Journal of Advanced Transportation

Volume 2019, Article ID 4068783, 12 pages

https://doi.org/10.1155/2019/4068783

## Ship’s Trajectory Planning Based on Improved Multiobjective Algorithm for Collision Avoidance

State Key Laboratory of Integrated Optoelectronics College of Electronic Science and Engineering Jilin University, Changchun, China

Correspondence should be addressed to Hongbo Wang; nc.ude.ulj@obgnoh_gnaw

Received 27 December 2018; Revised 25 February 2019; Accepted 11 March 2019; Published 9 April 2019

Academic Editor: Aboelmaged Noureldin

Copyright © 2019 Jinxin Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With vigorous development of the maritime trade, many intelligent algorithms have been proposed to avoid collisions due to resulting casualties and increased costs. According to the international regulations for preventing collisions at sea (COLREGs) and the self-evolution ability of the intelligent algorithm, the collision avoidance trajectory can be more consistent with the requirements of reality and maritime personnel. In this paper, the optimization of ship collision avoidance strategies is realized by both an improved multiobjective optimization algorithm NSGA-II and the ship domain under the condition of a wide sea area without any external disturbances. By balancing the safety and economy of ship collision avoidance, the avoidance angle and the time to the action point are used as the variables encoded by the algorithm, and the fuzzy ship domain is used to calculate the collision avoidance risk to achieve collision avoidance. The simulation results show that the proposed method can optimize the ship collision avoidance strategy and provide a reasonable scheme for ship navigation.

#### 1. Introduction

Collisions are one of the biggest problems in terms of safe navigation at sea. With the development of science and technology, a substantial amount of equipment has been developed to avoid collisions, such as the automatic identification system (AIS), automatic radar plotting aid (ARPA), and global positioning system (GPS) [1, 2]. This equipment can clearly determine the navigation data of a target ship via radar and satellite positioning to conduct analyses and decision avoidance actions via navigators. However, the number of casualties and economic losses caused by collisions is still high each year. According to the investigation, the main reason for this is due to subjective judgment errors. Therefore, it is the main research problem of the researchers to provide reasonable collision avoidance strategy for navigators.

Collision avoidance is simply the reprogramming of the navigation path of a ship that intersects another route to prevent collision. In early navigations, collision avoidance was conducted based on the experience of seafarers (i.e., qualitative research on the regulations for preventing collisions at sea (COLREGS)), which has great instability. In recent years, along with the development of science and technology, the ARPA, AIS, and other marine auxiliary equipment have been widely used, and navigation information (e.g., the sailing speed, latitude, and destination of a ship) is obtained by specific equipment. Therefore, a new method for collision avoidance decisions was generated (i.e., the distance to the point of approach (DCPA) and time at the point of approach (TCPA)); the DCPA and TCPA can be used to plan ship avoidance behaviours [3] (i.e., the quantitative study of collision avoidance rules). However, such a method is only a rough evaluation of this action, and it sometimes results in an incorrect behaviour detection.

With the continuous success of intelligent algorithm practices, some algorithms are used to discover better collision avoidance strategies, such as genetic algorithms (GAs), the ant colony algorithm, and danger immunity algorithm [4–7]. The principle of the optimized collision path avoidance method is to avoid collisions with minimum loss. An intelligent algorithm is used to make the avoidance behaviour more reasonable and accurate. For example, Lyu used the artificial potential field method to plan the route of ships with a single TS avoidance and multiship avoidance [8]. Tsou completed the optimization of the collision avoidance path by using the ant colony algorithm to develop the real-number coding of avoidance parameters [9]. Mostefa adopted the GA to optimize the collision path in a fuzzy environment [10]. And to reduce the effect of human factors, Kang can use a particle swarm optimization (PSO) algorithm to plan ship paths [11]. Xu et al. proposed an autonomous collision avoidance method by training deep convolutional neural network [12]. In order to better judge the existence of danger, Chen et al. used the velocity obstacle approach to study collision avoidance of ships [13].

In the above method, the choice of a collision path is regarded as a problem based on multiple criteria and nonlinearity, and path planning is carried out through the combination of the DCPA and TCPA and algorithms. However, risk discernment between the DCPA and TCPA cannot sufficiently reflect the occurrence of collisions; namely, these methods cannot consider the information of a target ship and the opportune moment. To solve this problem, Szlapczynski introduced two new parameters in the field of ships: the degree of domain violation (DDV) and the time to domain violation (TDV), which were used to replace the DCPA and TCPA [14]. This method is based on an off-centred elliptical domain to calculate the time of the target ship's intrusion into the ship domain, and the fuzzy principle is used to estimate the extent of the target ship's intrusion into the fuzzy domain. Therefore, the navigation strategy for ships is planned based on the principle of noninvasive ship domains. At the same time, in most of above-mentioned researches, the optimization function is always defined as a single-objective optimization or transformed to a single-objective optimization by the weights allocation. But because of imperfection of single-objective optimization and the difficulty to determine the weight value, the trajectory of collision avoidance is not reasonable. Therefore, multiobjective algorithm is necessary for collision avoidance planning.

In this paper, in order to make the distance between the own ship and the target ship more appropriate and to consider the irregularity of the ship domain, it is considered that both ship domains exist at the same time. And the Szlapczynski’s method was applied to calculate the risk of collision between two ships; the maximum of the two ships’ risk is taken as the objective of algorithm optimization [14–16]. At the same time, the multiobjective optimization algorithm is used to optimize the collision avoidance parameters by considering two objectives (i.e., security and economics) [17]. And the multiobjective algorithm is improved by referring to the danger model theory [18], that is, mapping the dominated solution to the vicinity of the nondominant solution can effectively accelerate the convergence speed of the multiobjective algorithm. The whole collision avoidance trajectory only considers one avoidance, so the optimization variable of trajectory takes into account the time of action point and the angle of avoidance at the action point, which makes the collision avoidance trajectory instruction more clear.

The rest of the paper is organized as follows. The ship maneuverability equation, fuzzy ship domain, and basic parameter calculations are introduced in Section 2. Section 3 introduces the multiobjective optimization algorithm (NSGA-II) and the application of the combined algorithm and ship domain in the optimization of the collision avoidance strategy. In Section 4, a simulation example based on this method is given for the collision situation; finally, the summary and conclusions of the methods are given in Section 5.

#### 2. The Ship Motion Model, the Ship Domain, and Parameter Calculation

##### 2.1. Ship Motion Model

Because ships are subjected to a variety of forces during movement, it is necessary to consider six degrees of freedom to accurately reflect the movement of ships, which requires too many parameters and are too complicated. A complicated and vulnerable ship model may contain too many parameters, which are difficult to estimate and analyze. Therefore, the mathematical model of the ship is always an approximate model. In this paper, we used mathematical models from the Maneuvering Motion Group (MMG), which was established by the second meeting of the Japan Towing Tank Committee in March 1976. The linear surge velocity of the ship (), linear sway velocity (), yaw angular velocity (), and rudder angle () represent the state and control variables of the mathematical model. The mathematical model for ship motions with three degrees of freedom is considered here:where and denote the sum of the added masses and the mass of the ship in the -and -directions, respectively; and denote the velocities along the - (towards the front) and -axes (towards the starboard), respectively; , , and represent the surge force, sway force, and yaw moment, respectively; and and denote the moment of inertia of the ship and yaw rate, respectively.

In this study, the longitudinal motion of a ship considers the propelling force and fluid resistance of the ship. In addition, the transversal movement of a ship reflects only the effect of its lateral hydrodynamic force. The propelling force and transversal resistance should be considered for the yaw rotation of the ship. Thus, the response model is as follows:where , , and are flow resistant coefficients, and , , and are the proportional coefficients associated with the ship's length, which are calculated as follows (3).where and refer to the ship's length and command rudder angles, respectively; and are constants; and and represent the maximum speed and maximum propulsion, respectively.

##### 2.2. Ship Domain and Parameter Calculation

Ship safety domains are widely used in the study of collision avoidance, where early domain models are based on the statistical analysis of radar data, such as the Fuji ship domain and Goodwin ship domain, which originates from the empirical analysis method [19]. Currently, more analyses of ship domains are based on expert knowledge and theoretical analysis. For example, Wang proposed the quaternion ship domain (QSD) based on theoretical analysis [20], and Dinh proposed the polygonal ship domain based on the combination of analyses and statistics [21]. In this study, the model of the Kijima ship is adopted by taking into account the advance and tactical diameter [22]; the ship domain model is defined as follows:where , , , and represent the four radii of the ship domain. is the ship's course. is the coordinate of ship. where and are the advance and the tactical diameter, respectively.

If there are no and values for the own ship, the ship motion mathematical model is used to calculate their values, where different ships with different ship parameters obtain a specific ship domain. In the case of not knowing the target ship parameters, the following formula can be utilized [20]:where represents the speed of the ship. Then, the collision risk is determined by the principle of nonaggression on the two ship domains, and the related parameters are calculated as follows.

*(**1) The Parameters of Distinguishing Risk*. In this paper, the conventional DCPA and TCPA discriminant methods are not used, but the methods of Szlapczynski are imitated. We introduce the fuzzy ship domain, which is used to address the above four ship radii.where is used to represent the spatial collision risk in the fuzzy ship domain, which can be determined by the DDV. Here, indicates the most dangerous scenario, and indicates the most secure scenario. It can be seen that when , the ship domain is the reference domain. Figure 1 shows the principle of risk determination [14].