A Novel Decision Support Methodology for Autonomous Collision Avoidance Based on Deduction of Manoeuvring Process

Abstract

In the last few years, autonomous ships have attracted increasing attention in the maritime industry. Autonomous ships with an autonomous collision avoidance capability are the development trend for future ships. In this study, a ship manoeuvring process deduction-based dynamic adaptive autonomous collision avoidance decision support method for autonomous ships is presented. Firstly, the dynamic motion parameters of the own ship relative to the target ship are calculated by using the dynamic mathematical model. Then the fuzzy set theory is adopted to construct collision risk models, which combine the spatial collision risk index (SCRI) and time collision risk index (TCRI) in different encountered situations. After that, the ship movement model and fuzzy adaptive PID method are used to derive the ships’ manoeuvre motion process. On this basis, the feasible avoidance range and the optimal steering angle for ship collision avoidance are calculated by deducting the manoeuvring process and the modified velocity obstacle (VO) method. Moreover, to address the issue of resuming sailing after the ship collision avoidance is completed, the Line of Sight (LOS) guidance system is adopted to resume normal navigation for the own ship in this study. Finally, the dynamic adaptive autonomous collision avoidance model is developed by combining the ship movement model, the fuzzy adaptive PID control model, the modified VO method and the resume-sailing model. The results of the simulation show that the proposed methodology can effectively avoid collisions between the own ship and the moving TSs for situations involving two or multiple ships, and the own ship can resume its original route after collision avoidance is completed. Additionally, it is also proved that this method can be applied to complex situations with various encountered ships, and it exhibits excellent adaptability and effectiveness when encountering multiple objects and complex situations.

1. Introduction

1.1. Background

In recent years, autonomous ships have received a lot of attention and development in the maritime industry. The International Maritime Organization has been committed to the research on the relevant technologies and regulations of Maritime Autonomous Surface Ships (MASS) [1]. Improving the intelligence level of ships is crucial to the safety of ship navigation. Although some advanced technologies and methods have been developed and applied to ships, collision accidents still happen from time to time. Actually, a report published by the European Maritime Safety Agency (EMSA, 2020) showed that contact and collision incidents of ship accounted for 32% of all navigational casualties between 2014 and 2019 [2]. Ship collision accidents are a major threat to the safety of maritime navigation, and may cause serious casualties, economic losses and marine environmental pollution, etc. Therefore, to reduce the navigational risk and casualties caused by human factors, it is of great significance to develop a novel autonomous collision avoidance decision support methodology or system to help ships to make secure and expeditious decisions to avoid collisions.

Making a ship collision avoidance decision is a complex process, especially in the multi-object environment and restricted waters. At present, many technologies and algorithms have been developed for the autonomous collision avoidance problem of MASS, such as the Artificial Potential Field (APF) [3,4], Particle Swarm Optimization (PSO) [5], Rapidly exploring Random Tree (RRT) [6], velocity obstacle (VO) [7], genetic algorithm (GA) [8], Artificial Neural Network (ANN) [9], Deep Reinforcement Learning (DRL) [10], and so on. In the future, all kinds of vessels, including autonomous vessels and MASS, will be expected to follow the existing guidelines based on good seamanship and the International Regulations for Preventing Collisions at Sea (COLREGs). Considering that autonomous collision avoidance is a highly complex problem, our primary aim in this study is to design a ship manoeuvring process deduction-based dynamic adaptive autonomous collision avoidance decision support methodology for autonomous ships and MASS, which take into account the COLREGs and good seamanship mentioned above as well as ship manoeuvrability.

1.2. Related Studies

As a key technology to realize ship automation, intelligent collision avoidance technology has attracted more and more attention from researchers in recent years [11]. Diverse solutions can be found in the literature related to ship collision avoidance [12,13]. In general, these collision avoidance methods can be divided into path generation methods and intelligent optimization methods. The path generation algorithms mainly include the A* algorithm, the APF algorithm, the RRT algorithm and the VO algorithm. The A* algorithm is an intelligent search algorithm that mainly considers the start position and the destination, which has better performance and accuracy. The APF model has been extensively used in the field of the autonomous collision avoidance of ships [14]. Lv et al. [4] and Lazarowska et al. [15] proposed a method for safe vessel trajectory planning based on the APF model, respectively. At present, the RRT algorithm and its modified algorithm are widely adopted for ship optimal path planning [6]. Based on the problem of optimal path planning for ships in the perspective of real-time applications, Zaccone et al. [16] proposed an optimal path planning algorithm for autonomous ships based on modified RRT. Chiang et al. [17] proposed a COLREGs-compliant RRT-based motion planner for Autonomous Surface Vehicles’ navigation. This algorithm has a higher navigation success rate and COLREGs compliance compared to other methods. The VO algorithm is a classic collision avoidance algorithm in the field of mobile robots. At present, many scholars have applied it to the study of ship collision avoidance. Huang et al. [18] built a collision avoidance decision system based on a non-linear VO model. It can assist the marine navigator to make collision avoidance decisions. Chen et al. [19] presented an improved time discretized non-linear velocity obstacle algorithm to detect multi-ship encounter situations using historical automatic identification system (AIS) data.

In the last two decades, researchers have put forward many new intelligent optimization methods and achieved fine results. Ni et al. [8] generated a collision-free optimal path for autonomous ships based on multiple genetic algorithms. Xie et al. [20] presented a collision avoidance method based on an improved Q-learning beetle swarm antenna search algorithm and ANN for USV. An autonomous collision avoidance decision system based on the ANN and fuzzy logic methods was designed by Ahn et al. [21]. This system can calculate ship collision risk in real time. As an important learning method of machine learning, DRL has been widely used for intelligent autonomous systems due to its excellent adaptive and self-learning capabilities for complex systems. Based on the DRL model, Zhao et al. [22,23] established a novel collision avoidance decision system for autonomous ships. However, this system is only suitable for two-ship encounters, not for multi-ship scenarios, and restricted waters. In order to solve the above problem, Sawada et al. [1] proposed an automatic collision avoidance algorithm for ships based on the DRL algorithm. Shen et al. [24] designed a new method based on deep Q-learning to realise the automatic collision avoidance of ships. This model is also suitable for restricted waters. However, most studies in this field only focus on the computation of collision-free paths without obeying the rules of the COLREGs.

As a significant component of realizing autonomous ships, collision avoidance decision-making systems have attracted more attention from researchers in recent years. At present, many scholars are carrying out research work related to the development of collision avoidance decisions systems, such as a collision avoidance decision-making system, autonomous collision avoidance system, etc. [9,25,26,27]. Zhang et al. [28] and Mizythras et al. [29] introduced a distributed anti-collision decision support system. Among these, Mizythras’s system takes into account the ship’s manoeuvrability and propulsion system performance. Wang et al. [25] proposed a collision avoidance decision-making system designed for autonomous ships. However, the states, actions and trigger conditions defined in the FSM model are easily affected by subjectivity and have great uncertainty. Pietrzykowski et al. [30] presented a summary of the research on navigational decision support systems. This also pointed out that the usability of navigational decision support systems on vessels has been confirmed by the actual users of the navigational decision support system.

Ship manoeuvrability has a very important impact on the safety of ship navigation and the process of ship collision avoidance. However, at present, most of the above researches have only focused on the intelligent algorithms of being collision free and ignored the kinematical constraints of ships. As a matter of fact, research results will be more reliable if ship manoeuvrability is fully considered in the process of collision avoidance decision making. Li et al. [31] presented a dynamic path planning model based on the Morphin algorithm, which considers a ship’s manoeuvrability. However, the proposed model is greatly affected by human factors, and it is difficult to balance the relationship between the time cost of the model’s construction and the number of layers of the search tree. Wang et al. [32] developed a dynamic support system for ship collision avoidance by combining the ship manoeuvring motion model and the control mechanism of ships’ manoeuvring motion. However, this system is only suitable for a two ship encounter scenario and not applicable to the collision avoidance of the ships at different speeds. Generally, the complete ship collision avoidance manoeuvring process includes three stages: ships’ manoeuvring process, course keeping and returning to the original route. After the collision avoidance is completed, the ship should return to the original route. In other words, the own ship (OS) is considered to be back on the original route when the target ship (TS) is finally past and clear. Regarding the problem of resuming sailing, many scholars [1,25,33,34] have transformed it into the constraint conditions of the given decision variables, thereby obtaining a course manoeuvring degree to resume the original route.

1.3. Contributions and Outlines

Despite a lot of research work and achievements being completed on ship collision avoidance, there are still some unignorable shortcomings in the available studies: most of the researches only focus on the intelligent algorithms of being collision free without obeying the rules of the COLREGs, and they seldom consider the impact of the TS’s action uncertainty on collision avoidance decisions. Moreover, although some studies consider the constraints of the COLREGs rules, most of them rarely consider the ship’s manoeuvrability, COLREGs, good seamanship and uncertainty of the TS’s movement for collision avoidance at the same time.

The main motivation and contribution of this work is to present a decision support methodology of dynamic adaptive autonomous collision avoidance based on the ship manoeuvring process deduction method for autonomous ships. This methodology can solve the problem of the autonomous collision avoidance conundrum when encountering multiple objects and complex situations. Furthermore, it takes full account of various factors, including the COLREGs, ship manoeuvrability, good seamanship, multiple objects and complex encounter situations, and the TS’s uncoordinated or temporary actions.

Given the above, some highlights of our paper are:

(1)

A ship manoeuvring process deduction-based dynamic adaptive autonomous collision avoidance decision support methodology is established.

(2)

The COLREGs rules, good seamanship and ship manoeuvrability are comprehensively considered in the decision support methodology for autonomous collision avoidance.

(3)

A new collision risk evaluation model is constructed on the basis of the fuzzy set method to synthesize the SCRI and TCRI. This model considers the ship’s movement process and calculates the collision risk among ships in a dynamic way.

(4)

The impact of the TS’s action uncertainty on the collision avoidance decision is considered by the ship collision avoidance decision systems constructed in this paper.

(5)

The method constructed in this research is suitable for two-ship and multi-ship encounter situations, which is indispensable for collision avoidance systems for MASS.

The remaining sections of the paper are arranged as follows: In Section 2, the structure of the proposed method is clarified. In Section 3, the functionality of the collision avoidance decision support methodology is presented, describing the formulation for the collision risk calculation, autonomous collision avoidance method, resume-sailing model and collision avoidance algorithm implementation process. In Section 4, the proposed decision support methodology is validated through five cases. Subsequently, the experimental results analysis and discussions are made in Section 5, and in Section 6, the conclusion of this study is drawn.

2. Proposed Framework

In order to cope with the unpredictable manoeuvres of the TS adaptively, based on the ship manoeuvring mathematical model group (MMG) model and fuzzy adaptive proportion integration differentiation (PID) method, this paper proposes a ship manoeuvring process deduction-based dynamic adaptive autonomous collision avoidance decision support method for autonomous ships. Among them, the information of the OS and the TS obtained from the automatic identification system (AIS) and automatic radar plotting aids (ARPA) is the input, and the output is the collision avoidance decision scheme. The specific implementation steps are as follows:

Firstly, the system obtains the basic collision avoidance parameter information by AIS and ARPA. This information includes the ship velocity, ship position, course, true bearing and so on. Then, the collision risk judgment is made. If collision risks exist, the collision avoidance decision-making scheme and the resume-sailing angle are calculated based on the constructed collision avoidance decision-making model; if there are no collision risks, the OS keeps its current course and speed. Finally, a feasible collision avoidance decision scheme is given based on the constructed collision avoidance decision model. The process includes the execution of a control system consisting of the MMG model and PID. Based on the real-time updated ship information, the collision avoidance manoeuvring decision is executed cyclically.

The errors of the collision avoidance decision scheme in this method mainly include three aspects: the information error of the ship collision avoidance parameters, the error of the MMG model parameters and the error of the PID parameters. The effects of these errors can be eliminated or reduced by: improving equipment accuracy, selecting an appropriate MMG model to improve its adaptability and having prior knowledge to optimize controller parameters. For other errors, they can be compensated by designing an adaptive system. Based on the ship collision avoidance information at the current time $T_0$, the adaptive system will calculate and execute the optimal decisions scheme during a fixed time interval $\Delta t$. The error from $T_0$ to $T_0+\Delta t$ will be compensated if the system circularly recalculates and executes the new optimal decisions scheme based on the information after time step $\Delta t$. The time series rolling calculation method by quickly updating input information is taken in the adaptive method. The influence of the residual error on the manoeuvring scheme can therefore be compensated.

The framework of this research mainly consists of three parts. The first part is calculating the dynamic movement parameters of the OS and the TSs in real time and determining the collision risk between ships in different encounter situations. In the second part, the dynamic adaptive autonomous collision avoidance model is developed by combining the ship motion mathematical model, the fuzzy adaptive PID control model and the modified VO method. In the third part, in order to solve the resume-sailing problem, the LOS guidance system is adopted to resume the original route of the OS. The ship collision avoidance decision-making system considers various factors including the ship’s manoeuvrability, ship encounter situation, good seamanship and COLREGs. The framework of the decision support methodology for autonomous collision avoidance is drawn in Figure 1.

3. Decision Support Methodology

3.1. The Dynamic Calculation Model of Collision Avoidance Parameters

The determination of ship collision avoidance parameters is the basis of collision risk calculation and ship collision avoidance decisions. In this section, collision avoidance parameters between ships are calculated dynamically based on ship manoeuvring motion model. The ship collision avoidance parameter is shown below.

Figure 2 shows the relative position of two ships in the applied coordinate systems for a typical crossing situation. The speed and course of each ship are represented as $V_{OS}$, $V_{TS}$, ${\phi }_0$ and ${\phi }_T$, respectively. Supposing that the initial position and relative distance of the OS is $OS\left(0,0\right)$ and $R_0$, respectively. Relative bearing angle between OS and TS is ${\alpha }_{OT}$.

The relative speed of the OS and TS on the $X$-axis and $Y$-axis can be calculated by

$$\{\begin{array}{c}{v}_{x_R}=v_{TS}\sin {\phi }_T-v_{OS}\sin {\phi }_0\\ v_{y_R}=v_{TS}\cos {\phi }_T-v_{OS}\cos {\phi }_0\end{array}$$

(1)

$$V_{OT}=\sqrt{v_{x_R}^2+v_{y_R}^2}$$

(2)

At time $t$ after the OS takes evasive action, the position $TS\left(x_T,y_T\right)$ of the OS is

$$\{\begin{array}{c}{x}_0\left(t\right)={{\displaystyle \int }}_0^t{V}_{OS}\sin {\phi }_{0}dt\\ y_0\left(t\right)={{\displaystyle \int }}_0^t{V}_{OS}\cos {\phi }_{0}dt\end{array}$$

(3)

Then the relative displacement from the TS to the OS is expressed as follows

$$\{\begin{array}{c}\Delta x=R_0\sin ({\phi }_0+{\alpha }_{OT})+{{\displaystyle \int }}_0^t(V_{OS}\sin {\phi }_0-V_{TS}\sin {\phi }_T)dt\\ \Delta y=R_0\cos ({\phi }_0+{\alpha }_{OT})+{{\displaystyle \int }}_0^t(V_{OS}\cos {\phi }_0-V_{TS}\cos {\phi }_T)dt\end{array}$$

(4)

At time $t$, the relative distance $R_T$ between the OS and TS can be obtained as follows

$$R_T=\sqrt{\Delta x^2+\Delta y^2}$$

(5)

Then, as indicated in Figure 2, the distance to closest point of approach (DCPA) between OS and TS can be calculated as follows

$$DCPA=R_T\sin ({\phi }_R-{\alpha }_T-\pi )$$

(6)

and the time to closest point of approach (TCPA) is expressed as

$$TCPA=R_T\cos ({\phi }_R-{\alpha }_T-\pi )/V_{OT}$$

(7)

where ${\phi }_R$ is relative course, ${\alpha }_T$ is the true relative bearing to TS, which can be given as follows

$${\phi }_R=\{\begin{array}{cc}\arctan (v_{x_R}/v_{y_R}),& v_{xR}\ge 0{{\displaystyle \cap }}^{ }{v}_{yR}\ge 0\\ \arctan (v_{x_R}/v_{y_R})+\pi ,& (v_{xR}<0{{\displaystyle \cap }}^{ }{v}_{yR}<0){{\displaystyle \cup }}^{ }(v_{xR}\ge 0{{\displaystyle \cap }}^{ }{v}_{yR}<0)\\ \arctan (v_{x_R}/v_{y_R})+2\pi ,& v_{xR}<0{{\displaystyle \cap }}^{ }{v}_{yR}\ge 0\end{array}$$

(8)

$${\alpha }_T=\{\begin{array}{cc}\arctan (\Delta x/\Delta y),& v_{xR}\ge 0{{\displaystyle \cap }}^{ }{v}_{yR}\ge 0\\ \arctan (\Delta x/\Delta y)+\pi ,& (v_{xR}<0{{\displaystyle \cap }}^{ }{v}_{yR}<0){{\displaystyle \cup }}^{ }(v_{xR}\ge 0{{\displaystyle \cap }}^{ }{v}_{yR}<0)\\ \arctan (\Delta x/\Delta y)+2\pi ,& v_{xR}<0{{\displaystyle \cap }}^{ }{v}_{yR}\ge 0\end{array}$$

(9)

3.2. Collision Risk Method

The collision risk index (CRI) is used to assess the probability and severity of a ship collision with other ships in the vicinity, and its value ranges from 0 to 1 [25]. The value of CRI can be affected by various kinds of factors. In this section, considering the ship domain, relative position, DCPA, TCPA, manoeuvrability and vessel velocity, the fuzzy set method is adopted to construct a new collision risk model, which combines SCRI and TCRI in different encounter situations. The collision risk model for different situations is constructed below according to the types of encounter situations.

(a) 

Head-on situation

The SCRI is a measure of the collision probability, which can be determined by taking the minimum safe distance between two ships in danger of collision as the main indicator. Accordingly, it can be measured by whether TS will eventually enter the OS’s domain. According to the COLREGs and good seamanship, the value of the SCRI is either 1 or 0. The SCRI is expressed as follows

$$u_{sH}=\{\begin{array}{c}1,\exists {\left(x,y\right)}^t\in SDo{m}^t,t\in \left[0,TCPA\right]\\ 0,\forall {\left(x,y\right)}^t\notin SDo{m}^t,t\in \left[0,TCPA\right]\end{array}$$

(10)

where, $u_{sH}$ is the membership function of the fuzzy set $U_{sH}$, ${\left(x,y\right)}^t$ represents the position coordinates of the TS at time t, $SDo{m}^t$ represents the sets of location point elements at time t in the OS’s domain. For this encounter situation, this paper uses the elliptical ship domain, where semi-major axis is 8 L (8 times ship length) and semi-minor axis is 4 L.

The TCRI is affected by factors such as time to close situation (TCS), DCPA, etc. On the basis of referring to existing research [35], the formula for determining the TCRI is

$$u_{tH}=\{\begin{array}{cc}1,& TCS\le 0\\ {\left(\frac{k-1}{k-1+\frac{TCS}{TCPA}}\right)}^{3.03},& TCS>0 and D<D_s\\ 0,& D\ge D_s\end{array}$$

(11)

where, $k=\sqrt{R_T^2-DCP{A}^2}/\sqrt{D^2-DCP{A}^2}$,$u_{tH}$ is the membership function of the fuzzy set $U_{tH}$, TCS represents the time from the current moment to the first time point of a close-quarter situation. $R_T$ is the distance between OS and TS. $D_s$ is a constant with a value of 5$\mathrm{nm}$.

Thus, the collision risk model in the head-on situation can be written in Equation (12)

$$u_{CRI}=u_{sH}\otimes u_{tH}$$

(12)

where $\otimes$ is the risk synthesis operator.

(b) 

Overtaking situation

According to the requirements of the rules on the formation of overtaking situation, when the rear ship catches up with the preceding ship and the distance is less than 3 nm, the distance condition for the formation of overtake is satisfied [35]. Therefore, in overtaking situation, the value of $R_T$ in the TCRI is 3 nm. Other parameters are the same as the collision risk model for head-on situation, and for elliptical ship domain, where semi-major axis is 5 L and semi-minor axis is 4 L.

(c) 

Crossing situation

According to the definition of SCRI, the SCRI in the crossing encounter situation is the same as the model of the other two encounter situations. The TCRI of crossing situation should satisfy both conditions of $D<5 \mathrm{nm}$ and $TCS\le 20 \min$. Therefore, the TCRI in the crossing encounter situation takes the smaller of these two values.

For the first case, when the potential collision risk exists, $D<D_s$ and $TCPA>0$, the TCRI under the crossing encounter situation is the same as Equation (11).

$$u_{tC}^1=u_{tH}$$

(13)

For the second case, when the potential collision risk exists, $TCS\le 20 \min$ and $TCPA>0$, the TCRI under the crossing encounter situation is as follows

$$u_{tC}^2=\{\begin{array}{c}1, TCS\le 0\\ {(1-\frac{TCS}{1200})}^{3.03},0<TCS<20\\ 0, TCS\ge 20\end{array}$$

(14)

The TCRI of crossing situation is

$$u_{tC}=\min (u_{tC}^1,u_{tC}^2)$$

(15)

Thus, the collision risk model in the crossing situation can be written in Equation (16)

$$u_{CRI}=u_{sC}\otimes u_{tC}$$

(16)

where $\otimes$ is the risk synthesis operator.

3.3. Autonomous Collision Avoidance Method

VO algorithm was first proposed by Fiorini and Shiller [36], and is an effective and simple method collision avoidance method, such as robots’ collision avoidance and ships’ obstacle avoidance [7,18,37]. According to its principle, VO can calculate the speed sets of all ships that may cause collision risk. Thus, in this paper, the MMG, fuzzy adaptive PID control model and modified VO algorithm are used to derive the ships’ manoeuvre motion process. On this basis, the feasible avoidance range and optimal steering angle of ships’ collision avoidance can be calculated.

Assume that the position and velocity of OS and TS are denoted as $P_{OS}$, $P_{TS}$, $V_{OS}$ and $V_{TS }$, respectively, $D$ represents the safe distance between OS and TS. Hence, the possible position of OS when a collision happens is termed as “Conflict Position $ConfP$”.

$$ConfP\left(O,D\right)=\left\{P\Vert P_{TS}-P_{OS}\Vert \le D\right\}$$

(17)

where $\Vert ·\Vert$ is the geographic distance between two vessels. $P$ is denoted as a position. If the distance between the OS and TS is less than the threshold$D$, a collision will definitely occur. In other words, the two ships will collide at time $t_n$, with the following conditions fulfilled

$$P_i\left(t_n\right)\in P_j\left(t_n\right)\otimes ConfP\left(O,D\right)$$

(18)

where operation $\otimes$ is the Minkowski addition, which means adding $P_j$ to each element in $ConfP$. Assuming that kinematic information of both ships is known, Equation (18) can be substituted with Equation (19)

$$V{O}_{OS|TS}={{\displaystyle U}}_t^N\left(\frac{P_{TS}\left(t\right)-P_{OS}\left(t_0\right)}{t-t_0}\right)\otimes \frac{ConfP\left(O,D\right)}{t-t_0}$$

(19)

where $N$ is an infinite number. If the OS keeps up this vector velocity all the time, there will definitely be collisions in the future ($t_0\to N$).

In Figure 3, the TS and OS form a starboard crossing situation. Assuming that the steering angles of OS to avoid the TS to the right and left are ${\theta }_1$ and ${\theta }_2$, respectively, when OS alters to the starboard side or port side, the target course is $C+{\theta }_1$ and $C+{\theta }_2$. If the ship’s manoeuvrability is not considered, the critical trajectories of the OS are straight lines $L_1’$ and $L_2’$. From the moment the ship steers to the starboard to time $T_1$, the OS and TS are located at point $A_1$ and $B_1$, respectively, and at this time the OS just passes through the fore of the TS. From the moment when OS steers to the port to time $T_2$, the OS and TS are located at point $A_2$ and $B_2$, respectively, and at this time the OS just passes through the aft of the TS. Due to the non-linear characteristics of the ship’s manoeuvring model, it takes a period of time for the ship to maintain heading stability. Therefore, if the ship’s manoeuvring is considered and the fuzzy adaptive PID method is used to control the steering of the ship, the ship trajectory is the curve line $L_1$ and $L_2$.

In this case, the TS will enter the OS’s ship domain if $C+{\theta }_1$ and $C+{\theta }_2$ are used as the target heading angle for collision avoidance. In summary, if the ship manoeuvrability constraints of the OS are not considered, and the collision avoidance scheme is performed according to the original collision avoidance angle, the two ships will collide.

If the steering angles of OS to the left or right are less than ${\theta }_1$ and ${\theta }_2$, respectively, the TS will enter the OS’s ship domain. Then the steering angle interval $\left({\theta }_1,{\theta }_2\right)$ is the obstacle range of the speed vector from the TS to OS. For multi-ship encounter situation, the feasible manoeuvring range of OS is the complement of the union of the speed vector obstacle range for each TS

$$C_{range}=\overline{U_{i=1}^n{\theta }_i ,}\left(i=1,2\right)$$

(20)

For any course altering angle ${\theta }_i$, as long as the course of OS is not in the speed obstacle range of all TSs when the redirection is completed, then this altering angle belongs to the feasible manoeuvring range. The algorithm proposed to obtain the dynamic feasible manoeuvring range is denoted in Algorithm 1.

Algorithm 1. Algorithm for calculating dynamic feasible manoeuvring range.

Input: the position $P_{OS}^{\left(0\right)}$, $P_{TS}^{\left(0\right)}$; the speed $v_{OS}^{\left(0\right)}$, $v_{TS}^{\left(0\right)}$; the course $C_{OS}^{\left(0\right)}$, $C_{TS}^{\left(0\right)}$

Output: dynamic feasible manoeuvring range $\left[{\theta }_{i1},{\theta }_{i2}\right]$

1:    Initialize the i = 1, $\Delta t=1$

2:    Initialize the $\theta$ = −90

3:    for $u_{CRI}>0$ do

4:      for $i\le 361$ do

5:        Calculate the target course $C_t=C_0^{\left(0\right)}+\theta$

6:        Put target course $C_t$ into course control system

7:        Update: $P_{OS}^{\left(i*\Delta t\right)}$, $P_{TS}^{\left(i*\Delta t\right)}$ $v_{OS}^{\left(i*\Delta t\right)}$, $v_{TS}^{\left(i*\Delta t\right)}$, $C_{OS}^{\left(i*\Delta t\right)}$, $C_{TS}^{\left(i*\Delta t\right)}$

8:          for each TS do

9:            Calculate whether the TS enters OS’s ship domain

10:            If TS enter OS’s ship domain then

11:              $\theta =\theta +0.5$

12:              i = i + $\Delta t$

13:            else

14:              break

15:          end for

16:      end for

17:    end for

18:    return: feasible manoeuvring range $\left({\theta }_{i1},{\theta }_{i2}\right)$

Theoretically, any course altering angle within the feasible manoeuvring range can make the giving-way ship safely avoid all TSs. However, considering the safety and economy in navigation, the course altering angle should not be too large or too small, so it is very necessary to choose an appropriate altering angle. Based on this, this study introduces the surplus amount ${\theta }_k$, the optimization steering angle $\theta$ of ship collision avoidance can be expressed by Equation (21).

$$\theta =\{\begin{array}{cc}{\theta }_{min}+{\theta }_k,& \theta \in C_{range}\\ {\theta }_{min},& \theta \notin C_{range}\end{array}$$

(21)

where ${\theta }_{min}$ is the minimum altering angle in the feasible manoeuvring range, and ${\theta }_k$ is the surplus amount, which can be adjusted according to specific circumstances.

3.4. Resume-Sailing Model

The LOS algorithm is a classic trajectory control algorithm, which is not model dependent. The target heading is only related to the unmanned ship’s real-time position and target course [22]. In this study, the LOS guidance strategy, which is widely used in path tracking, is adopted for the problem of resuming route and heading keeping.

The sketch map of the resume-sailing model is shown in Figure 4, where the LOS position $P_{LOS}$ is the point along the path that the ship should point to. OS is sailing from the start position $P_s\left(x_s,y_s\right)$ to destination $P_n\left(x_n,y_n\right)$. After completing the avoidance process, the ship applies the LOS strategy to resume route. Make the OS’s current position be located at the centre of a circle with a radius of n times its length. The circle intersects the line between $P_s\left(x_s,y_s\right)$ and $P_m\left(x_m,y_m\right)$, and $P_{LOS}$, the closest point $\mathrm{to} P_m\left(x_m,y_m\right)$ is selected as the turning point.

In LOS guidance system, OS is guided to resume route by the minimum error ${\psi }_P$ between the actual heading angle $\psi$ and the LOS angle ${\psi }_{LOS}$. The LOS angle ${\psi }_{LOS}$ can be calculated by the following equation

$${\psi }_{LOS}=arcsin(\frac{x_{LOS}-x}{R_{LOS}})$$

(22)

where $R_{LOS}$ is the radius of the circle, which satisfies the following Equation

$$R_{LOS}^2={(x_{LOS}-x)}^2+{(y_{LOS}-y)}^2$$

(23)

Then the resume-sailing angle is tracking error; it can be calculated by

$${\psi }_P=\psi -{\psi }_{LOS}$$

(24)

3.5. Design of Adaptive Autonomous Collision Avoidance Algorithm

In order to realize the ship’s adaptive autonomous collision avoidance in complex encounter situations, a ship manoeuvring process deduction-based dynamic adaptive autonomous collision avoidance decision support method (Figure 5) is constructed in this study. This system can acquire the dynamic and static information of the TSs in real time and calculate the course altering angle required at the current time and input it into the course control system with the interval of fixed calculation step $\Delta t=1 \mathrm{s}$. The ship motion model is used to deduce the movement trend of the OS and the TSs within a certain period of time, and the information of the OS and the TSs is updated in real time through rolling calculations to realize autonomous collision avoidance.

The specific implementation process is as follows:

Step 1: Obtain the static and dynamic information of ships, and calculate the collision avoidance parameters considering the ship manoeuvring in real time;

Step 2: Identify the ships’ encounter situation, and calculate the collision risk between ships according to the collision risk model in Section 3.2;

Step 3: According to the autonomous collision avoidance model constructed in Section 3.3, calculate the feasible manoeuvring range that allows all dangerous TSs to be cleared;

Step 4: Calculate the optimization steering angle of ship collision avoidance based on the feasible manoeuvring range;

Step 5: Determine the target course after completing the avoidance and redirection according to step 4, control the ship’s steering through the course control system and calculate the corresponding rudder angle;

Step 6: Substitute the rudder angle into the MMG model to calculate the dynamic and static information of OS and the TS at the next moment in the manoeuvre process. After updating the information, go to step 1 until the TS is finally past and clear;

Step 7: Take the completion of the ship avoidance as the initial moment, and search for the time point at which all obstacles can be avoided at one-second intervals, and make it the return time point;

Step 8: Calculate the resume-sailing angle according to the resume-sailing model;

Step 9: Control the ship to resume sailing according to the course control system.

4. Case Study

4.1. Experimental Settings

In this section, to validate the feasibility and effectiveness of the decision support methodology proposed in this paper, five different types of ship encounter scenarios are designed to illustrate the application of the autonomous collision avoidance system in maritime navigation. The scope of the experimental cases includes two-ship encounter scenarios, multi-ship encounter scenarios, the TS maintaining course and speed, and the TS suddenly changing course, etc. In addition, to further verify the effectiveness of the decision support methodology, we recorded the collision avoidance parameter information such as the DCPA, TCPA, D, and course per unit time step. $T_0$, $T_1$ and $T_2$ are the start time, the middle time and the end time during the collision avoidance process, respectively. The unit of the relative distance is in nautical miles, shown as (nm), the unit of ship speed is knots (kn), the unit of the DCPA is meters (m), the unit of the TCPA is seconds (s), and the unit of the course is degrees (°). In order to more intuitively display the information such as the motion process and relative distance between ships, a geographical location (Lon. 123°42.8′ E, Lat. 29°24.0′ N) is determined as the origin of the simulation experiment, and an O-X-Y coordinate system with the origin as the centre and nautical miles as the unit is established. The longitudinal and transverse distance from the ship’s current position to the coordinate axis is used as the ship’s position coordinate in the simulation experiment diagram in this paper. The initial information of the two-ship and multi-ship cases are listed in

Table 1. Settings of two-ship scenarios.

Case	Ship List	Position	Course (°)	Velocity (kn)	Distance (nm)	Ship Length (m)
Scenario 1	OS	(123°46.519′ E, 29°24.877′ N)	006.5	12	0	225
	TS	(123°46.823′ E, 29°29.763′ N)	186	10	4.8532	180
Scenario 2	OS	(123°46.519′ E, 29°24.877′ N)	040	14	0	225
	TS	(123°48.636′ E, 29°27.213′ N)	040	5	2.9507	180
Scenario 3	OS	(123°46.897′ E, 29°25.019′ N)	022	12	0	225
	TS	(123°49.964′ E, 29°29.231′ N)	235	11	4.9422	180

and

Table 2. Settings of multi-ship scenarios.

Case	Ship List	Position	Course (°)	Velocity (kn)	Distance (nm)	Ship Length (m)	Course Altering Angle (°)
Scenario 4	OS	(123°46.521′ E, 29°24.222′ N)	022	11	0	225	+16
	TS1	(123°47.420′ E, 29°29.052′ N)	185	10	4.8613	180	+12
	TS2	(123°49.892′ E, 29°27.988′ N)	250	8	4.7404	180	−15
Scenario 5	OS	(123°48.391′ E, 29°26.212′ N)	000	12	0	225	+23
	TS1	(123°49.532′ E, 29°30.150′ N)	225	10	4.0571	180	0
	TS2	(123°45.525′ E, 29°30.042′ N)	135	12	4.5814	180	+12
	TS3	(123°46.854′ E, 29°26.046′ N)	035	10	1.3675	180	0
	TS4	(123°47.925′ E, 29°31.042′ N)	180	10	4.8558	180	0
	TS5	(123°50.315′ E, 29°29.547′ N)	250	12	3.7158	180	−10

Note: “+” means alter course to starboard side, the symbol; “−” means alter course to port side.

. Moreover, this paper adopts the classic three-degree-of-freedom MMG; the specific parameters are available in the literature [38]. To verify the precision of the MMG model, the Panama maximum size bulk carrier HUAYANG DREAM is simulated in our study. The simulation results are shown in Appendix A (

Table A1. HUAYANG DREAM’s parameters.

Parameter	Value	Parameter	Value
LOA	225 (m)	Acreage of rudder	56.88 (m2)
Draft	14.5 (m)	Displacement	90,000 × 103 (kg)
$C_b$	0.8715	Density of sea water	1000 (kg/m3)
$C_p$	0.8739	RPM	90 (r/min)
Breadth	32.5 (m)	Propeller pitch	4.738 (m)

, Figure A1 and Figure A2). It can be found that although there are some slight differences between the MMG model and the real ship, the accuracy is generally acceptable. The fuzzy adaptive PID control model is used to control the ship’s manoeuvres, and the process of the ship’s course/track control system to control the ship’s manoeuvres is simulated. Details about fuzzy PID are provided in the literature [39]. In this chapter, the constructed collision avoidance decisions method is connected with the intelligent navigation simulation research platform, and the effectiveness of the collision avoidance decisions method is verified through the simulation platform.

4.2. Simulation Scenario 1

In the current status, the course of the OS and TS are 006.5° and 186°, respectively. At this point, according to COLREGs rule 14 and the collision risk model, the two ships are in a head-on situation and there is a collision risk. Every ship should alter their course to the starboard side to avoid the collision. However, there may be situations where the TS keeps her course and speed, and the avoid collision action is taken by the OS solely. Therefore, this scenario is divided into two conditions (situation 1: the TS keeps course and speed; situation 2: the TS alters course to the starboard side) to simulate and verify the collision avoidance decision model.

Figure 6a,b are the simulation results under these two situations when the TS keeps its course and speed and alters its course to the starboard side to avoid collision (the TS alters to starboard by 6°), respectively. For situation 1 and situation 2, according to the decision support methodology constructed in this article, the OS should alter course to the starboard side by 8° and 6°, respectively. The real-time parameter changes are shown in Figure 7. Figure 7a shows the ship’s distance curves between the OS and TS in the two situations. The DCPA value of the OS and TS first increases and remains stable until the OS starts to resume to the original route, as shown in Figure 7b. Figure 7c gives the curves of the TCPA. Figure 7d shows the course change of the OS during the whole collision avoidance process.

4.3. Simulation Scenario 2

In scenario 2, the initial course of the OS and TS are the same, namely 040°. According to COLREGs rule 13, the OS and TS are in an overtaking situation. The OS is a give-way ship and should take charge of performing conflict avoidance actions. According to the calculation result of the autonomous collision avoidance model, the course of the OS should alter 15° to starboard. The results of the ship collision avoidance decisions and manoeuvres are shown in Figure 8a. Figure 9 shows the real-time parameter changes under the crossing encounter situation.

4.4. Simulation Scenario 3

In this simulation scenario, the two ships are in a crossing situation, so the OS should take charge of performing conflict avoidance actions. Figure 8b shows the initial positions and paths of the simulation ships involved in the experiment. According to the autonomous collision avoidance model, the OS makes the decision of altering to starboard by 17°. Due to the influence of ship manoeuvrability, the OS can keep her course stable after course altering is finished, and will keep the new course until 202 s.

Figure 9 shows the real-time parameter changes under the crossing encounter situation and overtaking encounter situation. The relative distance between the ships is shown in Figure 9a. Figure 9b,c show the curve of the DCPA and TCPA between the OS and TS, respectively. Figure 9d shows the course change of the OS during the whole collision avoidance process.

4.5. Simulation Scenario 4

The scenario considered in this part is a typical three-ship crossing encounter situation. According to the COLREGs rule, the OS, TS1 and TS2 have an obligation to alter their courses to starboard to give way to TS2, TS1 and the OS, respectively. The collision avoidance system recognises that TS1 and TS2 have suddenly altered course to the starboard by 12° and 15°, respectively. According to the autonomous collision avoidance support methodology constructed in this paper, the OS should alter to starboard by 16°.

Figure 10 shows the initial positions of the simulation ships. Figure 11a shows the ship’s relative distance curves between TS1, TS2 and the OS, which reaches the lowest point in 839 s and 941 s, respectively, and the minimum distances are 1414 m and 1181 m, respectively. The DCPA values of the OS with TS1 and TS2 increase continuously and remain stable until the start of resuming the original route, as shown in Figure 11b. The TCPA values between the ships change to negative at 839 s and 942 s in Figure 11c, respectively. Figure 11d shows the course change of the OS during the whole collision avoidance process.

4.6. Simulation Scenario 5

The scenario considered in this part is a typical and more complicated six-ship encounter situation. In this scenario, TS2 and TS3 are located at the far left and form left-crossing encounter situations with the OS. TS4 is located in the left front direction of the OS and forms a head-on situation with the OS. TS1 and TS5 are located in the right front direction of the OS; they all form crossing encounter situations with the OS.

In this scenario, the collision avoidance support methodology recognises that the TS2 is altering 12° to the starboard and TS5 is altering 10° to the port. According to the autonomous collision avoidance system, the OS can only clear all target ships by altering course 23° to starboard. Figure 12 show the initial positions and paths of the experimental ships. The real-time parameter changes under a multi-ship encounter situation are shown in Figure 13. Figure 13a shows the ship’s relative distance curve between the OS and the TSs in this scene. It can be seen that the minimum distance between the OS and each TS is larger than the required safe passing distance (grey dotted line). The changes in the DCPA curve between the OS and TSs are shown in Figure 13b. The TCPA values between the OS and TSs change to negative at 724 s, 757 s, 458 s, 830 s and 622 s in Figure 13c, respectively. Figure 13d shows the course change of the OS during the whole collision avoidance and reversion of course process.

5. Discussions and Analysis

5.1. Results and Discussion

Five different types of ship encounter scenarios are designed to verify the feasibility and effectiveness of the decision support methodology for autonomous collision avoidance in this paper. The results and discussion are as follows:

For Scenario 1, it is divided into two situations (the TS keeps its course and speed; the TS alters its course to the starboard side). By comparing the two situations, it can be seen that in the same scenario, the OS’s alteration angle of course is 8° when the TS is keeping speed and course, and when the TS also changes her course for collision avoidance, the OS only alters her course angle by 6°.

Due to the influence of ship manoeuvrability, in these two situations, the OS can only keep her course stable for a short while after changing her course and maintains the new course until 672 s and 685 s, respectively. At 1579 s and 1589 s, the OS completes the resume-sailing process and resumes to the original route in these two scenarios, respectively, with the courses of the OS both 006.5°. As can be seen from Figure 6a, the minimum distances between the TS and OS are almost the same in these two scenarios, which are 1156 m and 1175 m, respectively, and both larger than 899 m. It can be seen that the OS can avoid collision through a smaller redirection angle when the TS also redirects to a certain angle to avoid a collision. Namely, this simulation result is consistent with navigation practice.

For scenarios 2 and 3, the TSs all keep their course and speed; the OS is a give-way vessel. According to the autonomous collision avoidance method, the OS makes a collision avoidance decision of altering to the starboard by 15° and 17°, respectively. By analysing the experimental results, we can see that safe collision avoidance can be achieved well in these two scenarios.

Scenarios 4 and 5 are both multi-ship encounter situations, in which the impacts of the TSs’ course changes on the collision avoidance decision during the avoidance process were considered. For example, for scenario 5, ST2 alters 12° to the starboard side and TS5 alters 10° to the port side; the other ships keep their speed and course. The collision avoidance method shows that the OS needs to alter to the starboard by 23° to clear all ships. In Figure 13a, it can be seen that the ship’s distance curves gradually decrease at first, after reaching the lowest point in 723 s, 756 s, 846 s, 928 s and 619 s, respectively, and then increase gradually. The minimum distances between the OS and TSs are 1810 m, 3123 m, 1932 m, 1689 m and 1623 m, respectively. The minimum relative distance between the OS and all TSs is greater than the safe distance. This means that the collision never occurred. The TCPA values between the OS and TSs changes to negative at 724 s, 757 s, 458 s, 830 s and 622 s in Figure 13c, respectively. Figure 13d shows the course change of the OS; the curve can effectively show the course changes of the OS during the whole collision avoidance process. Although the encounter situation in this scenario is more complicated, the decision support methodology can safely avoid all ships through steering to the starboard by 23°, and, finally, realize the resumption to the original route.

In summary, for all scenarios, the minimum relative distances between the OS and TSs during collision avoidance is greater than the safety distance, which are clearly shown in Figure 7a, Figure 9a, Figure 11a and Figure 13a. Figure 7d, Figure 9d, Figure 11d and Figure 13d all show that the OS has good tracking performance for the expected courses, reflecting the manoeuvring characteristic of ship motion control. The simulation results show that the proposed method can be applied to complex scenarios such as two-ship and multi-ship encounters, showing excellent adaptability to and effectiveness in managing complex multi-target situations. In addition, the decision support methodology can take appropriate collision avoidance actions even when the TS changes her course, the collision avoidance manoeuvre of which is effective and reliable.

5.2. Comparison Analysis

In this paper, we propose a decision support methodology of dynamic adaptive autonomous collision avoidance based on ship manoeuvring process deduction for the autonomous ship. This methodology can effectively solve the problem of autonomous collision avoidance under different encounter scenarios. At present, relevant scholars have proposed various methods and techniques for the problem of collision avoidance, such as [4,8,11,18,33,40,41]. However, compared with other research results, this paper has some differences and advantages.

Different from vehicles, ship motion has the characteristics of large inertia, time delay and being non-linear. Therefore, it is very necessary to consider ship manoeuvrability in the decision-making scheme of collision avoidance. Some related studies [11,14,33] ignore ship manoeuvrability, which increases the gap between the collision avoidance algorithms or decision-making systems and practical applications. In addition, most of the researches only focus on the intelligent algorithms of avoidance collision, ignoring the ship manoeuvrability, good seamanship and COLREGs. In this paper, the MMG model and fuzzy adaptive PID method are used to derive the ships’ manoeuvre motion process. On this basis, this paper proposes a dynamic adaptive autonomous collision avoidance system based on the second-level update of information, which also takes into account the COLREGs rules, good seamanship and ship manoeuvrability.

In addition, few studies consider the impact of the TS’s action uncertainty on the collision avoidance decisions. In this paper, we mainly focus on the change of a ship’s course. Most studies assume that the TS is sailing at a constant speed and course, which does not conform to the actual situation of navigation. Even though some algorithms take into account the motion characteristics of the TS, most of them are based on assumptions. In addition, most existing collision avoidance models or systems rarely consider the problem of resuming the original route after collision avoidance. For the safety of ship navigation, the vessel should resume the original route after the collision avoidance action has been successfully completed. In this study, we propose a dynamic adaptive autonomous collision avoidance model based on second-level updating of information, which can solve the problem where other ships do not comply with COLREGs or suddenly take action during the collision avoidance process, and build a resume-sailing model based on a LOS guidance system.

In summary, we present a decision support methodology of dynamic adaptive automatic collision avoidance based on ship manoeuvring process deduction for an autonomous ship. The decision support methodology has intact avoidance manoeuvres, including collision risk detection, collision avoidance manoeuvres and resuming to the original route. It takes full account of various factors, including COLREGs, ship manoeuvrability and good seamanship. Furthermore, this methodology can solve the problem of the autonomous collision avoidance when encountering multiple objects, complex situations and the TS’s uncoordinated or temporary actions.

6. Conclusions

In this paper, a decision support methodology of dynamic adaptive autonomous collision avoidance based on ship manoeuvring process deduction for autonomous ships was proposed. The system takes full account of various factors, including COLREGs, ship manoeuvrability and good seamanship. In order to judge the risk of collision between ships in different encounter situations, a new collision risk model is constructed on the basis of the fuzzy set method to synthesize the SCRI and TCRI. The MMG model and fuzzy adaptive PID method are used to derive the ships’ manoeuvre motion process. On this basis, the feasible manoeuvring range and optimum steering angle of collision avoidance are calculated according to the deduction of the manoeuvring process and modified VO method. Finally, the dynamic adaptive autonomous collision avoidance model is developed. The feasibility and effectiveness of the decision support methodology proposed in this paper is verified through simulation experiments under five different scenarios.

Although the autonomous collision avoidance system we established is proved to be reasonable, effective and feasible, there are still some deficiencies. For narrow waters or restricted waters, due to the limited manoeuvrability of ships, it is difficult to achieve an effective collision avoidance only by changing course. However, collision avoidance strategies of changing both speed and course are more consistent with navigation practice. Therefore, further work should be focused on collision avoidance strategies that take both course and speed changing into consideration, and carry on simulations and field tests in more complex situations and restricted waters.