A Collision Risk-Based Ship Domain Method Approach to Model the Virtual Force Field

Transcription

1 A Collision Risk-Based Ship Domain Method Appoach to Model the Vitual Foce Field Tengfei Wang a,b,c, Xinping Yan a,b *, Yang Wang a,b, and Qing Wu a,b,c a Intelligent Tanspotation System Reseach Cente, Wuhan Univesity of Technology, Wuhan Hubei , China b National Engineeing Reseach Cente fo Wate Tanspot Safety, Wuhan Hubei , China c School of Logistics Engineeing, Wuhan Univesity of Technology, Wuhan Hubei , China Abstact: Ship domain is a concept which is widely used in eseach on collision avoidance and taffic engineeing among othes. The pape offes a systematic and citical eview of the newe ship domain models and elated eseach. It discusses multiple diffeences in appoach to ship domain concept: fom definitions and safety citeia, though eseach methodologies and factos taken into account, to sometimes mostly diffeent esults obtained by vaious authos. Then, an attempt of applying the isk based ship domain is made to build a new VFF in this pape. The aim of this appoach is to establish a Vitual Field Foce method(vff) model with clea scientific meaning of isk and the ship domain model is used as a bidge duing this pocess. The VVF method pesented in this pape can be detailed and quantitative intepetation the collision isk of multi-ship encounte scenaio. It can povide an essential basis fo decision-making in multi-ship collision avoidance. Keywods: Maitime Safety, Ship Domain, Collision isk, VFF. 1. INTRODUCTION The concept of ship domain was widely used in the field of ship collision isk assessment and collision avoidance decision-making since the 1970s[1, 2]. Fom then on, it becomes an impotant tool to estimate the safe distance o safe aea aound the own ship in an encounte situation. Although thee is neve a complete and pecise definition of ship domain especially when it comes to the details such as the tems of size and shape, the geneal pinciples of this concept ae neve change: ship domain is an aea that it can be used to evaluated and visualize the collision isk with taget ships in cuent scenaio. It is moe intuitive and taking the speed and couse change into account in some tems compaed with CPA, anothe geometic method widely used in ship collision avoidance. Although thee is not a clea classification of ship domains, it can be divided into thee main methods: developed by theoetical analyses, based on expets knowledge and depended on wok expeience. These thee methods ae not mutually exclusive, and a ship domain model is usually constucted by a combination of vaious methods in actual use., e.g. Dinh and Im [3]. What all models have in common is that they ae influenced by wate egions, albeit at diffeent levels. Unde the condition of capacity o wateway isk, the paticula wate egion which is of inteest is mainly detemined by its shape, taffic density and taffic pattens. Fo instance, the wate can be divided into thee types in collision avoidance eseach: open wates, esticted (but consideable) wates o naow wateways. The methods of detemining and calculating ship domains have developed ove time. Ealy models wee often based on statistically pocessed maine ada data[1, 2, 4]. This kind of empiical appoach has become the mainsteam method, with continuous development, the data souce changed fom ada to AIS and moe advanced statistical methods have been applied to data pocessing [5, 6]. Analytical appoach [7, 8], expet navigatos knowledge[9], o a combination of both[3] is widely used especially it comes to collision isk analysis, nea miss detection o collision avoidance decisionmaking suppoting systems. The Vitual Field Foce method(vff) model[10] is a classical deteministic appoach method fo obot path planning, in which the seach aea of obot is changed into a vitual isk field. In VFF method, the safe path can be found along the vitual foce. While thee ae a lot of similaities in the

2 connotations and application between the concept of influence ange of obstacles in VFF and ship domain, VFF is used to analysis ship domain in moe details[11], and the ship domain is used to make the meaning of the isk value in VFF cleae[12]. Duing the development of unmanned suface vessels (USV) and unmanned cagos, the application of VFF in decision-making of unmanned ships is getting moe and moe attention. Bucknall et.[13, 14] developed a path planning method fo USV based on both VFF and ship domain, which can be used in a time-vaiant maitime envionment. Most of the appoach in unmanned ships ae mainly based on VFF as a continuation of obotics in the field of navigation, and the backgound of the isk of ship domain has gadually been neglected. To educe this gap, an attempt of applying the isk based ship domain is made to build a new VFF in this pape. The aim of this appoach is to establish a VFF model with clea scientific meaning of isk and the ship domain model is used as a bidge duing this pocess. The pape is oganized as follows: diffeent kinds of definitions of ship domain ae pesented in Section 2, followed by the analysis and discussion. Then in Section 3, seveal classic ship domain models ae mainly discussed in details. Based on these analysis, a collision isk-based ship domain method which can appoach to collision avoidance decision-making systems fo unmanned cago ship is pesented in Section 4. a case study is pesented in Section 5, followed by discussion and conclusions in Section SHIP DOMAINS DEFINITIONS, METHODS AND FACTORS TAKEN INTO ACCOUNT 2.1. Definitions of Ship Domains Although all eseaches popose vaious dimensions of the ship domain models to fit thei appoaches, it must be pointed out that these dimensions may lead to diffeent vessel spacing, depending on the specific definition, application scenaios and elevant safety standads. Theefoe, fou typical definitions ae eviewed and discussed hee, and the typical methods and factos accoding to diffeent kinds of ship domains ae discussed late in this section. These fou main definitions of ship domain ae the cicula domain [15, 16], Fujii [1] s and Coldwell [4] s elliptical domain and M. Goodwin [2] s cicle secto domain, the details of shape and size of each domain ae depicted in Fig. 1. Except of the diffeence of the shape and size between these models, the isk citeia which often combined with ship domain in pactice is anothe majo cause of diffeences. Fig. 2 illustates the mainly used fou kinds of isk citeia, which ae: A) own ship s (OS) domain is only concened and should keep a taget ship (TS) out of this ang; B) any TS s domain is only concened and OS should keep out of this ang; C) OS s and TS s domains can be ovelapped but evey domain should keep clea; D) neithe OS s and TS s domains should be ovelapped. R=3L A=4L B=1.6L R1=0.85nm R2=0.70nm A=6L B=1.75L A=5L B=2.5L A=1.1L R3=0.45nm B=0.75L Cicula Domain Weng et al. (2012) Elliptical Domain Fuji and Tanaka (1970) Cicle secto Domain Goodwin (1975) Elliptical Domain fo ovetaking Coldwell (1983) Elliptical Domain fo head-on and cossing with an additional aft secto Coldwell (1983) Figue 1: Definition of fou typical ship domains

3 At beginning, these citeia ae always epesented with ship domain togethe by eseaches. In Fujii [1] ship domain definition, the give way ship have the duty to avoid to violate the stand-on ship s domain, so the isk citeia is one of A and B. While in Coldwell [4] ship domain, evey ship should only be esponsible fo he own secuity, that s obviously the case of A. As fo M. Goodwin [2], the ship domain is defined and analyzed unde the pemise that neithe OS o TS s domains should be violated duing an encounte situation, that is the same meaning like case C. While in the latest eseach like Andew, et al. [15] and Wang and Hoong-Cho [16], the ship domain is defined that should not be ovelapped any time, which is the case D. With the pomotion and application of the concept of ship domain, the ship domain and isk citeia Ae combined in diffeent ways, which also makes the model of ship domain become wide vaiety. As one of the main factos of collision isk analysis, the ship domain and its companied isk citeia epesent the undestanding and attitude towads collision isk. Because diffeent ship domain model could lead to a diffeent safety aea in shape and size between encounteed ships, and lagely affect the collision isk identification and confomation as well as the pocess of collision avoidance decisionmaking duing a ship s navigation. As the effective spacing between the encounteed ships is an impotant index fo collision safety the lage effective spacing thee is, the safe the encounteed ships will be. The calculation fomula of effective spacing of the isk citeia A and isk citeia B fo fou typical ship domains and seven encounte situations ae given in Table 1. As is depicted in Fig. 1, the effective spacing in isk citeia C is the lage one among isk citeia A and B, and the isk citeia D is the sum of A and B. Figue 2: Diffeent domain-based isk citeia The encounte situations ae divided into seven scenaios athe than the typical thee (head-on, cossing and ovetake), as the effective spacing is diffeent when diffeent sides of OS face to the TS. The seven types of encountes ae pesented in details in [17]. Then the values ae calculated by setting the ships dimensions of OS and TS as 160m and 200m in length, and 20m and 30m in beam. Fig. 3 illustates these calculation esults. By this way the effective spacing of ship domains unde diffeent isk citeia can be compaed intuitively. The pesented esults in Table1 and Fig.3. yield the conclusions as follows: 1) The isk citeia A (fist line in fig.3.) may lead to a elatively small spacing fo a cossing encounte situation, no matte fom asten o ahead of a TS. Specifically, when OS is a Stand-on ship, which epesents the TS appeaing on staboad, the effective space is lage enough to meet the equiements of COLREGS. When OS is a Give-way ship, which epesents the TS appeaing on pot, the effective space is quite small and OS should take measues ealie to keep a safe situation. 2) The isk citeia B (second line in fig.3.) is simila with isk citeia A. The only diffeence is that the ship domain is set on the base of TS athe than OS. Just like it in isk citeia A, when OS is a Give-way ship, the ship domain is not enough to keep safe.

4 3) The isk citeia C (thid line in fig.3.) is moe easonable fo all the illustated encountes. While, the isk citeia D (foth line in fig.3.) may lead to a too lage spacing between ships, and a too lage spacing usually means less economical and unnecessay. 4) The isk citeia A and B in fact analysis the same poblem fom diffeent pespectives (fom OS s pespective o TS s pespective). This asymmetical domains in a same scenaio may lead to a diffeent assessment by OS and TS, which phenomena was fist analysis by Jingsong, et al. [18] in a head-on encounte eseach. Even these diffeent assessments always exist in pactice, they will lead to a misundestanding between involved ships and constitute a hazad. By compaing all these fou isk citeia, it might be concluded that the isk citeia C(Fig.2c) is moe easonable, economic, and fit well with the typical definitions of ship domain. While, it should be noted that all above conclusions ae dawn unde the vey common situation. Fo some othe special aeas, such as habo aeas, busy inland ive o naow channels, thee ae some special changes in ship domain model and isk citeia to fit the situation[15, 16, 19]. Table 1: Appoximated minimum effective spacing fo fou domains (OS and TSs length and beam ae: L 1, B 1, L 2, B 2, espectively. 1nm=1852m) Encounte/Safety condition Head-on (pot to a taget) Head-on (staboad to a taget) Cossing ahead of a taget on staboad Cossing asten of a taget, which appoached fom staboad Cossing ahead of a taget on pot Cossing asten of a taget, which appoached fom pot Ovetaking (pot to a taget in Goodwin model) Domain by Risk Citeia A Risk Citeia B Cicula 3L 1-0.5B 1 3L 2-0.5B 2 Fuji 1.6L 1-0.5B 1 1.6L 2-0.5B 2 Goodwin 0.7nm-0.5B nm-0.5B 2 Coldwell 1.75L 1-0.5B L 2-0.5B 2 Cicula 3L 1-0.5B 1 3L 2-0.5B 2 Fuji 1.6L 1-0.5B 1 1.6L 2-0.5B 2 Goodwin 0.85nm-0.5B 1 0.7nm-0.5B 2 Coldwell 3.25L 1-0.5B L 2-0.5B 2 Cicula 3L 1-0.5B 1 3L 2-0.5L 2 Fuji 1.6L 1-0.5B 1 4L 2-0.5L 2 Goodwin 0.85nm-0.5B nm-0.5L 2 Coldwell 3.25L 1-0.5B 1 6.1L 2-0.5L 2 Cicula 3L 1-0.5B 1 3L 2-0.5B 2 Fuji 4L 1-0.5L 1 1.6L 2-0.5B 2 Goodwin 0.85nm-0.5L nm-0.5B 2 Coldwell 1.75L 1-0.5L 1 3.9L 2-0.5B 2 Cicula 3L 1-0.5B 1 3L 2-0.5L 2 Fuji 1.6L 1-0.5B 1 4L 2-0.5L 2 Goodwin 0.7nm-0.5B nm-0.5L 2 Coldwell 1.75L 1-0.5B 1 6.1L 2-0.5L 2 Cicula 3L 1-0.5B 1 3L 2-0.5B 2 Fuji 4L 1-0.5L 1 1.6L 2-0.5B 2 Goodwin 0.85nm-0.5L nm-0.5B 2 Coldwell 3.25L 1-0.5L 1 3.9L 2-0.5B 2 Cicula 3L 1-0.5B 1 3L 2-0.5B 2 Fuji 1.6L 1-0.5B 1 1.6L 2-0.5B 2 Goodwin 0.7nm-0.5B nm-0.5B 2 Coldwell 1.75L 1-0.5B L 2-0.5B 2

5 Fuji Domain Coldwell Domain Cicula Domain Goodwin Domain Head-on (pot to a taget) Head-on (staboad to a taget) Cossing ahead of a taget on staboad Cossing asten of a taget, which appoached fom staboad Cossing ahead of a taget on pot Cossing asten of a taget, which appoached fom pot Risk Citeia D Risk Citeia C Risk Citeia B Risk Citeia A Ovetaking (pot to a taget in Goodwin model) Figue 3: Appoximated minimum effective spacing (in metes) fo fou domains (OS and TSs length and beam ae: 160m, 20m, 200m, 30m, espectively. 1nm=1852m) 2.2. Methods and Factos of Ship Domains The definition and isk citeia detemine the basic pinciples of ship domain, fo instance the geneal shape, size and usage scenaios. Then, the method of ship domain pesents the details of building a paticula model, including specific shapes and boundaies, and values of paametes. In most cases, thee ae thee main methods to detemine a ship domain: expeience-based, numeical and analysisbased. In pactice, these thee methods ae not mutually exclusive, and moe and moe moden mathematical methods ae appoached to fix the complex scenaios[20, 21] expeience-based ship domain models In expeience-based methods, ship domain is egaded as a visualized epesentation of the expeience of the cew, and the cew obey this domain duing the navigation. The main wok of expeience-based method is finding these existing domains as well as the ules behind them, then developing the model fo futue use. AIS data is the most impotant esouce fo the expeience-based method, it can be used to analysis cew s diving habits, summaize ules and validate the model. Benefit fom the well-functioning AIS data acquisition system all ove the wold, AIS data can be achieved and collection by eseaches. Then, the paametes can be detemined by analysing the navigation in the suitable wate aea. Fo instance, the length of the ship field in the cossing situation can be obtained by analysing the taffic flow in which feies paticipate in the Fehman Belt stait[5], and simila with the width o angle of the domain. This kind of domain is often ellipse with an iegula bounday. And the ship does not locate in the cente of the ellipse, as the staboad side need moe space fo head-on and cossing encountes. By studying the AIS data, Wang and Hoong-Cho [16] daw a conclusion that thee is a linea function between the size of the domain and the ship, and a quadatic function between the size of the domain and the ship s speed. Based on this assumption, the values of domain s length and speed can be detemined pecisely. In ode to balance the impact on diffeent domains, a smalle weight is assigned to the ships with lage minimal distances. The expeience-based ship domains ae intuitive and data-based, they ae poweful tools in modelling the collision isk situation and deepening the undestanding of safety in navigation. Howeve, the shape of this kind of ship domain is always iegula cicle o ellipse with an unsmooth bounday, and the size is changing accoding to data. Obviously, it is difficult to use the model in a timely isk identification and decision-making in an intelligent system numeical ship domain models Fo the deficiency of the expeience-based method, people began to ty to use the function fitting method to detemine the ship domain. Benefit fom the vaious moden egession functions, thee ae a plenty of choices to find the suitable method fo the numeical ship domain model. The ship domain based on numeical method has a egula shape, which can educe the computation and easy to use.

6 One of a typical numeical ship domain is pesented by Zhu, et al. [22] based on a neual netwok. This eseach is constucted of the cew s expeience data and a back popagation neual netwok (BPNN). The data is the assessments of diffeent encounte scenaios collected fom the cew, and the BPNN is developed to summaize the data and fom the ules. The COLREGs, envionment situations and OS and TS s ship size ae also factos taken into account. Pietzykowski pesented a numeical fuzzy ship domain fo open[23] and naow[19] wates. These two papes ae combinations and extensions of woks by Jingsong, et al. [18] and Zhu, et al. [22] and the application of fuzzy neual netwoks and is the main innovation point. The diffeent kinds of encounte situations and elative speed ae added into the method, thus the ship domain tuns into a changing model depending on the scenaios. The ship domains based on numeical method ae usually polygons with a smooth bounday sometimes oughly esembling cicles, the ship is in the aft section and pot side of ship domain athe than the cente, as the sta and foe side of ship need moe space to move as a Give-way ship. The shape and size of the domain also change accoding to the encounte type: in case of head-on encountes the size of the domain is much smalle and naowe than cossing. An advantage of the numeical method is that the whole aea within the ship domain bounday can be function fitted. It was found that accoding to cew s expeience the size of the ship domain is distibuted exponentially with the change of the safety peceived by human[23]. By following this ule, the value of collision isk at any point within the ship domain can be calculated, and the aea can be ebuilt with these isk value, which is often the fist step of path planning analysis-based ship domain models The analysis-based ship domain model is established though theoetical analysis, and the histoical data is used to modify the model. This type of model is theoetical, with a clea definition and a definite calculation method. The ship domain based on analysis has the simplest shape among the thee methods, while the foms of the domain ae also the most vaious. N. Wang et al.[7, 8, 24] poposed a complete analytical domain model named Quatenion Ship Domain (QSD) and fomed a dynamic analytical famewok[8]. The QSD is consisted of fou ac smooth connections (i.e. staboad, pot, foe and aft), and all paametes ae detemined by ship's speed, length and manoeuvability. By adding the factos such as envionment, human and equipment, QSD has been futhe developed into a Dynamic QSD[8], in which the dynamic means the ship domain can be e-sizes and e-shapes accoding to conditions in a paticula encounte situation. The analysis-based method contibutes a lot the developments of the concept of ship domain. The connotation of the concept is constantly being exploed, and the scope of application is expanding. The domain has been divided into blocking aea and action aea to distinguish the diffeent isk aeas and to facilitate tageted decision making[3]. The blocking aea is the least effective space to keep own ship safe, and should not be violated by othes. The action aea is a waning egion fo collision isk, all involved ships should take measues to educe the isk. The action aea is moe like a manoeuve aea which depends mostly on ship s manoeuvability. This method of dividing the ship domain accoding to the function is also poposed in [25]. The scope of application of ship domain is mostly in ocean o coastal wates, Andew, et al. [15] poposed a ship domain model fo the Rive Thames to enable the analysis of the inland ive taffic. All the size and shape of the domain has been changed to fit the paticula wate egion and inland ship chaacteistics accodingly. The analysis-based method gives eseaches a lot of fee space to constuct ship domain models that best suit thei needs. Howeve, pecisely because of this, these kinds of models ae often lack of applicable and it is difficult to diectly use it in othe wates. In addition, the ship domain deived by this method also have to be tested by histoical data (i.e. AIS data o cew s expeience), othewise it is not convincing. 3. PATH PLANING USING VVF METHOD

7 3.1. the ship domain model designed fo VFF VVF method will be used in this pat, in ode to contibute the path planning in details. The pupose of building the taget ships' potential field is to descibe the impact of the taget ships. Though the establishment of the taget ship potential field, the own ship and the taget ship can keep a safe distance by alteing the couse and the speed. Fo the taget ship, the isk of the vicinity of the taget ship in the vetical and hoizontal distibution along the taget ship is not unifom, taking the chaacteistics of the ship and the actual situation of navigation. Fo example, the main facto affecting the safety of a ship in the hoizontal diection is the distance between the ships and the speed is also an impotant facto in addition to the distance. Theefoe, the modeling of the taget ship potential field will also be combined with the vetical and hoizontal chaacteistics of diffeent models of design. In this pape, the main innovation of the taget ship potential field is the model used the ship s longitudinal influence as the skeleton, to extend the way to achieve the impact of the ship distibution of the desciption. In this pape, an impoved VFF model is poposed to model the isk field aound a dynamic vessel. In contast to taditional VFF, the epulsive foce field in this pape has consideed the effect of the elative velocity simultaneously. Such a featue inceases the method s capability to deal with dynamic encounte collision situation, which pemits the equiement of handling the status change of a sailing ship. To model a dynamic vessel, it is key point to fom the field shape changing with ship s specific velocity. It is designed as follows: when the ship is tavelling with low speed, a moe cicula field is constucted, othewise a half-elliptical field at the foe side is used fo a high speed ship. In addition, when own ship and taget ship ae both moving, the long axis changes along the elative velocity diection. The dimension of the new the epulsive foce field is computed by calculating aft and foe sections espectively. By using the following two equations, it is continuous between the conteminous sufaces of the aft and foe sections. The longitudinal potential of the taget ship is calculated as follows. The local coodinate system is established based on the diection of the taget ship body diection and the intesection of the ship's hoizontal axis and the vetical axis. The entie longitudinal potential field distibution is a piecewise function. The calculation fomula is shown as follows: ì Uship pî b ï v Aship = í ( pî a) ( v > 0) ï K - DS ï î 0 ( v 0) Whee, Uship is the ship potential constant, which epesents the maximum value of the ship's potential field; v is the elative speed of the own ship and the taget ship, when the speed of the two in the same diection, the speed of the own ship is geate than the taget ship v > 0, on the contay v < 0. K is the longitudinal distance between the own ship and the taget vessel; D S is a set safe distance, whee DS = v D T + DSmin, D T is the system delay, which is elated to senso delay and calculation delay, D S min is a set of extended safety distance. When the point p is in the aea b, The longitudinal potential field is distibuted as a constantu ship, Consideing the elative velocity v which is the taget ship and the ship, when v 0, the elative distance between the taget ship and the ship is gadually inceased, and the longitudinal potential value is 0. When v > 0, it indicates that the distance between the ship and the taget ship is gadually educed. The moe dangeous the potential value is, the moe the elative velocity is, the moe dangeous and the potential value is positively coelated with the elative velocity. The abovementioned longitudinal potential distibution eflects the isk distibution of the taget vessel in its longitudinal diection, the influence of the ship on its suounding envionment in its tansvese diection, and its oveall potential field is fomed on the basis of longitudinal, which is shown in Fig.4.

8 The calculation of the taget ship's potential is obtained by multiplying the longitudinal potential field A ship by the tansvese potential field. The hoizontal calculation ule is a kind of Gaussian function. The whole calculation method is shown in the fomula (6) e mn 2 æ D ö = Aship expç - 2 è 2s v ø Whee, D is the potential distance of moving ship in diffeent aea which is shown in Fig.4. s v is the convegence coefficient of the ship's potential, and detemines the hoizontal influence ange of the potential field. Ship B afoe=ve vgb vab vag Ship A aaft= G:Gound A:Ship A B:Ship B 3.2. the VFF model fo collision isk ecognize Figue 4: The Potential Distance of Moving Ship Afte building the new VFF model, the whole aea can be digitally econstucted by the taget ships isk field, as is depicted in Fig. 5. Evey point in this aea has a value of field stength, which is the sum of all the taget ships isk field. And the aim of own ship path planning is to find a tajectoy which can pass the encounte situation safely and back to the oiginal tajectoy finally, as is depicted in Fig. 6. While, in ode to find the way back to the oiginal tajectoy, it is equied to set a destination and constuct the attactive field about the destination. The attactive field is used to attact own ship back to the oiginal tajectoy. As the attactive field is monotonically inceasing with the distance, it is necessay to find a pope position point as a vitual destination. Fistly, thee should be enough distance between the destination and own ship at stat. Thus, aiving the destination means keeping away fom the cuent collision isk scenaio. Secondly, the destination cannot be too fa away fom own ship, in case the attactive field becomes too lage at some place to analyses.

9 Figue 5: Fou Visual Angles of the dynamic VFF of a moving ship Destination Ship 2 Destination Ship 2 Ship3 Ship3 Ship1 Own Ship Ship1 Own Ship Figue 6: the epulsive fields of 3 taget ships Fo most cases, the! "## function has a quadatic fom, which is monotonically inceasing with the distance too fast. Moeove, the quadatic fom bings geat computation as the distance is much lage in ships encounte situation than the common obot path planning scenaio. Thus, this pape choses anothe common! "## function which has the conical shape and linea fom. The calculation fomula is shown as follows:! "## = %& whee d = d q, q %&'(, the cuent distance fom destination; ξ is the attaction gain. Afte constucting the attactive field, the whole VFF model of the multi-ship encounte scenaio can be constucted with taget ships epulsive fields and vitual destination s attactive field. Fig. 6. can be impoved into Fig. 7. Destination Ship 2 Ship 2 Ship3 Own Ship Ship1 Ship3 Destination Ship1 Own Ship Figue 7: the VFF model of 3 taget ships and own ship s vitual destination

10 4. CONCLUSION Ship domain is a concept which is widely used in eseach on collision avoidance and taffic engineeing among othes. The pape offes a systematic and citical eview of the newe ship domain models and elated eseach. It discusses multiple diffeences in appoach to ship domain concept: fom definitions and safety citeia, though eseach methodologies and factos taken into account, to sometimes mostly diffeent esults obtained by vaious authos. Then, an attempt of applying the isk based ship domain is made to build a new VFF in this pape. The aim of this appoach is to establish a Vitual Field Foce method(vff) model with clea scientific meaning of isk and the ship domain model is used as a bidge duing this pocess. The VVF method pesented in this pape can be detailed and quantitative intepetation the collision isk of multi-ship encounte scenaio. It can povide an essential basis fo decision-making in multi-ship collision avoidance. Acknowledgements The fist autho has been suppoted by the China Scholaship Council (CSC) and the Fundamental Reseach Funds fo the Cental Univesities (Gant No. WHUT2017-YB-035). The eseach was sponsoed by gants fom the Fundamental Reseach Funds fo the Cental Univesities (WUT: 2018 Ⅲ 061GX) and the Key Poject in the National Science & Technology Pilla Pogam (Gant No.2015BAG20B05). Refeences [1] Y. Fujii, "Taffic Capacity," Jounal of Navigation, vol. 24, pp , [2] E. M. Goodwin, "A Statistical Study of Ship Domains," Jounal of Navigation, vol. 28, pp , [3] G. H. Dinh and N. K. Im, "The combination of analytical and statistical method to define polygonal ship domain and eflect human expeiences in estimating dangeous aea," Intenational Jounal of e-navigation and Maitime Economy, vol. 4, pp , [4] T. G. Coldwell, "Maine Taffic Behaviou in Resticted Wates," Jounal of Navigation, vol. 36, pp , [5] H. M. Gambog, J. T. Koldbog, L. S. L. Tue, M. Kistina, R. F. Mã Lsted, and E. Finn, "Empiical Ship Domain based on AIS Data," Jounal of Navigation, vol. 66, pp , [6] E. V. Ipeen, "Classifying Ship Encountes to Monito Taffic Safety on the Noth Sea fom AIS Data," Tansnav the Intenational Jounal on Maine Navigation & Safety of Sea Tanspotation, vol. 9, pp , [7] N. Wang, "An Intelligent Spatial Collision Risk Based on the Quatenion Ship Domain," Jounal of Ship Reseach, vol. 56, pp , [8] N. Wang, "A Novel Analytical Famewok fo Dynamic Quatenion Ship Domains," Jounal of Navigation, vol. 66, pp , [9] P. Zbigniew and U. Janusz, "The Ship Domain u2013 A Citeion of Navigational Safety Assessment in an Open Sea Aea," Jounal of Navigation, vol. 62, pp , [10] Khatib, "Real-time obstacle avoidance fo manipulatos and mobile obots," Intenational Jounal of Robotics Reseach, vol. 5, pp , [11] Y. Xue, D. Clelland, B. S. Lee, and D. Han, "Automatic simulation of ship navigation," Ocean Engineeing, vol. 38, pp , [12] C. K. Tam, R. Bucknall, and A. Geig, "Review of Collision Avoidance and Path Planning Methods fo Ships in Close Range Encountes," Jounal of Navigation, vol. 62, pp , 2009.

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