CR;
π/8 hasBehindED:5~11 π/8, included navigation scene have: OT;
HasFrontLeftED:3 pi/2~15 π/8, included navigation scene have: CR and OT;
HasFrontRightED: π/8~pi/2, included navigation scene have: CR and OT;
π/8 hasBehindLeftED:11~3 pi/2s, included navigation scene have CR;
HasBehindRightED: pi/2~5 π/8, included navigation scene have CR;
Wherein HO indicates end-on scene (Head-on encounter);CR indicates to intersect the scene (Crossing that meets
encounter);OT expression overtakes scene (Overtaking encounter).
5. a kind of autonomous Decision of Collision Avoidance of unmanned ship based on the study of adaptive sailing situation according to claim 1
Method, it is further characterized in that: the current environmental state information of unmanned ship described in S3 are as follows:
Wherein obstIndicate unmanned ship current ambient conditions information, vtIndicate the ship's speed of t moment,Indicate the boat of t moment
To δtIndicate the relative bearing of t moment unmanned ship and barrier, disU-PIndicate unmanned ship to port of destination
Distance, disU-OIndicate unmanned ship to barrier distance.
6. a kind of autonomous Decision of Collision Avoidance of unmanned ship based on the study of adaptive sailing situation according to claim 1
Method, it is further characterized in that: in S4 specifically in the following way:
Duration T will be observedPIn obtain historic state information and current state information are deposited in input feedback memory unit, construct base
In the length memory network training pattern in short-term of ship perception status data, shown in the following matrix of the environmental state information of acquisition:
And using LSTM as the Q value network of unmanned ship, setup parameter ω;Q(s,a,ω)≈Qπ(s, a), wherein s
Indicate that unmanned ship environment state space, a indicate the unmanned autonomous Decision of Collision Avoidance behavior of ship, then multiple Decision of Collision Avoidance
The collection of behavior is combined into autonomous Decision of Collision Avoidance space A;
Loss function is defined using mean square deviation in Q value:
WhereinIndicate that desired value symbol, r indicate that unmanned ship passes through excitation function and environmental interaction excitation obtained
Value, γ indicate decay factor;
Gradient of the calculating parameter ω about loss function:
Using stochastic gradient descent undated parameter ω, acquires and add up back in unmanned ship collision prevention behavior and ambient condition mapping
Maximum Q value is reported, and then obtains optimal autonomous collision prevention behavior.
7. a kind of autonomous Decision of Collision Avoidance of unmanned ship based on the study of adaptive sailing situation according to claim 6
Method, which is characterized in that the autonomous Decision of Collision Avoidance space of ship are as follows:
The observation behavior O of unmanned ship is generalized for discrete movementOrdinary circumstance
Under, the hunting action of unmanned ship is four, upper and lower, left and right discrete movement, is then increased when turning occurs in environment diagonal
The collision prevention behavior in line direction;
Centered on unmanned ship particle, define practical autonomous Decision of Collision Avoidance spatial model A be upper and lower, left and right, upper left,
Upper right, lower-left and the discrete movement of bottom right eight:
A=[- 1,1 0,1 1,1-1,0 1,0-1 ,-1 0 ,-1 1 ,-1].
8. a kind of autonomous Decision of Collision Avoidance of unmanned ship based on the study of adaptive sailing situation according to claim 6
Method, which is characterized in that excitation function R is by close to target point rdistanceWith avoidance safety rcollosionTwo parts composition, shape
Formula are as follows:
Wherein λdistanceAnd λdistanceRespectively indicate the weighted value influenced close to target point and avoidance on total excitation function, (xt,
yt) indicate coordinate points position of the unmanned ship t moment in environmental model, (xO,yO) indicate barrier in environmental model
Coordinate points position, (xP,yP) indicate coordinate points position of the destination in environmental model, NobsIndicate that unmanned ship is current
Barrier quantity in need of consideration under state;∨ is the "or" in logical language, and Z indicates navigation safety meeting distance, and
Captain L is positively correlated.
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