A Construction Method of a Sequential Decision Chain for Unmanned-Ship Autonomous Collision Avoidance Based on Human-Like Thinking

Abstract

As one of the key technologies restricting the development of intelligent ships, autonomous collision avoidance has attracted the attention of many scholars all over the world. Existing research on collision-avoidance behavior focuses more on collision risk assessment and local path-planning methods for studies on the human-like sequential logic of the whole collision-avoidance process, as well as the decision-making process of various stages. Further in-depth thinking is needed urgently. Based on this, a construction method of a human-like sequential decision chain for the autonomous collision avoidance of unmanned ships is proposed through the construction of a collision-avoidance rule base and strategy set, efficient data access based on the Knowledge Graph concept, global collision risk assessment considering sequential decision process, and the construction of a complete collision-avoidance logic process to simulate the decision-making process of humans in complex multi-ship encounters in open waters. For multi-ship encounter scenarios, considering the sequential decision-making process of collision avoidance, a method was proposed to divide the collision risk of the target ship into direct collision risk and potential collision risk. The validity and reliability of the constructed sequential decision chain are verified by simulation experimental results. The results show that the method is effective for collision avoidance (especially multi-ship collision avoidance) in open waters and can provide a theoretical basis and technical support with good interpretability for the decision-making process of an unmanned ship’s autonomous collision avoidance.

1. Introduction

In recent years, with the rapid development of intelligent maritime science and technology, the intelligent ship has become a highly pursued frontier technology. Intelligent navigation technology is the core technology of the intelligent ship, which integrates advanced electronic, communication, and computing systems to achieve autonomous perception, path-planning, decision-making, and control for ships. The aim is to enhance safety, reliability, economy, and environmental sustainability. Although remarkable progress has been made, there are still some difficulties and challenges [1]. As one of the key technologies of the intelligent navigation of ships, autonomous collision avoidance has been widely considered by scholars in relevant research fields worldwide since its rationality and effectiveness directly affect the safety of navigation [2]. Undoubtedly, ship collision-avoidance research makes a significant contribution to minimizing damage to the marine ecosystem and promoting the healthy and sustainable development of the marine ecological environment. There is so much environmental information and so many influencing factors that need to be analyzed and considered for collision avoidance (CA) by ships. The ambiguity of the description of collision avoidance between multiple ships in the International Regulations for Collision Avoidance at Sea (COLREGS), such as “common practices of seafarers” and “good seamanship”, further increases the difficulty of decision-making for collision avoidance (especially multi-ship collision avoidance). Therefore, to ensure the safe autonomous navigation of ships, there are still some problems to be solved. For example, how to give full consideration to the “ordinary practice” and “good seamanship” of experienced ship pilots, quickly develop collision-avoidance strategies adapted to complex encounter situations, and avoid risks safely and efficiently, and how to scientifically and effectively verify the effectiveness and reliability of collision-avoidance strategy.

Representative studies on ship collision-avoidance behaviors are mainly as follows:

In early relevant studies, Lee et al. [3] introduced an expert system and action space search algorithm into the existing collision-avoidance system. The design of the expert system is simplified, and the rationality of system decisions is improved. To build a decision-making system for automatic collision avoidance of ships, Zheng et al. [4] combined their practice of collision avoidance at sea and learned from the ideas of stimulating response theory to propose a collision risk model that can be evaluated from both time and space perspectives. Ahn et al. [5] integrated a fuzzy reasoning system with an expert system, utilized neural networks to compute collision risk, and established the relationship between the nearest encounter distance and the shortest encounter time through KT equation simulations. Perera et al. [6] proposed a collision-avoidance model for intelligent ships, which is based on the fuzzy logic reasoning method, combining the captain’s navigation experience and professional knowledge. Szlapczynski et al. [7] proposed a visible interfering ship information display method for collision-avoidance maneuvering. It mainly displays target ship motion parameters, whether the collision-avoidance strategy combined with its speed and course will collide with the interfering ship, and whether it conforms to COLREGS. Zhang et al. [8] proposed a distributed real-time collision-avoidance method for a multi-ship encounter situation. According to COLREGS requirements, collision avoidance in two scenarios, where all ships comply with the rules and some ships do not comply with the rules, is simulated and tested. Johansen et al. [9] proposed a model predictive control-based collision-avoidance method for ships, which considers COLREGS. Based on the prediction of the obstacle or ship trajectory, the rule compliance, as well as the risk of various control behaviors, are evaluated, and the optimal control behavior is selected. Liu et al. [10] provided an overview of the latest developments in USVs (unmanned surface vehicles) research and pointed out the challenges and future trends of USVs moving toward a more practical GNC (guidance, navigation, and control) capability. Tsou [11] adopted the Electronic Chart Display and Information System (ECDIS) as the navigation decision information support platform. Real-time information received by Automatic Identification System (AIS) is used to construct the forecast danger area of multi-target ships. Through the integration of the GIS module, the collision avoidance and route of the ship collision-avoidance system are selected under the condition of design optimization calculation and careful consideration of navigation, which provides a decision-making reference for the collision avoidance of ships. Zhao et al. [12] proposed a COLREGS-compliant real-time collision-avoidance method for USVs. Evidence-based reasoning theory is used to assess the collision risk when encountering obstacles and to provide early warning of possible collisions. An improved ORCA (optimal reciprocal collision-avoidance) algorithm is used to determine collision-avoidance maneuvers that conform to COLREGS. Lazarowska [13] proposed a Trajectory Base Algorithm for ship collision avoidance in the coexistence environment of dynamic and static obstacles to calculate the safe and optimal trajectory, in which both the COLREGS and the ship motion characteristics were considered. Kozynchenko et al. [14] applied dynamic predictive guidance techniques to solve the ship collision-avoidance problem, which was formulated as an optimal control problem and then transformed into a nonlinear eigenvalue problem describing the ship motion. Huang et al. [15] proposed an intelligent collision-avoidance method based on the Velocity Obstacle (VO) algorithm when multiple ships encounter. This study introduced advanced collision-avoidance algorithms from other related fields into the study of ship collision-avoidance methods, providing a new idea for further research. Szlapczynski et al. [16] adopted the ship domain to determine the latest moment of collision-avoidance operation to avoid the intrusion of ships into other ship domains when giving way. Lisowski et al. [17] proposed a model of collision-avoidance decision process in multi-ship encounter situations. Dynamic games, multi-stage position games, and multi-step matrix games are applied to ship motion control. Woo et al. [18] proposed a raster map method to represent ship encounter situations and explored ship collision-avoidance decisions through reinforcement learning based on raster maps. Shaobo et al. [19] proposed a ship’s autonomous collision-avoidance decision-making system based on an improved speed obstacle method. The effectiveness of the system was verified by simulation experiments under 10 different scenarios. Liang et al. [20] improved the traditional A* algorithm for the problem of ship autonomous navigation and collision avoidance and applied it to global route planning. A minimum steering method suitable for dynamic collision avoidance is proposed, considering COLREGS constraints. He et al. [21] constructed a digital traffic environment and used the speed barrier method and dynamic collision-avoidance mechanism to build an adaptive navigation decision model suitable for open water. The conformity of the model to COLREGS and good seamanship is verified by simulation experiments. Yuan et al. [22] proposed a two-stage collision-avoidance path-planning method for inland river ferries. Zhang et al. [23] proposed a knowledge-based approach for ship collision-avoidance decision support using AIS data. Based on the historical AIS data, the knowledge base of ship collision-avoidance behavior was constructed. Based on the constructed scene similarity model, ship trajectories in similar scenes were integrated to form collision-avoidance paths.

In addition, some research work considering human thinking in the collision-avoidance process has been carried out by scholars. Li et al. [24] introduced an anthropomorphic intelligent collision-avoidance decision (PIDVCA) scheme that incorporates COLREGS, seamen’s ordinary practice, good seamanship, dynamic risk assessment, and the concept of focused ship avoidance. They also provided an evaluation criteria framework for the scheme. Campbell et al. [25] reviewed the COLREGS-based USV collision-avoidance research status and pointed out that the handling of complex encounter scenarios requires the quantitative expression of COLREGS and the use of human-like thinking. At the same time, the ability to handle emergency scenarios as well as unforeseen situations is also crucial. Lisowski [26] proposed a model that defines the ship’s state equation and control constraints. The objective function for ship control is expressed using integral payment. This model enables the simulation of navigators’ collision-avoidance operations and decision-making processes based on COLREGS. Lisowski [27] introduced a ship collision-avoidance decision-making model for multi-ship encounters, which integrates theories of dynamic games, multi-stage position games, and multi-step matrix games for ship motion control. It considers the relative motions of multiple ships during collision avoidance and determines the optimal timing for proactive control. Xue et al. [28] studied the humanoid decision method of intelligent ships and proposed a knowledge-learning model under multiple environmental constraints for the automatic acquisition and representation of decision-making knowledge of watchkeepers. Liu et al. [29] respectively constructed a conventional and intelligent ship collision-avoidance decision-making model conforming to COLREGS for mixed navigation in open waters. Among them, the conventional model also considers the human thinking mode. Then, based on the prediction of the motion state of conventional ships, a coordination mechanism for notifying the collision-avoidance intention of conventional ships is established. Akdağ et al. [30] emphasized the importance of cooperative collision avoidance between ships in a maritime traffic environment where large ships coexist with ordinary ships. Based on the experience and lessons learned, a high-level architecture of collaborative collision-avoidance protocol is presented. Jiang et al. [31] proposed a decision model based on deep reinforcement learning (DRL) and considering the attention distribution mechanism of ship pilots, in which assessment of collision risk and planning of ship movement was mainly considered. Rothmund et al. [32] proposed a method using dynamic Bayesian networks to infer the intention of collision-avoidance actions of other ships in open waters, further improving the safety of results. Song et al. [33] proposed an integrated classification model based on supervised learning for ship collision-avoidance course prediction, aiming to simulate the human collision-avoidance decision-making process to predict the CA steering direction of ship operators. Higaki et al. [34] proposed a human-like automatic collision-avoidance path-planning method based on generative adversative imitation learning (GAIL). Applying GAIL to ship collision avoidance addresses the challenge of designing appropriate rewards in DRL and the limitations of inverse reinforcement learning (IRL) to generate collision-avoidance routes that mimic the performance of human experts.

It can be seen that in most relevant studies, more attention is focused on collision risk assessment, local path planning, and other methods, as for studies on human-like sequential logic of the whole collision-avoidance process, as well as the decision-making process of various stages, further in-depth thinking is needed urgently. The situation mentioned here refers to the ship’s group situation [35], which refers to the state and situation constituted by the deployment and behavior of all traffic entities in the target ship’s interest perception area. It contains all the information that the traffic entity can perceive, including the information obtained by the seaman’s “proper lookout” and the ECDIS, AIS, and other navigational aids. To simplify the analysis process, the traffic entity in this paper mainly refers to all the moving and static ships in the surface area of the target ship’s interest perception area. Based on the in-depth analysis of the ship group situation, a construction method of the sequential decision-making chain for the ship’s autonomous collision avoidance based on human-like thinking is proposed, which is under the premise of fully considering the COLREGS and the direct collision risks and potential collision risk of the target ship, to provide a better interpretable strategic reference for the autonomous collision avoidance of unmanned ships.

Since this study mainly focuses on open waters, considering the complexity of process analysis and the characteristics of ship behavior in open waters, collision avoidance between moving or stationary ships is mainly studied. Ship encounter scenarios are classified from the perspective of the target ship, and the most complex scenario is used as an example to give the complete construction method of the human-like thinking sequential decision-making chain for collision avoidance. Specifically, the detailed methods or flowcharts for the construction of the human-like thinking process are given for stages of situation cognition, collision risk identification, collision avoidance rule base and strategy set construction, generation of human-like thinking sequential collision-avoidance strategy, avoidance process monitoring and strategy correction, and ship resumption condition judgment, respectively. Drawing on the idea of the Knowledge Graph, two-ship encounter situation is abstracted into a kind of triad consisting of a head entity, a relation, and a tail entity to achieve efficient access to ship entity and relationship data; the global collision risk assessment of multi-ship encounter scenario is realized by considering the direct collision risk and potential collision risk comprehensively. Finally, the reliability of the proposed human-like thinking sequential decision chain construction method for unmanned ships’ autonomous collision avoidance is verified through multiple simulations in randomly set multi-ship encounter scenarios where the target ship and the interfering ships adopt different strategies, respectively.

The rest of the paper is organized as follows: Section 2 outlines the proposed method and the design of the simulation verification experiment. Section 3 presents the experimental results. In Section 4, the experimental results are analyzed, and the research limitations and prospects are discussed. Finally, Section 5 concludes the paper.

2. Materials and Methods

2.1. Classification of Ship Encountering Scenarios

In this paper, ship encounter scenarios are classified from the target ship’s perspective to analyze the corresponding collision-avoidance decision-making process of human-like thinking according to different scenarios. For example, as for a common two-ship encounter scenario, COLREGS is the main basis to determine the encounter situation. The strategy of the target ship is determined according to the current motion state of the two ships, the regulation of collision-avoidance responsibility and obligation in COLREGS, and the periodic status monitoring of the collision-avoidance process and timely correction of the established strategy, when necessary, until passing the interfering ship. For a multi-ship encounter scenario, it is not only necessary to analyze the encounter situation of two ships between the target ship and each interfering ship but also to comprehensively analyze that of all interfering ships, predict the actions of each interfering ship, and determine the collision-avoidance strategy. Furthermore, it is necessary to periodically monitor the status of the strategy implementation process and timely correct and update the established strategy, when necessary, until all interfering ships are cleared. To ensure the comprehensiveness of scene expression, the specific classification is shown in Figure 1. In this paper, the most complex scenario in which the target ship must fulfill both stand-on ship’s and give-way ship’s obligations is taken as an example.

2.2. Autonomous Collision-Avoidance Sequential Decision Chain Based on Human-Like Thinking

Cognition is the premise of decision-making. The real-time, comprehensiveness, and accuracy of the target ship’s cognition of its current situation directly affect the science and rationality of collision-avoidance decisions. The importance of situation awareness can also be demonstrated by the clause “proper lookout” in COLREGS. Based on accurate cognition of the situation, it is considered whether collision-avoidance manipulation is necessary and what kind of collision-avoidance manipulation should be adopted to achieve a satisfactory effect. The overall diagram of the human-like thinking sequential decision chain is shown in Figure 2, where CA represents collision avoidance.

Human thinking is often in a mixed state where image thinking and abstract thinking are intertwined, with abstract thinking focusing on features and image thinking focusing on details. Therefore, to realize the simulation of human-like decision-making thinking, not only the overall features of thinking need to be extracted, but also the concrete details need to be analyzed in real time. In other words, it requires conscious and in-depth thinking about the features and details of what usually seems to be unconscious behavior in time-varying environments.

2.2.1. Situation Cognition

The cognition of the situation should strive to be comprehensive and accurate. Considering the requirements of COLREGS on the light’s visibility distance of ships with a length of 50 m or more and the customary practice of a captain with rich sailing experience to judge the encounter situation, this paper mainly focuses on the water area within 6 nautical miles around the target ship and defines it as the target ship’s interest perception area. That is the area that the target ship focuses on and has a great influence on its navigation safety. To ensure the comprehensiveness of situation cognition, the encounter situation of all two ships in the interest perception area is recognized, and the comprehensive impact of all ships on the target ship’s sailing is evaluated.

In this paper, the classification of two-ship encounter situation is integrated with existing research methods [36], and the conflict encounter situation types are subdivided into nine types, i.e., $T_1,T_2,\cdots ,T_9$, which corresponds to the situation where the interfering ship is located in the nine subregions $E_1,E_2,\cdots ,E_9$ of the target ship’s interest perception region (among them, $E_8$ and $E_9$ are two implied overtaking subregions, which means the target ship is located in $E_5$ and $E_4$ subregions of the interfering ship, respectively), and form the basic encounter situation (head-on, crossing, and overtaking) with the target ship, respectively, as shown in Figure 3.

The situation is time-varying, necessitating the continuous updating of ship status information in the interest perception area based on the actual position and status of the target ship. Thus, the representation of the situation should facilitate frequent additions and deletions of ship data to ensure real-time and accurate situation cognition.

To make the expression structure of the situation more simple, intuitive, and easy to update the data at any time, this paper draws on the idea of the Knowledge Graph and abstracts the two-ship encounter situation into a kind of triad consisting of a head entity, a relation, and a tail entity. The entity attributes contain information about the target ship or the interfering ship’s own attributes and motion state, and the relationship attributes contain information about the type of encounter situation formed between two entities, the relative position and relative motion relationship between two entities (take the head entity as the reference), all of which are expressed using the frame representation, as shown in Figure 4, where LTP represents the local target point, Pos represents the position, and RS represents relative speed.

The cognition of the situation not only includes its expression but also includes its prediction. Specific research [37] has been conducted on this segment of the content. Limited by space, only the methods adopted in the research are briefly introduced here. The decision process of the target ship under a multi-ship encounter situation is abstracted into the dynamic game process of bounded rationality of multiple ships, and then converted into the game process between the target ship and the situation for solving, and the solution satisfying all game participants is obtained, i.e., the situation that the target ship will face next. Since ships in open water generally give priority to the strategy of only changing course [38], in this paper, the strategy of course adjustment is mainly considered, which is more in line with the requirements of COLREGS on collision avoidance of ships in open waters and the ordinary practice of seamen. By predicting the situation of the target ship, the set of the most suitable course values can be obtained, which can be used as a reference for collision-avoidance strategy.

2.2.2. Collision Risk Recognition

After ensuring a comprehensive and accurate cognition of multi-ship encounter situations, the next crucial step is to evaluate the necessity of collision-avoidance decisions. It is generally believed that only when the target ship has a certain collision risk will the specific collision-avoidance strategy be formulated and the collision-avoidance action be taken. In this paper, it is argued that two kinds of conditions should be involved in this collision risk. One is direct collision risk (DCR), which arises directly from an encounter situation between the target ship and interfering ships. The other is potential collision risk (PCR), which contains PCRIS and PCRTS. PCRIS means potential collision risk resulting from interfering ships’ avoidance actions, while PCRTS means potential collision risk resulting from target ship’s avoidance actions.

Collision risk, the magnitude of which is evaluated with $u_T=u_{dT}\oplus u_{tT}$ [39]. The value can represent the comprehensive evaluation of the collision risk degree of two ships from the perspective of space and time. For the DCR, when the collision risk between the target ship and an interfering ship is equal to 1, it is considered that there is a large DCR. Collision-avoidance actions should be taken against the interfering ship, which should be marked as a dangerous interfering ship. As for the remaining interfering ships that are not marked as dangerous (recorded as ordinary interfering ships), potential collision risk PCRIS and PCRTS will be judged. For the determination of PCRIS, first, the action strategy is determined according to whether there is a large collision risk between an ordinary interfering ship and other ships in its interest perception area to determine whether the ordinary ship needs to take collision-avoidance actions. Then, for ordinary interfering ships that need to take collision-avoidance actions, the action strategy is determined according to the situation of all dangerous interfering ships in its interest perception area (the formulation method of collision-avoidance strategy will be presented in detail in Section 2.2.5), which is taken as the prediction of the interfering ship’s actions. Finally, according to the action-predicted results of the ordinary interfering ship and the collision risk between the target ship and the interfering ship’s predicted results, it will be determined whether the influence of the interfering ship should be taken into account when formulating the collision-avoidance strategy of the target ship. If the collision risk is equal to 1, it is considered that there is a large PCRIS. It is necessary to focus on the impact of the interfering ship’s possible collision-avoidance actions on the strategy formulation of the target ship, and it is labeled as a sub-dangerous interfering ship. For the other ordinary interfering ships, the action prediction results are speed and course preservation. For the determination of PCRTS, the need to adjust the established avoidance strategy of the target ship is determined based on the collision risk condition between the target ship and the ordinary interfering ships under the avoidance strategies initially developed by the target ship based on DCR and PCRIS. If the collision risk is equal to 1, it is considered that there is a large PCRTS, and the target ship’s strategy needs to be adjusted to reduce the collision risk.

Therefore, the recognition results of collision risk will determine whether the target ship needs to adopt collision-avoidance maneuvering and the interfering ships’ conditions that need to be mainly considered in the process of formulating collision-avoidance strategies. The specific conditions are shown in Equations (1)~(4):

(1) If,

$$\exists {IS}_i, DCR\left(TS,{IS}_i\right)=1$$

(1)

then $AR\left({IS}_i\right)$, and ${IS}_i$ will be marked as a dangerous interfering ship;

(2) If,

$$\exists {IS}_j,PCRIS\left({IS}_j\right)=1$$

(2)

then $TR\left(I{S}_j\right)$, and ${IS}_j$ will be marked as a sub-dangerous interfering ship;

(3) If,

$$\forall {IS}_i, DCR\left(TS,{IS}_i\right)<1$$

(3)

then $NAR\left(TS\right)$;

(4) If,

$$\left\{\begin{array}{c}\exists {IS}_i,AR\left(I{S}_i\right)\\ \exists {IS}_k,PCRTS\left({IS}_k\right)=1\end{array}\right.$$

(4)

then, in the formulating process of the collision-avoidance strategy of the target ship aiming at the interfering ship ${IS}_i$, the influence of the interfering ship ${IS}_k$ should also be considered at the same time until the conditions listed in Equation (4) are not met. If the conditions are always true, the first possible risk will be preferentially considered for strategy making, which will then be taken as the final strategy.

In the above, $TS$ represents the target ship, ${IS}_i$ and ${IS}_j$ represent the i-$th$ and j-$th$ interfering ships ($i=\mathrm{1,2},\dots ,n$; $j=\mathrm{1,2},\dots ,n$), respectively, ${IS}_k$ represents the k-$th$ ordinary interfering ship ($k=\mathrm{1,2},\dots ,n$), $DCR\left(TS,{IS}_i\right)$ is the DCR between the target ship and the i-$th$ interfering ship, $PCRIS\left({IS}_i\right)$ is the PCR due to the possible avoidance action of the i-$th$ interfering ship, $PCRTS\left({IS}_k\right)$ is the collision risk between the target ship and the k-$th$ ordinary interfering ship due to the possible avoidance action of the target ship, $AR\left(I{S}_i\right)$ means it is needed to take avoidance or straight sailing action against the i-$th$ interfering ship, and $TR\left(I{S}_j\right)$ means it is needed to focus on the influence of the j-$th$ interfering ship, and $NAR\left(TS\right)$ means the target ship does not need to take targeted avoidance or straight sailing action.

In conclusion, through the recognition of collision risk, the target ship determines the collision-avoidance strategy interval aiming at dangerous interfering ships and adjusts the strategy interval aiming at sub-dangerous interfering ships and ordinary interfering ships, respectively, until no new collision risk is caused or a lower collision risk is reached.

2.2.3. Quantitative Analysis of COLREGS and Construction of Collision-Avoidance Rule Base

For the quantitative analysis of COLREGS, the basic principle is that for the relatively clear quantitative regulations or requirements in COLREGS, the rules are extracted directly by the generative representation method. For some qualitative requirements in COLREGS and the expression of good seamanship, as well as the generative representation method, research results in this field and the ordinary practice of seamen are fully integrated to realize the rule-based analysis for the ambiguous semantic expression of collision avoidance.

To quantify COLREGS, the first step is to quantify the encounter situation of two ships. According to the division of the encounter situation of the two ships in Section 2.2.1 and referring to existing research methods [40], the two-ship encounter situation is quantitatively expressed, as shown in

Table 1. Quantitative expression of two-ship encounter situation.

Encounter Situation	Distance and Collision Risk	Relative Bearing	Situation Details	$\mathit{I}\mathit{S}\mathit{S}\mathit{R}\mathit{C}\mathit{o}\mathit{d}\mathit{e}$	$\mathit{T}\mathit{S}\mathit{S}\mathit{R}\mathit{C}\mathit{o}\mathit{d}\mathit{e}$	Action Direction
Overtaking	$\left\{\begin{array}{c}DIS\le 3n mile\\ u_T=1\end{array}\right.$	$\left\{\begin{array}{c}{\theta }_I\in [112.5°,180°)\\ {\theta }_T\in ({\theta }_I+180°,360°)\end{array}\right.$	$IS$ overtakes $TS$ on the starboard side	$E_{4f}$	$E_{7v}$, $E_{1f}$,	front
		$\left\{\begin{array}{c}{\theta }_I\in [180°,210°)\\ {\theta }_T\in (0°,{\theta }_I-180°)\end{array}\right.$	$IS$ overtakes $TS$ on the port side	$E_{4b}$	$E_{1b}$, $E_{2v}$	front
		$\left\{\begin{array}{c}{\theta }_I\in [210°,247.5°)\\ {\theta }_T\in (0°,{\theta }_I-180°)\end{array}\right.$	$IS$ overtakes $TS$ on the port side	$E_5$	$E_{1b}$, $E_{2v}$	front
		$\left\{\begin{array}{c}{\theta }_T\in [210°,247.5°)\\ {\theta }_I\in (0°,{\theta }_T-180°)\end{array}\right.$	$TS$ overtakes $IS$ on the port side	$E_8$($E_{1b}$, $E_{2v}$)	$E_5$	starboard
		$\left\{\begin{array}{c}{\theta }_T\in [180°,210°)\\ {\theta }_I\in (0°,{\theta }_T-180°)\end{array}\right.$	$TS$ overtakes $IS$ on the port side	$E_8$($E_{1b}$, $E_{2v}$)	$E_{4b}$	port
		$\left\{\begin{array}{c}{\theta }_T\in [112.5°,180°)\\ {\theta }_I\in ({\theta }_T+180°,360°)\end{array}\right.$	$TS$ overtakes $IS$ on the starboard side	$E_9$($E_{7v}$, $E_{1f}$)	$E_{4f}$	port
Head-on	$\left\{\begin{array}{c}DIS\le 6n mile\\ u_T=1\end{array}\right.$	${\theta }_I,{\theta }_T\in \left[0°,6°\right]\mathrm{U}[354°,360°)$	Head-on	$E_1$	$E_1$	starboard
Crossing	$\left\{\begin{array}{c}DIS\le 6n mile\\ u_T=1\end{array}\right.$	$\left\{\begin{array}{c}{\theta }_I\in (6°,67.5°)\\ {\theta }_T\in (247.5°,360°)\end{array}\right.$	Small Angle crossing on the starboard side	$E_2$	$E_6$, $E_7$, $E_{1f}$	starboard
		$\left\{\begin{array}{c}\begin{array}{c}{\theta }_I\in \left[67.5°,112.5°\right)\\ {\theta }_T\in \left({\theta }_I+180°,360°\right)\end{array}\\ V_I/V_T\le 0.95\end{array}\right.$	Large Angle crossing on the starboard side	$E_3$	$E_{6v}$, $E_7$, $E_{1f}$	port
		$\left\{\begin{array}{c}\begin{array}{c}{\theta }_I\in \left[67.5°,112.5°\right)\\ {\theta }_T\in \left({\theta }_I+180°,360°\right)\end{array}\\ V_I/V_T>0.95\end{array}\right.$	Large Angle crossing on the starboard side	$E_3$	$E_{6v}$, $E_7$, $E_{1f}$	starboard
		$\left\{\begin{array}{c}{\theta }_I\in [247.5°,292.5°)\\ {\theta }_T\in (0°,{\theta }_I-180°)\end{array}\right.$	Large Angle crossing on the port side	$E_6$	$E_{1b}$, $E_2$, $E_{3v}$	front
		$\left\{\begin{array}{c}{\theta }_I\in [292.5°,354°)\\ {\theta }_T\in [0°,112.5°)\end{array}\right.$	Small Angle crossing on the port side	$E_7$	$E_{1b}$, $E_2$, $E_3$	front

.

In the table: $TS$ represents the target ship, $IS$ represents the interfering ship, $ISSRCode$ represents the target ship sub-region code to which the interfering ship belongs, $TSSRCode$ represents the interfering ship sub-region code to which the target ship belongs, ${\theta }_I$ is the bearing of the interfering ship relative to the target ship, ${\theta }_T$ is the bearing of the target ship relative to the interfering ship, $DIS$ is the distance between the target ship and the interfering ship, $u_T$ is the collision risk, $E_{if}$ is the front fine molecule region of $E_i$ along the clockwise direction, $E_{ib}$ is the rear fine molecule region of $E_i$ along the clockwise direction ($E_1$ and $E_4$ subregions are divided into front and rear fine molecule regions with $0°$ and $180°$ as the dividing line, respectively), $E_{iv}$ indicates that the boundary on one side of $Ei$ sub-region is taken to be dynamically adjusted according to the relative azimuth, “action direction” refers to the action direction of the target ship, $V_I$ represents the speed of the interfering ship, and $V_T$ represents the speed of the target ship.

The collision-avoidance rule base is constructed according to relevant expressions of avoidance actions under basic encounter situations in COLREGS and the ordinary practices of seamen. The format of each generative representation is shown in Figure 5. To facilitate the construction of generative representation, according to the regulations of the two-ship encounter situation in COLREGS, the ship that needs to take avoidance measures is called a “give-way ship” in this paper. For example, when two ships are in a head-on situation, each of them is a “give-way ship”.

2.2.4. Collision-Avoidance Strategy Set Construction

In COLREGS, it is required that any change in course and (or) speed to avoid collision should be large enough to be easily detected by other ships’ vision or radar, avoiding a series of small changes. Therefore, to make the ship’s actions more easily recognized by other ships, the minimum steering amplitude is set at $20°$ in this paper. The generating process of the target ship’s course adjustment strategy set is as follows:

Starboard steering strategy: For the incoming ship on the starboard side, if the target ship is a give-way ship, the minimum steering amplitude is increased based on the relative bearing ${\theta }_I$ of the incoming ship as the minimum value of the target ship’s steering amplitude interval and the target ship’s steering amplitude interval ${[\theta }_I+20°,180°$] is obtained. For the incoming ship on the port side, the target ship alters course to starboard with the interval of $[20°,180°$]. For the target ship overtaking the interfering ship on the port side, the target ship is the give-way ship. If the Distance to the Closest Point of Approach $DCPA>0$, the target ship alters course to starboard to pass the stern for collision avoidance, increase the minimum steering amplitude as the minimum value of the target ship’s steering amplitude interval based on the relative orientation ${\theta }_I$ of the interfering ship and obtain the target ship’s steering amplitude interval ${[\theta }_I+20°,180°$]. For the target ship on the starboard side to overtake the interfering ship, the target ship is the give-way ship. The avoidance strategy conflict or under the urgent situation, if $DCPA>0$, the target ship alters course to starboard to avoid a collision, increase the minimum steering amplitude as the minimum value of steering amplitude interval based on the heading difference $\delta \theta$ with the interfering ship, and obtain the target ship’s steering amplitude interval $[\delta \theta +20°,180°$].

Port steering strategy: As stipulated in COLREGS, under the crossing encounter situation, it is not recommended to take a port turn to the incoming ship on the port side, and under the head-on encounter situation, the target ship should alter course to starboard. Therefore, the main consideration is the target ship overtaking the interfering ship. For the target ship overtaking the interfering ship on the port side, the target ship is the give-way ship. If $DCPA\le 0$, it indicates that the target ship will pass the bow of the interfering ship. If collision risk exists, the target ship will alter course to port to avoid collision, and the minimum steering amplitude will be added based on the course difference $\delta \theta$ between the target ship and the interfering ship as the minimum steering amplitude interval to obtain the steering amplitude interval of the target ship $[\delta \theta +20°,180°$]. For the target ship overtaking the interfering ship on the starboard side, the target ship is the give-way ship. When the urgent situation is not formed, the target ship alters course to port to pass the stern and gives way. Based on the relative bearing ${\theta }_I$ of the interfering ship, the minimum steering amplitude is added as the minimum value of the steering amplitude interval of the target ship, and the steering amplitude range ${[\theta }_I+20°,180°$] of the target ship is obtained. For the target ship overtaking the interfering ship on the starboard side, in the case of avoidance strategies conflict or under urgent situation, if $DCPA\le 0$, the target ship alters course to port to pass the stern and gives way. Based on the relative bearing ${\theta }_I$ of the interfering ship, increase the minimum steering amplitude as the minimum value of the steering amplitude interval of the target ship, and obtain the steering amplitude interval ${[\theta }_I+20°,180°$].

Straight sailing strategy: For the starboard incoming ship, if the target ship is a straight sailing ship, it indicates that the target ship is being overtaken. In the case of avoidance strategies in conflict or under urgent situations, the target ship can adopt the strategy of altering course to port or starboard, and the steering range is $[0°,112.5°$]. For the port incoming ship, if the target ship is a straight sailing ship, in the case of avoidance strategies conflict or under urgent situation, the target ship can adopt the strategy of altering course to starboard, and the steering range is $[20°,112.5°$].

Meanwhile, considering that the steering amplitude is usually given some special integers, the preferred value set in this paper is {20°, 25°, 30° $\dots$ 170°, 175°, 180°}.

2.2.5. Sequential Collision-Avoidance Strategy Generation

In a multi-ship encounter scenario, the general idea of generating the collision-avoidance strategy for an ordinary interfering ship (i.e., predicting the action of the ordinary interfering ship) is as follows: From the perspective of the ordinary interfering ship, all dangerous interfering ships in its interest perception area are obtained. If there is no dangerous interfering ship, it is assumed that the ship will maintain speed and course. If there is one dangerous interfering ship, the most likely collision-avoidance action that should be taken against the dangerous interfering ship will be taken as the prediction of this ordinary interfering ship’s action. If there are two or more dangerous interfering ships, the final strategy is determined according to the overlapping result of collision-avoidance strategy intervals aiming at different dangerous interfering ships, which will be taken as the result of action prediction of this ordinary interfering ship. Specifically, if there is a completely overlapping strategy interval (overlapped part of collision-avoidance strategy interval for all dangerous interfering ships), the most likely value within the interval (the minimum value of steering amplitude within the strategy interval) will be selected as the prediction result. Otherwise, the priority is determined according to the TCPA when the target ship and the interfering ship reach the closest distance, i.e., the smaller the TCPA, the more priority given to the corresponding strategy interval until there is no completely overlapping strategy interval. Select the most possible value within the completely overlapping interval as the prediction result.

In a multi-ship encounter situation, the general idea of collision-avoidance strategy generation for the target ship is as follows: First, for each dangerous interfering ship, the collision-avoidance action plan of the target ship is determined as a straight sailing, port steering, or starboard steering according to the collision-avoidance rule base, and then the collision-avoidance strategy interval of the target ship aiming at different dangerous interfering ships is determined. The intersection of the above strategy intervals is used as the final collision-avoidance strategy interval aiming at dangerous interfering ships. Then, the target ship’s collision-avoidance strategy interval is adjusted according to the prediction result of the action of the sub-dangerous interfering ship. In other words, the complete overlapping interval of the collision-avoidance strategy intervals of the target ship aiming at different sub-dangerous interfering ships are obtained and then intersect with the interval of a collision-avoidance strategy aiming at dangerous interfering ships. Finally, the target ship’s steering amplitude is determined according to the collision risk between the target ship and the ordinary interfering ship under the strategy corresponding to the interval value. The logic flow of the target ship’s collision-avoidance strategy generation is shown in Figure 6.

To simplify the analysis process, in this paper, it is assumed that the ship keeps full speed, the steering trajectory is circular, and the longitudinal distance when it turns 90° in the course of full rudder rotation is multiplied by a certain relaxation coefficient as the ship’s steering radius, as shown in Equation (5):

$$R_T=D_V\ast C_X$$

(5)

where $R_T$ represents the ship’s steering radius (unit: $\mathrm{m}$), and $D_V$ represents the longitudinal distance (unit: $\mathrm{m}$) when the ship’s course turns 90°. According to IMO Resolution A.749(18) and sea trial experience, $D_V$ in this paper is 2.5 times the ship length and $C_X$ is the relaxation coefficient, valued at 1.2 in this paper.

The schematic diagram of the ship steering trajectory planning method is shown in Figure 7, where $S(a,b)$ represents the current position of the ship; $E(c,d)$ represents the endpoint of the planned avoidance steering trajectory; $V$ represents the current speed of the ship (unit: $\mathrm{k}\mathrm{n}$); $V\mathrm{’}$ represents the speed at the endpoint of the planned steering trajectory (unit: $\mathrm{k}\mathrm{n}$); $\alpha$ represents the current course angle of the ship (unit: $°$); $\theta$ represents the angle of the ship avoidance steering amplitude (unit: $°$); $R_T$ represents the ship steering radius (unit: $\mathrm{m}$); $o\mathrm{’}$ represents the center of the circle of avoiding steering trajectory.

According to the ship’s steering amplitude and speed, the total sailing time on the steering trajectory of this section can be calculated, and the formula is shown in Equation (6), where $T_{turningCA}$ represents the total sailing time of the steering avoidance trajectory segment (unit: $\mathrm{s}$); $\left|V\right|$ represents ship speed. Other letters have the same meanings as in Figure 7.

$$T_{turningCA}=\frac{2\ast \pi \ast R_T\ast \theta }{360\ast \left|V\right|\ast 0.514}$$

(6)

Based on the total duration of steering trajectory navigation and the simulation decision period, the number of decisions experienced during the steering navigation can be obtained, and each steering magnitude is determined and used in simulation calculation.

2.2.6. Avoidance Process Monitoring and Strategy Correction

If a give-way ship reaches the endpoint of the planned steering trajectory and the stand-on ship has not yet moved abaft the give-way ship’s beam, the give-way ship, on the premise that there is no new collision danger, shall continue to give way following its current course until the stand-on ship has moved abaft the give-way ship’s beam and the distance between the two ships is greater than safe distance. If there is a new collision risk, the original collision-avoidance strategy is modified to avoid the new dangerous interfering ship. The monitoring and strategy correction process of avoidance is shown in Figure 8.

2.2.7. Judgment of the End Condition of Collision Avoidance and the Ship’s Resumption

Although in the collision-avoidance strategy formulation process, the influence of the dangerous, sub-dangerous, and ordinary interfering ship on the navigation of the target ship are all considered at the same time, the initial motive of the avoidance action is still to avoid direct collision risk with the dangerous interfering ship. Therefore, the main basis for judging the end conditions of avoidance in this paper adopts the relative position relationship between the target ship and the key dangerous interfering ship. The key dangerous interfering ship is the dangerous interfering ship, which has the greatest collision risk with the target ship, and the TCPA is as small as possible. For the judgment of whether the avoidance action of the target ship is finished in the head-on and crossing encounter situation, the main basis is whether the conflict encountered interfering ship has been located abaft the target ship’s beam and whether the distance between the two ships has been greater than safe distance. For the judgment of whether the avoidance action of the overtaking ship is finished under the overtaking situation, the main basis is whether the overtaken ship has been located abaft the overtaking ship’s beam and whether the distance between the two ships has been greater than the safe distance. Meanwhile, if the distance between the target ship and the ship being given way is increasing continuously and has been greater than 2 times the safe distance, it is also considered that the avoidance action is over. The logical process of judging the end condition of the collision avoidance process under the above three encounter situations is the same, as shown in Figure 9.

Once the steering avoidance process is complete with no new collision risk, the resumption condition is assessed. In other words, based on the resumption steering trajectory planning method, if the collision risk between the target ship and any interfering ship is 1 at the end of steering, it indicates that the resumption condition is currently unavailable, and the ship is prohibited from resuming sailing. If the resumption condition is met, the target ship’s resumption course is determined based on its local trajectory endpoint. If not, the ship will continue in its straight sailing state until the resumption condition is met. The logical flow of the give-way ship’s resumption sailing process is shown in Figure 10.

The steering radius used during the resumption trajectory planning process is identical to that used in the collision-avoidance trajectory planning process. Figure 11 shows the schematic diagram of the give-way ship’s resumption trajectory planning method, where $S$ represents the ship’s current position; $L$ represents the position of the ship’s local target point; $M$ refers to the center of the steering trajectory; $E$ represents the tangent point of the arc derived from the local target point, ensuring that the ship’s speed direction at the end of the steering trajectory is from point E to point L.

According to the geometric relationship, the total time that the ship sails on this section of the resumption steering trajectory can be calculated, and the formula is shown as Equation (7), where $T_{turningRS}$ represents the total duration of sailing on the resumption steering trajectory section (unit: $\mathrm{s}$); $\theta \mathrm{’}$ represents the resumption steering amplitude angle. The meanings of the rest of the letters are the same as that in Equation (6).

$$T_{turningRS}=\frac{2\ast \pi \ast R_T\ast \theta \prime }{360\ast \left|V\right|\ast 0.514}$$

(7)

where $\theta \prime$ is calculated according to the steering direction. If it is a “port steering”, the formula is shown as Equation (8), where $cogV$ represents the ship’s current course, which can be read directly from the ship entity data; $cogV\prime$ represents the ship’s course at the end of the resumption steering trajectory, which can be calculated by the $ML$ vector direction and angle $\gamma$. The coordinates of point $M$ are calculated according to the coordinates of point $S$, steering direction, and steering radius $RT$.

$${\theta }^{\prime }=\left\{\begin{array}{c}cogV+360-cog{V}^{\prime }, if cog{V}^{\prime }>cogV\\ cogV-cog{V}^{\prime },if cogV\prime \le cogV\end{array}\right.$$

(8)

If it is “starboard steering”, the calculation formula is shown as Equation (9).

$${\theta }^{\prime }=\left\{\begin{array}{c}cogV\prime +360-cogV, if cog{V}^{\prime }<cogV\\ cogV\prime -cogV,if cogV\prime \ge cogV\end{array}\right.$$

(9)

2.3. Validation of the Decision-Making Chain

To verify the effectiveness of the human-like thinking sequential decision-making chain proposed in this paper, different navigational strategies are assigned to the target ship and the interfering ship, respectively. Subsequently, the navigational states of both ships are compared and analyzed based on different strategy selections. In view of the dangers and high costs of multi-ship encounter experiments with real ships, the proposed approach is temporarily validated through simulation experiments.

2.3.1. Experimental Ships and Parameters Setting

Based on the two-ship encounter situation partitioning method adopted in this paper, an interfering ship is randomly generated within 12$n miles$ around the target ship in subregions $E_1,E_2,\dots ,E_7$, and their radial extension regions. The key parameters of the target ship and interfering ships are shown in

Table 2. Parameters setting of the target ship and interfering ships.

Ship Category	Parameter Name	Value Set
target ship	length ($\mathrm{m}$)	165
	width ($\mathrm{m}$)	24
	speed ($\mathrm{k}\mathrm{n}$)	10
interfering ship	length ($\mathrm{m}$)	150
	width ($\mathrm{m}$)	22
	speed ($\mathrm{k}\mathrm{n}$)	10
	amount	7
	parameter tolerance ($\%$)	50

. To facilitate the presentation of results, a 1-h experiment duration was chosen. Each ship’s local target point is determined by its initial course and speed, and its coordinate is calculated after 2 h from its starting position, which remains unchanged throughout the whole simulation process.

The parameter tolerance in the table is defined for the relevant parameters of interfering ships, allowing for random fluctuations within a range of 50% in their length, width, and speed from the set values. This allows for the simulation of diverse ship sizes and speeds in the scenario, capturing the inherent randomness of real-world situations.

2.3.2. Experiment Strategy Setting

To fully take into account the interfering ship’s compliance with the rules, deviation from the rules, and action uncertainty in the actual sailing scenarios and to more intuitively present the implementation effect of the collision-avoidance strategy, four kinds of collision-avoidance strategies are adopted in the experiment, which are: straight sailing strategy, COLREGS-only considered strategy, human-like thinking strategy (proposed in this study), and random strategy.

The straight sailing strategy involves maintaining a constant course and speed.

The COLREGS-only considered strategy focuses on avoiding the riskiest interfering ship based on the COLREGS, selecting the ship with the highest collision risk. However, when multiple dangerous interfering ships exist, the one with the minimum TCPA value will be chosen.

The human-like thinking strategy proposed in this paper, on the premise of giving full consideration to COLREGS, the dangerous interfering ships, sub-dangerous interfering ships, and ordinary interfering ships are all considered at the same time.

The random strategy means that ships randomly select one of the above three strategies at the initial moment and subsequently adhere to their selected strategy throughout the experiment.

The target ship is set to adopt the COLREGS-only considered strategy and the human-like thinking strategy, respectively, and the interfering ship selects the above four strategies successively, thus obtaining eight strategy combination modes and numbering them successively. To ensure the objective presentation of the comparative effectiveness between the COLREGS-only considered strategy and the human-like thinking strategy, the consideration of COLREGS in the two strategies is the same, including the judgment of the encounter situation, the formulation of the avoidance strategy interval of the two ships and so on.

Table 3. Navigation strategy setting of target ship and interfering ships.

Target Ship’s Strategy	Interfering Ships’ Strategy	Strategy Combination Number
$COLREGSOnly$	$DirectRoute$	STC1
	$COLREGSOnly$	STC2
	$Humanoid$	STC3
	$Random$	STC4
$Humanoid$	$DirectRoute$	STC5
	$COLREGSOnly$	STC6
	$Humanoid$	STC7
	$Random$	STC8

provides the specifics of the experimental strategy setup, where $DirectRoute$ represents straight sailing strategy; $COLREGSOnly$ denotes the COLREGS-only considered strategy. $Humanoid$ signifies the strategy based on the proposed sequential decision chain construction method for human-like thinking. $Random$ indicates that the above three strategies are randomly selected.

2.3.3. Experiment Data Processing

To carry out the simulation experiment smoothly, a special simulation experiment system is developed using C# language in the Visual Studio 2017 environment. In the simulation system, the head entity, relation entity, and tail entity are all stored in the form of a structure. Real-time position data of the ship is calculated according to the uniform linear motion based on the current speed and course of each ship in each simulation cycle, and the calculation results are stored in each ship entity. During the whole experiment, the structural data of the target ship and interfering ships were recorded periodically. Special relevant data-extraction programs are written to extract the data required for the analysis of the experimental results from the corresponding structural data in batches. This mainly includes the time series of coordinate values for all ships ($CVTMSFAS$); time series of the real-time distance percentage between the target ship and its local target point to the initial distance ($DPTMSFTS$); time series of the minimum distance between target ship and interfering ship ($DSMinTMSTTI$); time series of minimum distances between all ships ($DSMinTMSFAS$); time percentage of collision risk value 1 for each ship ($CR1TMPAS$); average value of time percentage of collision risk value 1 for each ship under the same strategy combination ($CR1TMPASAV$); and time series of distance between target ship and each interfering ship ($DSTMSTTI$).

$CVTMSFAS$ can be extracted directly from ship entity parameters, i.e., X, Y.

$DPTMSFTS$ calculated based on ship entity parameters. The calculation method is shown in Equation (10).

$$P_{dttp}=\frac{Dis(PosReal,PosLocalTP)}{Dis(PosStart,PosLocalTP)}\ast 100\%$$

(10)

where $P_{dttp}$ denotes $DPTMSFTS$; $Dis(Pos1,Pos2)$ represents the distance between two points; $PosReal$ represents the current coordinate value; $PosLocalTP$ represents the coordinate value of ship’s local target point; $PosStart$ represents the starting point’s coordinate value adopted in calculating the local target point’s coordinates.

$DSMinTMSTTI$ is obtained directly by comparing experimental data.

$DSMinTMSFAS$ is obtained by comparing, in turn, the distance between any two ships at different times.

$CR1TMPAS$ is obtained by counting the number of collision risks of 1 for each ship in the whole simulation period and then calculating its ratio to the total decision times.

$CR1TMPASAV$ is obtained by calculating the mean value of $CR1TMPAS$ of all ships under the same strategy combination.

$DSTMSTTI$ is obtained directly by distance calculation.

3. Results

Taking the strategy combination STC2 and STC6 as an example, the relative positions and attitudes of each ship in the encounter scenario at the simulation moment $t=0 \mathrm{s}$, $1200 \mathrm{s}$, $2400 \mathrm{s}$, and $3600 \mathrm{s}$ are as shown in Figure 12 and Figure 13, respectively. To enhance the visualization of results, the ship display size is amplified to 15 times the actual size. The white triangle with an arrow represents the target ship, and the yellow triangle with an arrow represents the interfering ship. Three circles are drawn around the target ship. The innermost red circle is a 3$n miles$ distance circle, the middle yellow circle is a 6$n miles$ distance circle, and the outermost yellow-green circle is a 12$n miles$ distance circle.

The above experiment is labeled as Exp0010. To further verify the reliability of the method, 39 more replicate experiments were conducted. The experimental strategy set utilized in Section 2.3.2 was used, while interfering ships were randomly regenerated before each round of experiments, following the procedure detailed in Section 2.3.1. Taking the first 8 experiments as an example, the relative positions and attitude relationships of the ships at the initial moments are shown in Figure 14. The ship drawing size was magnified 20 times to facilitate observation.

3.1. Results of a Single-Round Experiment

Taking experiment Exp0010 as an example, time series curves of all ships’ coordinates were obtained under different strategy combinations. Figure 15 shows the $CVTMSFAS$ curve in the case of strategy combinations STC1–STC4, and Figure 16 shows that of STC5–STC8. In each figure, the coordinate values of the X-axis and Y-axis represent the X-coordinate and Y-coordinate of the ship position, respectively, and the Z-axis represents the simulation time. These two figures aim to present a complete set of simulation experiment processes, both in terms of time and space, in the simplest way possible.

$DPTMSFTS$ curve under different strategy combinations is shown in Figure 17, in which the X-axis is the simulation time, and the Y-axis presents the $DPTMSFTS$ value.

$DSMinTMSTTI$ curve under different strategy combinations is shown in Figure 18, in which the coordinate value of the Y-axis means the minimum distance between the target ship and all interfering ships.

$DSMinTMSFAS$ curve is shown in Figure 19, in which the Y-axis coordinate value means the minimum distance value between all ships.

$CR1TMPAS$ conditions are shown in Figure 20. The Y-axis coordinate means $CR1TMPAS$ value and the X-axis coordinate value represents the strategy combination code. For example, the coordinate value 1 represents the strategy combination STC1.

Figure 21 shows the $DSTMSTTI$ curve under strategy combinations STC1–STC4, and Figure 22 shows that of STC5–STC8. The Y-axis coordinate value means the distance between the target ship and the interfering ship.

3.2. Repeated Experimental Results

Values of $DSMinTMSTTI$, $DSMinTMSFAS$, and $CR1TMPASAV$ in 40 experiments were statistically analyzed, as shown in Figure 23, Figure 24 and Figure 25, respectively. In each figure, the abscissa is the experimental code, i.e., 1 represents Exp0010, 2 represents Exp0020, etc. The meanings of curves in these figures are explained by taking Figure 23 as an example. The curve corresponding to STC1 presents the statistical result of the $DSMinTMSTTI$ value in the whole experiment under strategy combination STC1 in 40 experiments.

4. Discussion

4.1. Experimental Results Analysis

Figure 12, Figure 13 and Figure 14 show that the target ship and interfering ships, at the beginning of each experiment, were either in or likely to form a multi-ship encounter scenario in the next period, therefore satisfying the scenario design requirements.

4.1.1. Result Analysis of a Single-Round Experiment

Comparing the target ships’ navigation space–time trajectory in Figure 15 and Figure 16, it is clear that the human-like strategy proposed in this paper results in significant alterations to the trajectory, involving multiple course adjustments, in contrast to $COLREGSOnly$ strategy.

From the aspect of ship navigation efficiency, by comparing the $DPTMSFTS$ curves corresponding to STC1 and STC5, it can be seen in Figure 17 that compared with $COLREGSOnly$ strategy, the $Humanoid$ strategy proposed will slightly reduce navigation efficiency. The same conclusion can be drawn by comparing the corresponding curves of STC2 and STC6, as well as that of ST4 and ST8. This phenomenon is also easily understood: the ship’s steering avoidance action will inevitably lead to deviation from the original course, increase in travel, and eventually lead to the reduction of navigation efficiency. By comparing the corresponding curves of ST3 and ST7, it can be found that if all interfering ships adopt the $Humanoid$ strategy, the target ship’s sailing efficiency will be close to that of the $COLREGSOnly$ strategy when it also adopts the $Humanoid$ strategy.

From the analysis of ship navigation safety, it can be seen from Figure 18 that the target ship can keep a certain safety distance from the interfering ship to ensure navigation safety, whether it adopts the $COLREGSOnly$ or the $Humanoid$ strategy. Comparing the curves of STC1 with STC5, STC2 with STC6, ST3 with ST7, and ST4 with ST8, it can be seen that the minimum distance between the target ship and the interfering ship can be effectively improved in most cases by adopting the $Humanoid$ strategy, compared with the $COLREGSOnly$ strategy. Furthermore, a comparison of the corresponding curves of ST3 and ST7 with those of STC2 and STC6 shows that the minimum distance between the target ship and the interfering ship is significantly improved when all interfering ships adopt the $Humanoid$ strategy, indicating that the navigation environment of the target ship is significantly improved. It can be seen that the $Humanoid$ strategy proposed in this paper is more suitable for multi-ship encounter scenarios.

As can be seen from Figure 19, when all interfering ships adopt the $DirectRoute$ strategy, the minimum distance between ships is close to 0.5$n mile$, with high collision risk, which also indicates that the initial scene-setting of the experiment can meet the experimental requirements. It can be seen from the corresponding curves of STC2 and STC6 that when all ships or all interfering ships adopt the $COLREGSOnly$ strategy, the navigation risk situation is not significantly improved. However, it can be seen from the corresponding curves of STC3 and STC7 that when all ships or all interfering ships adopt the $Humanoid$ strategy, the minimum distance between all ships is significantly higher than that of other strategy combinations, which significantly reduces the collision risk.

In Figure 20, comparing the corresponding histograms of STC1 with STC5, STC2 with STC6, ST3 with ST7, and ST4 with ST8, respectively, it can be seen that when the target ship adopts the $Humanoid$ strategy, its $CR1TMPAS$ value is significantly lower than that of when it adopts the $COLREGSOnly$ strategy, indicating that the implementation of the $Humanoid$ strategy can quickly and effectively reduce the collision risk of the target ship. By comparing the corresponding histograms of ST3 and ST7 with that of other strategy combinations, it can be seen that when the $Humanoid$ strategy is applied to all ships or all interfering ships, the $CR1TMPAS$ value is generally lower than that under other strategy combinations. This indicates that the general implementation of the $Humanoid$ strategy can effectively improve the ship navigation environment conditions and reduce the collision risk, and also demonstrates the superiority of the $Humanoid$ strategy over the $COLREGSOnly$ strategy, particularly in multi-ship encounter scenarios.

By comparing Figure 21 and Figure 22, it can be seen that compared with the $COLREGSOnly$ strategy, the minimum distance between the target ship and the interfering ship is significantly increased under the $Humanoid$ strategy, which further ensures navigation safety. Moreover, by comparing the curve corresponding to STC3 and other strategy combinations in Figure 21 and the curve corresponding to STC7 and other strategy combinations in Figure 22, it can be seen that when all ships or all interfering ships adopt the $Humanoid$ strategy, the minimum distance between the target ship and interfering ship is improved. This further confirms that adopting the $Humanoid$ strategy can improve the navigation environment of the target ship.

4.1.2. Result Analysis of Repeated Experiments

In Figure 23, the corresponding curves of STC1 and STC5, STC2 and STC6, and ST4 and ST8 are, respectively, compared. It can be seen that compared with the $COLREGSOnly$ strategy, the minimum distance between the target ship and the interfering ship is significantly increased after adopting the $Humanoid$ strategy.

In Figure 24, the corresponding curves for STC1 and ST5 are basically at the bottom, and the minimum distance values between ships are small, reaching within 0.5$n mile$ in most cases, enough to indicate that there is a high collision risk between at least two ships in each experiment without avoidance measures taken by all the interfering ships. In some experiments, the minimum distance between ships is below $300 \mathrm{m}$, even close to $0$, indicating that there is at least a collision or a high collision risk between two ships in the scenario without avoidance measures. It also shows that the design of the initial scenarios can meet the experimental requirements. The curves corresponding to STC2 and STC6 show that the minimum distance between ships is significantly improved after all ships or interfering ships adopt the $COLREGSOnly$ strategy, and the curves corresponding to STC3 and STC7 show that the minimum distance between ships is significantly improved after all ships or interfering ships adopt the $Humanoid$ strategy, which, compared with the strategy combination STC2 and STC6, has a higher minimum distance value in most cases. This also indicates that the $Humanoid$ strategy seems more reliable.

In Figure 25, it can be seen from the corresponding curves of STC1 and ST5 that in the whole simulation process, when no avoidance measures are taken by interfering ships, the average time proportion of ship collision risk 1 fluctuates around 40%, which is significantly higher than that under other strategy combinations. By comparing the corresponding curves of STC2 and STC6 with those of STC3 and STC7, it can be observed that when all ships or all interfering ships adopt the $COLREGSOnly$ strategy, the sailing environment is improved, but the duration of collision risk is still significantly higher than that when all ships or all interfering ships adopt the $Humanoid$ strategy. This also indicates that compared with the $COLREGSOnly$ strategy, the $Humanoid$ strategy is more suitable for multi-ship encounter scenarios.

The random strategy set in this paper is to fully simulate the uncertainty of ship behavior in a real-world sailing environment. It can be seen from the experimental results in each figure (including the single-round and repeated experiments) that when the interfering ships all adopt the random strategy, the experimental data are basically between the results obtained by adopting the $COLREGSOnly$ and the $Humanoid$ strategies. This also suggests that the $Humanoid$ strategy can achieve stable and ideal effects when dealing with the uncertainty of actual scenarios.

In general, when all interfering ships choose the $DirectRoute$ strategy, the sailing efficiency is the highest, but safety cannot be guaranteed. To ensure navigation safety, efficiency must be sacrificed to some extent. In a multi-ship encounter scenario, the implementation of the $Humanoid$ strategy proposed can quickly and effectively reduce the collision risk, improve the navigation environment, and ensure safe navigation.

The main contributions of this paper are as follows: when evaluating the collision risk of the target ship, not only the interfering ship with direct collision risk but also the one with the potential collision risk is considered, which is analyzed through the prediction of the interfering ship’s action. Not only that, but we also take into account new collision risks that may result from the collision-avoidance strategy developed by the target ship based on the above risk factors. In this way, it can better present the assessment of the collision risk of the target ship from a global perspective, which is conducive to the improvement of decision-making reliability.

4.2. Research Limitations and Prospects

In the construction process of the sequential decision-making chain for an unmanned ship’s autonomous collision avoidance, not only the direct collision risk between the interfering ship and the target ship but also the possible collision-avoidance actions of the interfering ships that pose potential collision risks to the target ship and the new collision risks that may be caused by the possible actions of the target ship are considered, to ensure the safety of the collision-avoidance actions to the maximum extent.

As the study mainly focuses on open waters, course adjustment is mainly considered in collision-avoidance strategy making. Since there are so many factors affecting the ship’s actual trajectory, the steering trajectory is simplified to a circular arc to facilitate the study. As the ship’s dynamics are not fully considered, the same value is given to the ship heading and course during the simulation. However, a certain distinction is made in the algorithm, i.e., the calculation of the sub-region to which the interfering ship belongs during the encounter situation judgment is based on the reference of the target ship’s heading and the value of the target ship’s steering amplitude obtained under a strategy changes the original ship course value. In future work, ship dynamics will be fully considered to determine the precise adjustment strategy of speed and course, as well as the method of constructing an autonomous collision-avoidance human-like thinking process for unmanned ships adapted to restricted waters to meet the needs of unmanned ships for collision-avoidance decisions in different navigable waters.

Only collision avoidance between moving or stationary ships is considered. In future work, dynamic and static obstacles will be taken into account, or they will be equivalent to special moving or stationary ships, respectively, for research. In addition, the selection of many values is based on existing research results in the field or the ordinary practices of seamen, the accuracy and rationality of which still require further verification.

In practical sailing scenarios, since the relative bearing and other relational data of ships often have certain fluctuations, the method of encounter situation judgment based on the relative bearing relationship, distance, and collision risk of two ships in this paper still needs to be adjusted, to conform to an important principle of COLREGS, i.e., if there is doubt about a certain danger, it should be assumed existed, to ensure navigation safety to the maximum extent.

In addition, the results of existing research on situational prediction have not yet been integrated into this study, and their integration may lead to better results, which will be important research to be carried out in future research.

Although there are limitations, the sequential decision-making method proposed in this study is practical and easy to implement. The target ship’s attribute and motion status can be obtained from onboard equipment while interfering ships’ information can be periodically extracted through AIS. This method can be used to analyze and determine the navigation or collision-avoidance strategy that the target ship will adopt in response to a complex encounter situation. However, the navigation strategy provided in this study only represents a course adjustment strategy. To ensure navigation safety and avoid loss of interfering ships’ information, future research should focus on integrating information from cameras, LiDAR, and other sensing equipment.

5. Conclusions

To enhance the collision-avoidance decision-making capability of unmanned ships in multi-ship encounter scenarios at sea, a method for constructing an autonomous collision-avoidance sequential decision-making chain with human-like thinking is proposed in this article. The construction process mainly includes situation cognition, collision risk recognition, construction of collision-avoidance rule base and strategy set, generation of sequential collision-avoidance strategy with human-like thinking, collision-avoidance process monitoring and strategy correction, and judgment of sailing resumption conditions. Specific methods or flow charts are given, respectively. The encounter situation of two ships is abstracted into a triplet of head entity, relationship entity, and tail entity, which realizes the efficient access of ship entity and relationship data. A method is proposed to divide the collision risk of the target ship into direct collision risk and potential collision risk, considering which the global collision risk assessment of the multi-ship encounter scenario is realized. Simulation experimental results under multi-ship encounter scenarios indicate that the human-like thinking process constructed by the proposed method can assist in effective collision avoidance for dynamic and static ships, and the research results can provide interpretable references for navigation decisions of unmanned ships.

In view of the high risk and cost of real ship experiments in multi-ship encounter situations, such experiments have not yet been organized. When conditions are available, verification experiments using real ships will be conducted, in which the interference of wind, wave, current, tide, traffic separation scheme, and other external environmental factors on collision-avoidance actions will be taken into account to further ensure the reliability of the method and its applicability to actual sailing scenarios.