Fuzzy logic based decision making system for collision avoidance of ocean navigation under critical collision conditions

Transcription

1 J Mar Sci Technol (2011) 16:84 99 DOI /s x ORIGINAL ARTICLE Fuzzy logic based decision making system for collision avoidance of ocean navigation under critical collision conditions L. P. Perera J. P. Carvalho C. Guedes Soares Received: 27 September 2009 / Accepted: 12 August 2010 / Published online: 7 October 2010 Ó JASNAOE 2010 Abstract This paper focuses on a fuzzy logic based intelligent decision making system that aims to improve the safety of marine vessels by avoiding collision situations. It can be implemented in a decision support system of an oceangoing vessel or included in the process of autonomous ocean navigation. Although Autonomous Guidance and Navigation (AGN) is meant to be an important part of future ocean navigation due to the associated cost reduction and improved maritime safety, intelligent decision making capabilities should be an integrated part of the future AGN system in order to improve autonomous ocean navigational facilities. In this study, the collision avoidance of the Target vessel with respect to the vessel domain of the Own vessel has been analyzed and input, and output fuzzy membership functions have been derived. The if then rule based decision making process and the integrated novel fuzzy inference system are formulated and implemented on the MATLAB software platform. Simulation results are presented regarding several critical collision conditions where the Target vessel fails to take appropriate actions, as the Give way vessel to avoid collision situations. In these situations, the Own vessel is able to take critical actions to avoid collisions, even when being the Stand on vessel. Furthermore, all decision rules are formulated in accordance with the International Maritime Organization Convention on the International Regulations for Preventing L. P. Perera C. Guedes Soares (&) Centre for Marine Technology and Engineering (CENTEC), Technical University of Lisbon, Instituto Superior Tecnico Av. Rovisco Pais, Lisbon, Portugal guedess@mar.ist.utl.pt J. P. Carvalho INESC-ID, Technical University of Lisbon, Instituto Superior Tecnico Av. Rovisco Pais, Lisbon, Portugal Collisions at Sea (COLREGs), 1972, to avoid conflicts that might occur during ocean navigation. Keywords Autonomous Guidance and Navigation Collision avoidance IMO rules and regulations COLREGs Fuzzy logic Intelligent systems Decision making process Crash stopping 1 Introduction Autonomous Guidance and Navigation (AGN) Systems and their applications have been in the dreams of ship designers for several decades. The development of computer technology, satellite communication systems and electronic devices, including high-tech sensors and actuators, have turned these dreams into a possible reality when designing the next generation ocean AGN systems. The main functionalities of the Multipurpose Guidance, Navigation and Control (GNC) systems are summarized by Fossen [1] in a paper that focuses not only on coursekeeping and course-changing manoeuvres (a conventional auto pilot system), but also on integration of digital data (digital charts and weather data), dynamic position and automated docking systems. Recent developments of design, analysis and control of AGN systems are also summarized by Ohtsu [2], and several ocean applications of AGN systems have been further studied, theoretically as well as experimentally, by Healey and Lienard [3], Do and Pan [4] and Moreira et al. [5, 6]. This area is bound to become increasingly important in the future of ocean navigation due to the navigational cost reduction and improved maritime safety [1]. An intelligent decision making process is an important part of the future AGN systems in ocean navigation.

2 J Mar Sci Technol (2011) 16: However, conventional ocean navigational systems consist of human guidance and, as a result, 75 96% of marine accidents and casualties are caused by some type of human error [7, 8]. Since many of the wrong judgments and missed operations of humans at the ocean end in human casualties and environmental disasters, limiting human subjective factors in ocean navigation and replacing them by an intelligent decision making (DM) system for navigation and collision avoidance could reduce maritime accidents and their respective casualties. However, development of collision avoidance capabilities into the next generation AGN systems in ocean navigation is still in the hands of future researchers; this formation of the intelligent AGN systems has been characterized as enavigation [9]. A block diagram for the main functionalities of an AGN system integrating collision avoidance facilities is presented in Fig. 1. The terminology used in recent literature regarding the collision avoidance conditions designates the vessel with the AGN system as the Own vessel, and the vessel that needs to be avoided as the Target vessel. These definitions have been considered during the formulation of collision situations in this work. Many techniques have been proposed for avoidance of collision situations in recent literature, but in general those techniques ignore the law of the sea as formulated by the International Maritime Organization (IMO) in 1972 [10]. These rules and regulations are expressed in the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs). The present convention was designed to update and replace the Collision Regulations of 1960, which were adopted at the same time as the International Convention for Safety of Life at Sea (SOLAS) Convention [11]. The decision making process and strategies in interaction situations in ocean navigation, including collision avoidance situations, are presented by Chauvin and Lardjane [12]. The same work also presents the analysis of quantitative data describing the manoeuvres undertaken by ferries and cargo-ships and behaviour of the Give way and Stand on vessels with respect to verbal reports recorded on board a car-ferry in the Dover Strait. This paper further analyzes critical collision situations, where the Give way vessel failed to take action and the Stand on vessel had to take action to avoid collision conditions, with respect to the decision making process. Detection of the Target vessel s position and its velocity are two important factors assessing the collision risk in ocean navigation as illustrated in this study. Sato and Ishii [13] proposed combining radar and infrared imaging to detect the Target vessel conditions as part of a collision avoidance system. In the same work, collision risk was presented with respect to the course of the Target vessel and the proposed image processing based course measurement method. The size and shape of the vessel domain, the area bounded for dynamics of the marine vessel, are other important factors in assessing the collision risk in ocean navigation. Lisowski et al. [14] used neural-classifiers to support the navigator in the process of determining the vessel s domain, defining that the area around the vessel should be free from stationary or moving obstacles. In a similar approach, Pietrzykowski and Uriasz [15] proposed the notion of vessel domain in a collision situation as depending on parameters such as vessel size, course and heading angle of the encountered vessels in the same study. Fuzzy logic based domain determination system has been further considered in the same work. Kwik [16] presented the calculations of a two-ship collision encounter based on the kinematics and dynamics of the marine vessels. The analyses of collision avoidance situations are illustrated regarding the vessel velocity, turning rate and direction, and desired passing distance. Yavin et al. [17] considered the collision avoidance conditions of a ship moving from one point to another in a narrow zig-zag channel, and propose a computational open loop command strategy for the rudder control system associated with the numerical differential equation solver. Most restricted waters and channels have their own rules and regulations for navigation. One of the disadvantages in this approach is insufficient flexibility to implement rules and regulations in navigation. The design of a safe ship trajectory is an important part of the collision avoidance process, and it has normally been simulated by mathematical models based on manoeuvring Fig. 1 Autonomous Guidance and Navigation system

3 86 J Mar Sci Technol (2011) 16:84 99 theory [18]. An alternative approach based on neural networks has also been proposed by Moreira and Guedes Soares [19]. Modelling of ship trajectories in collision situations by an evolutionary algorithm is presented by Smierzchalski and Michalewicz [20], where comparison of computational time for trajectory generation with respect to other manoeuvring algorithms, and static and dynamic constrains for the optimization process of the safe trajectories, are also illustrated. The intelligent control strategies implemented in collision avoidance systems can be categorized as automata, hybrid systems, Petri nets, neural networks, evolutionary algorithms and fuzzy logic. These techniques are popular among machine learning researchers due to their intelligent learning capabilities. The soft-computing based artificial intelligence (AI) techniques, evolutionary algorithms, fuzzy logic, expert systems and neural networks and combinations of them (hybrid expert systems), for collision avoidance in ocean navigation are summarized by Statheros et al. [21]. Ito et al. [22] used genetic algorithms to search for safe trajectories on collision situations in ocean navigation. The approach is implemented in the training vessel Shiojimaru, integrating Automatic Radar Plotting Aids (ARPA) and a Differential Global Position System (DGPS). ARPA system data, which can be formulated as a stochastic predictor, is designed such that the probability density map of the existence of obstacles is derived from the Markov process model before collision situations, as presented by Zeng et al. [23] in the same experimental setup. Further, Hong et al. [24] have presented collision free trajectory navigation based on a recursive algorithm that is formulated by analytical geometry and convex set theory. Similarly, Cheng et al. [25] have presented trajectory optimization for a ship collision avoidance system based on a genetic algorithm. Liu and Liu [26] used Case Based Reasoning (CBR) to illustrate the learning of collision avoidance in ocean navigation from previous recorded data of collision situations. In addition, a collision risk evaluation system based on a data fusion method is considered and Fuzzy Membership Functions (FMF) for evaluating the degree of risk are also proposed. Further intelligent anti-collision algorithms for different collision conditions have been designed and tested on the computer based simulation platform by Yang et al. [27]. Zhuo and Hearn [28] presented a study of collision avoidance situations using a self learning neurofuzzy network based on an off-line training scheme. The study is based on two-vessel collision situations, and a Sugeno type fuzzy inference system (FIS) is proposed for the decision making process of the collision avoidance. However, the work presented in this paper is formulated with respect to the Mamdani type FIS. Fuzzy-logic based systems, which are formulated for human type thinking, facilitate a human friendly environment during the decision making process. Hence, several decision making systems in research and commercial applications have been presented before [29]. Automatic collision avoidance systems for ship systems using fuzzy logic based control systems have been proposed by Hasegawa [30]. The conjunction of human behaviour and the decision making process has been formulated by various fuzzy functions in Rommelfanger [31] and Ozen et al. [32]. A fuzzy logic approach for collision avoidance with the integration of a virtual force field has been proposed by Lee et al. [33]. However, the simulation results are limited to the two-vessel collision avoidance situations. Behaviour based controls formulated with interval programming for collision avoidance of ocean navigation are proposed by Benjamin et al. [34]. The collision avoidance behaviour is illustrated accordance with the Coast Guard Collision Regulations (COLREFGS-USA). Benjamin and Curcio [35] present the decision making process of ocean navigation based on an interval programming model for multi-objective decision making algorithms. The computational algorithm based on if then logic is defined and tested under simulator conditions by Smeaton and Coenen [36] regarding different collision situations. Further, this study focused on a rule-based manoeuvring advice system for collision avoidance. Cockcroft and Lameijer presented detailed descriptions of collision avoidance rules, how the regulations should be interpreted and how to avoid collision [11]. Further, the complexity of autonomous navigation, not only in the sea but also in the ground, has been discussed by Benjamin and Curcio [34] who, in the same work, discuss the legal framework, rules and regulations, and the importance of collision avoidance within a set of given rules and regulations. This paper focuses on a fuzzy logic based DM system to be implemented in ocean navigation to improve safety of the vessel by avoiding collision situations under critical collision conditions; the system is a continuation of the study of Perera et al. [37]. The experienced helmsman s actions in ocean navigation can be simulated by fuzzy logic based decision making process, and that could be one of the main advantages in this proposal. Even though similar approaches have been identified in the recent literature [30], some of the drawbacks of those studies are the ignorance of the COLREGs rules and regulations and of expert knowledge in ocean navigation (i.e. crash stopping manoeuvres) that have been extensively considered in this study. Further discussion on COLREGs rules and regulations and their importance in ocean navigation can be found in Sect. 2.

4 J Mar Sci Technol (2011) 16: COLREGs rules and regulations The COLREGs [10] include 38 rules that have been divided into Part A (General), Part B (Steering and Sailing), Part C (Lights and Shapes), Part D (Sound and Light signals), and Part E (Exemptions). There are also four Annexes containing technical requirements concerning lights and shapes and their positioning, sound signalling appliances, additional signals for fishing vessels when operating in close proximity, and international distress signals. However, the main focus in this study is the COLREGs Part B, concerning Steering and Sailing rules. It is a fact that the COLREGs rules and regulations regarding collision situations in ocean navigation have been ignored in most of the recent literature. The negligence of the IMO rules may lead to conflicts during ocean navigation. As for the reported data of maritime accidents, 56% of major maritime collisions include violations of the COLREGs rules and regulations [20]. Therefore, the methods proposed by the literature ignoring the COLREGs rules and regulations should not be implemented in ocean navigation. On the other hand, there are some practical issues regarding implementation of the COLREGs rules and regulations during ocean navigation. The Own vessel Head-on and Overtake situations are presented in Figs. 2 and 3. Consider the Crossing situations where the Own vessel is in Give way situations in Figs. 4, 5, 6, and 7 and in Stand on situations in Figs. 8, 9, 10 and 11, there are velocity constrains in implementing COLREGs rules and regulations of the Give way and Stand on vessel collision situations when the Target vessel has very low or very high speed compared to the Own vessel. Furthermore, the Target vessel overtake situation is presented in Fig. 12. On the other hand, a considerable amount of recent research has been focused on design and implementation of optimization algorithms to find the safest path to avoid Fig. 3 Overtake (Own vessel) Fig. 4 Crossing (Own vessel Give Way ) Fig. 2 Head-on (Own vessel) Fig. 5 Crossing (Own vessel Give Way )

5 88 J Mar Sci Technol (2011) 16:84 99 Fig. 6 Parallel-crossing (Own vessel Give Way ) Fig. 9 Parallel-crossing (Own vessel Stand On ) Fig. 10 Crossing (Own vessel Stand On ) Fig. 7 Crossing (Own vessel Give Way ) Fig. 11 Crossing (Own vessel Stand On ) Fig. 8 Crossing (Own vessel Stand On ) stationary and moving obstacles. These optimization algorithms always find the optimum solution for the safe trajectory based on assumptions; hence the optimum solutions may not be realistic and may not have intelligent features. As an example, it is observed that some of the optimization algorithms always find the safest path behind the Target vessel, which may lead to a conflict situation with the COLREGs rules and regulations where the Own vessel is in Stand on vessel situation. On the popular collision avoidance approach of repulsive force based optimization algorithms, the Own vessel is kept away from the obstacles by a repulsive force field. This concept may not be practical in situations of moving obstacles with very low speed or very high speed when compared to the Own vessel s speed. In addition, a complex orientation of obstacles may lead to unavoidable collision situations. On the other hand, repulsive force based optimization algorithms are tasked with finding a

6 J Mar Sci Technol (2011) 16: Fig. 12 Overtake (Target vessel) globally safe trajectory for Own vessel navigation, and this might not be a good solution for the localized trajectory search. In addition, the concepts of Give way and Stand on vessels that are derived in COLREGs rules and regulations during the repulsive force based optimization process are not taken into consideration, and therefore may not be honoured. Vessel course changes and/or speed changes in ocean navigation must be formulated in order to avoid collision situations. However, some of the recent collision avoidance applications have been focused specifically on controllability of either course or speed change. According to the COLREGs rule 8(b) [10]: Any alteration of course and/or speed to avoid collision shall, if the circumstances of the case admit, be large enough to be readily apparent to another vessel observing visually or by radar; a succession of small alterations of course and/or speed should be avoided Hence, integrated controls of course, as well as speed changes, should be implemented during ocean navigation to avoid collision situations. Similarly, special measures should be considered for integration of course and speed controls due to the fact that the Own vessel may not respond to the required changes of course or speed. The problems and suggestions that are discussed in this section have been further illustrated in the design process of the DM system in this study. Consider critical collision conditions, where the Give way vessel does not take any appropriate actions to avoid collisions, so therefore the Stand on vessel is forced to take actions to avoid collision situation; according to COLREGs rule 17(b) [10]: Fig. 13 Vessel collision situation When, from any cause, the vessel required to keep her course and speed finds herself so close that collision cannot be avoided by the action of the Give way vessel alone, she shall take such action as will best aid to avoid collision However, the decision making process of the Own vessel in a critical collision situation should be carefully formulated, because the collision avoidance in this situation alternatively depends on the Stand on vessel s manoeuvrability. Further, this situation might lead to a Crash stopping manoeuvre of the Stand on vessel due to a lack of distance for speed reductions. Hence, this study is focused on the critical collision conditions in which the Own vessel, even as the Stand on vessel, has to take actions to avoid the collision due to absence or negligence of actions from a Give way Target vessel. 3 Collision conditions Figure 13 presents two vessels in a collision situation. The Own vessel is initially located at the point O (x o, y o ), and the Target vessel is located at the point A (x a, y a ). The Own and Target vessels velocity and course conditions are represented by V o, V a and W o, W a. The speed and course of the Target vessel with respect to the Own vessel can be estimated using the range and bearing values in a given

7 90 J Mar Sci Technol (2011) 16:84 99 time interval. It is assumed that the Target vessel maintains constant speed, V a? V a, and course W a conditions. The relative speed and course of the Target vessel with respect to the Own vessel are defined as V a,o? V a,o and W a,o, and can be calculated from V a;o ¼ V a V o ð1þ The relative trajectory of the Target vessel has been estimated from the Eq. 1 with the derivation of the relative speed V a,o and relative course W a,o. In addition, the relative range and bearing of the Target vessel with regard to the Own vessel are derived as AO and h o, respectively. All angles have been measured regarding the positive Y-axis. The curve AB represents the relative path of the Target vessel with respect to the Own vessel and the collision encounter angle is represented by h a,o. Further, it is assumed that both vessels are power driven vessels (IMO categorization). Figure 14 presents a relative collision situation in ocean navigation that is similar to a Radar plot. The Own vessel ocean domain is divided into three circular sections with radius R vd, R b and R a. The radius R a represents the approximate distance to the Target vessel identification; this distance could be defined as the distance where the Own vessel is in a Give way situation and should take appropriate actions to avoid collision. The distance R b represents the approximate distance where the Own vessel is in a Stand on situation, but should take actions to avoid collisions, if necessary due to absence of the appropriate actions from the Target vessel. The circular region with the radius R vd represents the vessel domain. The distances of R vd, R b and R a are formulated with the Collision Distance FMF (see Fig. 15). The Own vessel Collision Regions are divided into eight regions from I to VIII (see Fig. 14). These regions are separated by dotted lines that are coincident with the Collision Regions (see Fig. 16) as formulated in the FMF. It is assumed that the Target vessel will be located within one of these eight regions and the collision avoidance decisions are formulated in accordance to each region. As represented in Target vessel position II in Fig. 14, the Target vessel positions have been divided into eight Fig. 14 Relative collision situation in ocean navigation

8 J Mar Sci Technol (2011) 16: divisions of vessel orientations regarding the relative course (II-a, II-b, II-c, II-d, II-e, II-f, II-g and II-h). These divisions are separated by dotted lines that are coincident with the Relative Collision Angle FMF (see Fig. 18). 4 Collision avoidance methodology 4.1 Identification of obstacles The stationary and moving obstacles in ocean navigation can be identified by several instruments and systems such as eye/camera, radar, Automatic Radar Plotting Aid (ARPA) and Automatic Identification System (AIS). ARPA provides accurate information of range and bearing of nearby obstacles and AIS is capable of giving all the information on vessel structural data, position, course, and speed. The AIS simulator and marine traffic simulator have been implemented on several experimental platforms for design of safe ship trajectories [38]. The method of identifying stationary and moving obstacles in this model is the collection of radar data. 4.2 Collection of navigational information Navigational information can be categorized into static, dynamic and voyage related information [39]. Static information is composed of Maritime Mobile Service Identity (MMSI), Call Sign and Name, IMO number, length and beam, type of ship and location and position of communication antenna. Dynamic information can be divided into vessel position, position time stamp, course over ground, speed over ground, heading, navigational status and rate of turn. Finally, voyage related information can be expanded into vessel draft, cargo type, destination and route plan. Collection of navigational information is an important part of the decision making process of the collision avoidance in ocean navigation and can be achieved by collaboration with the AIS. However, collection of the navigational information of the Target vessel has not been emphasized at this phase of the present work. 4.3 Analysis of navigational information The collected obstacles information should be considered for further analysis of navigational information. Three distinct situations involving risk of collision in ocean navigation have been recognized in recent literature [36]: Overtaking (see Figs. 3, 12); Head-on (see Fig. 2) and Crossing (see Figs. 4, 5, 6, 7, 8, 9, 10, 11). Therefore, these three situations have been analyzed in this work. However, in ocean navigation, complex collision situations involving a combination of the above situations can occur, and identification of each situation with respect to each of the collision conditions will useful for the overall decisions of ocean navigation. 4.4 Assessments of the collision risk The analysis of navigational information will help to assess the collision risk. The assessment of collision risk should be continuous and done in real-time by the navigational system in order to guarantee the safety of the Own vessel. As illustrated in the literature, the mathematical analysis of collision risk detection can be divided into two categories [39]: the Closest Point Approach Method (CPA-2D method) and the Predicted Area of Danger Method (PAD- 3D method). The CPA method consists of calculation of the shortest distance from the Own vessel to the Target vessel and the assessment of the collision risk, which can be predicted with respect to the Own vessel domain. However, this method is not sufficient to evaluate the collision risk, since it does not take into consideration the Target vessel size, course and speed. An extensive study of the CPA method with respect to a two-vessel collision situation has been presented by Kwik [16]. The PAD method consists of modelling the Own vessel s possible trajectories as an inverted cone and the Target vessel s trajectory as a cylinder, being the region of both objects intersection categorized into the PAD. The Target vessel size, course and speed can be integrated into the geometry of the objects of navigational trajectories. Tables 1 and 2 present the summarized collision risk assessments and decisions of the two-vessel collision situation in Fig. 14. The first column of the Tables 1 and 2 represents the Collision Regions (Reg.) with respect to the Own vessel, and the second column represents the Divisions (Div.) of the Target vessel orientations. The third column represents the Collision Risk (Risk) assessments with respect to each of the Collision Regions, which have been divided into three sections of Low Risk (Low), Medium Risk (Mid.) and High Risk (High). The Target vessel Relative Range (Range) from R vd to R a is presented in the fourth column, and from R a to R b is presented in the seventh column. The Relative Speed Ratio conditions (Sp. Cond.) of V a,o /V o are presented in the fifth and eighth columns. The velocity conditions of V a,o /V o, & and 0 are represented by approximately less than, equal, and greater than zero, respectively. Finally the decisions that need to be taken to avoid collision situations with respect to the COLREGs rules and regulations are presented in the sixth and ninth columns. The specific COLREGs rules and regulations that are considered during the decision making processes with respect to ocean navigation are Overtaking (Rule 13), Head-on (Rule 14) and Crossing (Rule 15) situations. With

9 92 J Mar Sci Technol (2011) 16:84 99 Table 1 Collision risk assessments and decisions for regions I to IV Reg. Div. Risk Range Sp. Cond. Decisions Range Sp. Cond. Decisions I d Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 NA V a,o /V o & 0 NA V a,o /V o 0 NA V a,o /V o 0 NA e High (R vd R a ) V a,o /V o 0 dw o [ 0 (R a R b ) V a,o /V o 0 dw o [ 0 V a,o /V o & 0 dw o [ 0 V a,o /V o & 0 dw o [ 0 V a,o /V o 0 dw o [ 0 V a,o /V o 0 dw o [ 0 f Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 NA V a,o /V o & 0 NA V a,o /V o 0 NA V a,o /V o 0 NA II e Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o [ 0 V a,o /V o & 0 dv o [ 0 V a,o /V o 0 dv o [ 0 V a,o /V o 0 dv o [ 0 f High (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dw o [ 0, dv o \ 0 V a,o /V o & 0 dw o [ 0, dv o \ 0 V a,o /V o 0 dw o [ 0, dv o \ 0 V a,o /V o 0 dw o [ 0, dv o \ 0 g Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dw o [ 0 V a,o /V o & 0 dw o [ 0 V a,o /V o 0 dw o [ 0 V a,o /V o 0 dw o [ 0 III f Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o [ 0 V a,o /V o & 0 dv o [ 0 V a,o /V o 0 dv o [ 0 V a,o /V o 0 dv o [ 0 g High (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o \ 0 V a,o /V o & 0 dv o \ 0 V a,o /V o 0 dv o \ 0 V a,o /V o 0 dv o \ 0 h Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o \ 0 V a,o /V o & 0 dv o \ 0 V a,o /V o 0 dv o \ 0 V a,o /V o 0 dv o \ 0 IV a Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o \ 0 V a,o /V o & 0 dv o \ 0 V a,o /V o 0 dv o \ 0 V a,o /V o 0 dv o \ 0 g Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o [ 0 V a,o /V o & 0 dv o [ 0 V a,o /V o 0 dv o [ 0 V a,o /V o 0 dv o [ 0 h High (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o \ 0 V a,o /V o & 0 dv o \ 0 V a,o /V o 0 dv o \ 0 V a,o /V o 0 dv o \ 0 NA not applicable respect to the COLREGs rules and regulations, the vessel coming from the starboard side has high priority for the navigation that had been called the Stand on vessel, as mentioned before. As noted from Table 1, the appropriate actions for collision avoidance from the Own vessel have been formulated in the Regions I, II, III and IV with the relative distance range of (R vd R a ) and (R a R b ). However, respecting the COLREGs rules and regulations, the vessel coming from the port side has low priority, so is known as the Give way vessel. Further, noted from the Table 2, the appropriate actions of collision avoidance from the Own vessel have been formulated in Regions V, VI, VII and VIII with the relative range of (R vd R a ). The range (R vd R a ) represents the region in which the Own vessel, as the Stand on vessel, might take appropriate actions to avoid critical collision situations. Even though the main decision making process in this study is based on the COLREGs rules and regulations, the COLREGs do not account for critical collision condition situations (see Table 2) in near proximity. Therefore the

10 J Mar Sci Technol (2011) 16: Table 2 Collision risk assessments and decisions for regions V to VIII Reg. Div. Risk Range Sp. Cond. Decisions Range Sp. Cond. Decisions V a High (R vd R a ) V a,o /V o 0 dw o \ 0 (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dw o \ 0 V a,o /V o & 0 NA V a,o /V o 0 dw o \ 0 V a,o /V o 0 NA b Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 NA V a,o /V o & 0 NA V a,o /V o 0 NA V a,o /V o 0 NA h Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 NA V a,o /V o & 0 NA V a,o /V o 0 NA V a,o /V o 0 NA VI a Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dw o [ 0 V a,o /V o & 0 NA V a,o /V o 0 dw o [ 0 V a,o /V o 0 NA b High (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dw o [ 0, dv o \ 0 V a,o /V o & 0 NA V a,o /V o 0 dw o [ 0, dv o \ 0 V a,o /V o 0 NA c Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o [ 0 V a,o /V o & 0 NA V a,o /V o 0 dv o [ 0 V a,o /V o 0 NA VII b Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o \ 0 V a,o /V o & 0 NA V a,o /V o 0 dv o \ 0 V a,o /V o 0 NA c High (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o \ 0 V a,o /V o & 0 NA V a,o /V o 0 dv o \ 0 V a,o /V o 0 NA d Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o [ 0 V a,o /V o & 0 NA V a,o /V o 0 dv o [ 0 V a,o /V o 0 NA VIII c Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dw o \ 0 V a,o /V o & 0 NA V a,o /V o 0 dw o \ 0 V a,o /V o 0 NA d High (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dw o \ 0, dv o \ 0 V a,o /V o & 0 NA V a,o /V o 0 dw o \ 0, dv o \ 0 V a,o /V o 0 NA e Mid. (R vd R a ) V a,o /V o 0 NA (R a R b ) V a,o /V o 0 NA V a,o /V o & 0 dv o [ 0 V a,o /V o & 0 NA V a,o /V o 0 dv o [ 0 V a,o /V o 0 NA NA not applicable decision making process under critical collision conditions have been based on expert knowledge in navigation (i.e. crash-stopping manoeuvres), as presented in Table Decisions on navigation The decisions of collision avoidance in ocean navigation are based on the speed and course of each vessel, distance between two vessels, distance of the closest point approach (R DCPA ) (see Fig. 13), time to DCPA, neighbouring vessels and other environmental conditions. The decision space of collision avoidance can be categorized into three stages for each vessel in an open ocean environment: When both vessels are at non-collision risk range, both vessels have the options to take appropriate actions to avoid a collision situation; When both vessels are at collision risk range, the Give way vessel should take appropriate actions to achieve safe passing distance in accordance with the COLREGs

11 94 J Mar Sci Technol (2011) 16:84 99 rules and regulations and the Stand on vessel should keep its course and speed; When both vessels are at critical collision risk range, and the Give way vessel does not take appropriate actions to achieve safe passing distance in accordance with the COLREGs rules, then the Stand on vessel should take appropriate actions to avoid the collision situation. In this study it is assumed that the Give way vessel does not take appropriate actions to avoid the collision situations, therefore the Stand on vessel should take appropriate actions to avoid the collision situation while respecting the COLREGs rules and regulations. 4.6 Implementation of decisions on navigation As the final step, the decisions on vessel navigation will be formulated with respect to the collision risk assessments. The actions that are taken by the Own vessel are proportional to the Target vessel behaviour as well as the COL- REGs rules and regulations. The expected Own and Target vessel actions of collision avoidance can be formulated into two categories: The Own vessel passage change (course change and/or speed change); The Target vessel passage change (course change and/ or speed change). The Own vessel Course Change (dw o ) collision avoidance decisions, as presented in columns six and nine of Tables 1 and 2, dw [ 0 and dw \ 0, represent the change of course to starboard and port side, respectively. Furthermore dv o [ 0 and dv o \ 0 represent increment and decrement of the Own vessel Speed Changes (dv o ), respectively. 5 Fuzzification and defuzzification The design process of the overall Fuzzy logic based DM system can be categorized into the following six steps: Identification of the input FMFs. Identification of the output FMFs. Creation of the FMF for each set of inputs and outputs. Construction of if then fuzzy rules to operate the overall system. Formulation of the fuzzy rules to execute the actions. Combination of the fuzzy rules and defuzzification of the output. formally different from the fundamental concept of probability [40]. The Core of the fuzzy set A is defined as the set of all elements of the universe typical to A that are associated with the membership value of 1 and that could be written as Core(AÞ ¼fx 2 XjAðxÞ ¼1g ð2þ where x is a generalized variable. The Support of the fuzzy set is defined as the set of all elements of X that have nonzero membership degree in A and that could be written as Supp(AÞ ¼fx 2 XjAðxÞ1g ð3þ The FMF for inputs, Collision Distance (R), Collision Region (h o ), Relative Speed Ratio (V a,o /V o ) and Relative Collision Angle (W a,o ), are presented in Figs. 15, 16, 17 and 18 respectively. Figures 19 and 20 are formulated for the output FMFs of Speed (dv o ) and Course (dw o ) change of the Own vessel. The Core and Supp variables are listed on the respective figures of inputs and outputs FMFs. A Mamdani type IF \Antecedent[ THEN \Consequent[ rule based system has been developed and inference via Min Max norm has been considered during this study. Finally the defuzzification has been calculated by the center of gravity method. 5.2 Fuzzy inference system The block diagram for FIS with integration of navigational instruments is presented in Fig. 21. The initial step of the FIS consists of data collection of the Target vessel position, speed and course. In the next step, the relative trajectory, relative speed and relative course of the Target vessel are estimated, considering Eq. 1. Then, the data is fuzzified with respect to the input FMF of Collision Distance (see Fig. 15), Collision Region (see Fig. 16), Relative Speed Ratio (see Fig. 17) and Relative Collision Angle (see Fig. 18). The if then fuzzy rules are developed (see Tables 1, 2) in accordance with the COLREGs rules and regulations and using expert navigational knowledge. The outputs of the rule based system are the 5.1 Fuzzy sets and membership functions FMF describes fuzzy sets that map from one given universe of discourse to a unit interval. This is conceptually and Fig. 15 Collision Distance FMF

12 J Mar Sci Technol (2011) 16: Fig. 16 Collision Region FMF Fig. 17 Relative Speed Ratio FMF Fig. 20 Speed Change FMF further expanded as the Course Control Commands and Speed Control Commands that can be implemented on Speed and Course Control Systems, as presented in Fig. 21. Fig. 18 Relative Collision Angle FMF 6 Computational implementation 6.1 Fuzzy membership functions and variables Fig. 19 Course Change FMF Collision Risk Warning and the fuzzy decisions. Finally the fuzzy decisions are defuzzified by the output FMF of Course Change (see Fig. 19) and Speed Change (see Fig. 20) to obtain the control actions that will be executed in the Own vessel s navigation. The control actions are The Fuzzy logic based DM system has been implemented on the MATLAB software platform. MATLAB supports the fuzzy logic schemes of Mamdani and Sugeno Types [41]. The Mamdani type fuzzy logic scheme consists of utilizing membership functions for both inputs and outputs. As previously mentioned, if then rules are formed by applying fuzzy operations to the Mamdani type membership functions for given inputs and outputs. Following values are considered for the simulations. Considering the Collision Distance FMF (see Fig. 15), the assigned distance values are R vd & 0.5 NM, R b & 5NM and R a & 10 NM. The variables of j 1 & 10, j 2 & 80, j 3 & 10, and j 4 & 80 have been considered for the Collision Region FMF (see Fig. 16). The Relative Collision Angle FMF (see Fig. 18) variables have been assigned as m 1 & 10, m 2 & 10, and m 3 & 10. Considering the

13 96 J Mar Sci Technol (2011) 16:84 99 Fig. 21 Block diagram for fuzzy inference system Fig. 22 Crossing situation Fig. 23 Crossing situation Relative Speed Ratio FMF (see Fig. 17), the assigned values are v 1 & 0.1 and v 2 & 5. The output FMF of Speed Change (see Fig. 20) has been derived with respect to the variables of 0 1 & 2, 0 2 & 10, and 0 3 & 20. Finally, the Course Change FMF (see Fig. 19) has been formulated by the variables of i 1 & 10, and i 2 & Simulation results Figures 22, 23, 24 and 25 present the MATLAB simulations for two-vessel collision situations considering different speed and course conditions in the Cartesian coordinate space. These figures contain the start and end

14 J Mar Sci Technol (2011) 16: Fig. 24 Crossing situation the collision point for both vessels (0, 5) are common to all simulations. It is assumed that the speed and the course of the Target vessel is always a constant. Two front crossing situations of two vessels are presented in Figs. 22 and 23. In both situations, the Target vessel is in the Give way situation and the Own vessel is in the Stand on situation. However, in the simulation, the Target vessel has not taken any appropriate actions to avoid the collision situations. Therefore the Own vessel changed its velocity and course to avoid the collision situation. In Fig. 22, the Own vessel changed its speed ratio to V o /V a = 0.38 and course W o = to the port side to avoid the collision and the minimum distance between both vessels is NM. Similarly, in the collision situation represented in Fig. 23, the Own vessel changed its speed ratio to V o /V a = and course W o = to port side in order to avoid collision, and the minimum distance between both vessels is NM. Figures 24 and 25 present back crossing situations of two vessels in ocean navigation. On Fig. 24, the Target vessel is in the Give way situation and the Own vessel is in the Stand on situation. However, in this simulation the Target vessel has not taken any appropriate actions to avoid the collision, hence the Own vessel has changed velocity and course to avoid collision situations. In this case the Own vessel changed speed ratio to V o /V a = and course W o = to the starboard side to avoid the collision, and the minimum distance between both vessels is NM. On the collision situation represented in Fig. 25, where the Target vessel overtakes the Own vessel, the Own vessel did not change speed ratio to (V o /V a ) but changed course W o = to the port side to avoid the collision. The minimum distance between both vessels is NM. 7 Conclusion Fig. 25 Overtake situation positions of the Own and Target vessels and their navigational trajectories. The vessel initial speed condition is V o /V a = 0.5 and initial course of the Own vessel is W o = 0. The start position of the Own vessel (0, 0) and This paper presents a fuzzy logic based DM system for collision avoidance of ocean navigation based on the COLREGs rules and regulations and human expert knowledge for critical situations. The critical collision conditions where the Own vessel under Stand on conditions take actions to avoid collision due to absence of the safety actions from the Target vessel, have been illustrated in the work. Even though crash stopping manoeuvres of the Own vessel are expected under critical collision conditions, it is observed that the DM system could be able to overcome Crash stopping manoeuvres by a fuzzy logic based smooth decision making process. As presented in Figs. 22, 23, 24, and 25, proper change of course and/or speed could overcome the Crash stopping manoeuvres in critical collision conditions, even within a

15 98 J Mar Sci Technol (2011) 16:84 99 short distance. Although successful computational results are obtained under critical collision conditions, it is assumed that more complex collision conditions in multivessel situations can possibly occur, and unexpected actions of the Target vessels could be experienced. Hence, higher capabilities must be formulated into the DM system to overcome such situations. Acknowledgments The research work of the first author has been supported by the Doctoral Fellowship of the Portuguese Foundation for Science and Technology (Fundação para a Ciência e a Tecnologia) under contract SFRH/BD/46270/2008. Furthermore, this work contributes to the project Methodology for ship manoeuvrability tests with self-propelled models, which is being funded by the Portuguese Foundation for Science and Technology (Fundação para a Ciência e Tecnologia) under contract PTDC/TRA/74332/2006. References 1. 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