Elsevier

Ocean Engineering

Volume 192, 15 November 2019, 106542
Ocean Engineering

Ship predictive collision avoidance method based on an improved beetle antennae search algorithm

https://doi.org/10.1016/j.oceaneng.2019.106542Get rights and content

Highlights

  • A simplified 3-DOF ship model is proposed for collision avoidance.

  • A predictive collision avoidance strategy is proposed based on MPC.

  • The original BAS algorithm is improved in this study based on antenna performances.

Abstract

To enhance the real-time performance and reliability of existing ship collision avoidance methods by collision risk prediction, a predictive collision avoidance method based on an improved beetle antennae search (BAS) algorithm for underactuated surface vessels is proposed. Firstly, a simplified 3-DOF hydrodynamic model based on Abkowitz model is proposed, which provides a model basis for real-time prediction of ship states and collision risks. Referring to the idea of model predictive control (MPC), a predictive optimization strategy for real-time collision avoidance is established by minimizing the safety cost and the economic cost, i.e., collision risk and control changes at the same time. Specifically, the proposed simplified 3-DOF model is used as the state predictive model and the International Regulations for Preventing Collisions at Sea (COLREGs) is considered as the control constraints. To solve the optimization problem, an improved BAS algorithm is proposed to enhance the optimization performance of the original BAS algorithm under the known constraints, which is applied to solve the predictive collision avoidance problem. Simulation experiments under several typical encounter scenarios are carried out based on KVLCC2 ship model, and the effectiveness of the improved BAS based predictive collision avoidance method is verified.

Introduction

Ship collision avoidance has been always a hot topic in maritime safety area (Zhao, 1996), which has attracted a lot of attention in the maritime industry recently with the introduction of the concept of the intelligent ship (Yun and Wei, 2017, Thieme et al., 2018). Advanced theories and methods such as expert system (Sosnin, 2009, Lee and Rhee, 2001), fuzzy control (Zhao et al., 1995, Hong et al., 1999b, Hong et al., 1999a, Perera et al., 2012), line-of-sight guidance (Wilson et al., 2003), genetic algorithm (Kim et al., 2017, Tsou et al., 2010), evidence reasoning (Zhao et al., 2016), neural network (Simsir et al., 2014, Ahn et al., 2012), artificial potential field (Mousazadeh et al., 2018, Xue et al., 2011), and swarm intelligence optimization algorithm (Ma et al., 2018, Lazarowska, 2015, Tsou and Hsueh, 2010), have been applied in the studies of automatic collision avoidance in the past decades.

In this section, a survey of the existing ship collision avoidance methods and the related works of the algorithms adopted in this study (i.e., model predictive control and beetle antenna search) are introduced.

The collision avoidance problems solved by these methods can be briefly divided to two categories: traditional path generation methods and intelligent optimization methods.

Path generation can be divided to global path generation and local path generation. Global path generation methods are represented by grid network based methods, e.g., A* and its improved algorithms (Tanakitkorn et al., 2014, Ma et al., 2014, Singh et al., 2018, Liu et al., 2019). Local path generation methods are mainly represented by artificial potential field (APF) and its improved algorithms (Xue et al., 2011, Xue et al., 2012).

As a heuristic search algorithm, A* (Hart et al., 1968) considers both the start position and the destination, which has global optimality. Original A* algorithm has two main shortcomings, i.e., the low search efficiency with a large grid map and the unsmooth paths with a low-resolution grid map (Cheng et al., 2014). Hierarchical Planning (Wang et al., 2014, Cheng et al., 2014) is a commonly used approach to deal with low efficiency problem by pre-processing a higher-level graph before path planning. Additional cost constraint or post-process with respect to the smoothness (Fernandes et al., 2015, Song et al., 2019) are the commonly used approaches to obtain smooth paths in A*.

APF uses artificial gravitational and repulsive field to model the navigation environment with a small computation (Kim et al., 2011). The generated paths of APF are smoother than those of the grid-based methods (e.g., A*), which are more suitable for ships. Related works of APF (Lyu and Yin, 2018, Lazarowska, 2018) for ship path planning have been carried out in past years. However, suffering from local optimum and oscillation (Mohanan and Salgoankar, 2018), the original APF is also difficult to be implemented in a practical complex environment.

In summary, path generation methods are relatively mature in ship collision avoidance. In spite of this, most path generation methods regard the ship as a mass point with less consideration of the inertia and nonlinear dynamics of real ships, which needs further research.

With the development of intelligent optimization algorithms, the quantitative study of ship collision risk based on optimization methods (e.g., fuzzy mathematics, neural networks, swarm intelligence and machine learning, etc.) has become the trend in ship collision avoidance field (Szlapczynski and Szlapczynska, 2017).

Fuzzy mathematics (Hasegawa et al., 1989) has been applied in the fuzzy classification and reasoning of ship collision risk for a long time. In aspect of fuzzy classification, the appropriate membership function is a key issue. In Hasegawa et al. (1989), the triangular and trapezoidal membership functions are proposed to represent different fuzzy variables of collision avoidance parameters. In further researches (Hara and Hammer, 1993), the subjective feelings of the crew are also considered in fuzzy classification. In aspect of fuzzy reasoning, Perera et al. (2011) uses fuzzy maximum first (FMF) for reasoning, and several representative achievements are achieved (Perera et al., 2014, Perera et al., 2012). In Park et al. (2007) a case-based Reasoning (CBR) fuzzy mathematical method is also used for collision avoidance and obtained reliable results (Park and Kim, 2011, Park et al., 2007). Generally, the output of fuzzy mathematics relies on the membership functions set in advance, which needs more prior knowledge. Besides, neural networks (Inaishi and Matsumura, 1992) is another powerful approach which has the ability to model the uncertain factors in reasoning the ship collision risk. Generally, the neural networks is commonly combined with fuzzy mathematics (Ahn et al., 2012) and expert system (ES) (Simsir et al., 2014) to realize the collision avoidance.

With the development of computer science, swarm intelligence and machine learning methods have become hot topics in ship collision avoidance. Ant colony optimization (ACO) (Lazarowska, 2014, Lazarowska, 2015, Tsou and Hsueh, 2010) and particle swarm optimization (PSO) (Ma et al., 2018, Naeem et al., 2016, Chen and Huang, 2012, Liu et al., 2017) are the most commonly used swarm intelligence algorithms in ship collision avoidance, which can obtain good results with an appropriate fitness function including the collision risk. Similar to swarm intelligence, the model-free reinforcement learning methods (Cheng and Zhang, 2018, Kim et al., 2019, Shen et al., 2019) also attract much attention in ship collision avoidance recently. However, the relative high computation of swarm intelligence and reinforcement learning methods have become the main barriers in the practical applications in ship collision avoidance.

Generally speaking, intelligent optimization methods establish the collision risk model and use a series of optimization algorithms to achieve collision avoidance. Benefiting from the consideration of the ship collision risk index (CRI), and international regulations for preventing collisions at sea (COLREGs) (Cockroft and Lameijer, 2004), most intelligent optimization methods can obtain reasonable collision avoidance results in typical encounter scenarios under the premise of real-time ability.

For underactuated surface vessels, accurate tracking of the planned path (Harris et al., 1999) is also necessary in a reasonable collision avoidance system. If the system does not fully consider the constraints and maneuverability of the ship motion, or the real-time performance cannot meet the control requirements (Tran et al., 2002), the effect of collision avoidance will become worse, which may lead to a large difference between the actual results and the expectation. At present, it is still difficult to realize effective automatic collision avoidance in consideration of constraints, ship’s maneuvering characteristics and COLREGs.

As an effective method to deal with the control constraints, model predictive control (MPC) method has the characteristics of rolling prediction and on-line optimization (Zheng et al., 2014), which is more suitable for real ship control with large inertia and hysteresis (Zhang et al., 2017). In the field of collision avoidance, distributed model predictive control (DMPC) method (Zheng et al., 2017, Negenborn and Maestre, 2014) has already been used in multi-agent cooperative collision avoidance to solve the problem of motion conflict between multi-autonomous individuals. Zheng et al. (2017) has proposed a novel cost-effective robust distributed control approach for waterborne autonomous guided vessels (AGVs), which models the price of robustness by explicitly considering uncertainty and system characteristics in a tube-based robust control framework. Dai et al. (2017) has also applied DMPC to multi-UAV motion planning, and the virtual state trajectory with compatibility constraints is used to guide the multi-UAV motion planning instead of the real trajectory, which guarantees the stability of the whole system. In Perizzato et al. (2015), DMPC is introduced into the collision avoidance of multi-autonomous ground robots, and the path planning of multi-robot is realized with external and internal collision avoidance constraints. In the aspect of ship collision avoidance, scholars mainly regard the ship domain model as a constraint condition of MPC to solve the collision avoidance problem. Abdelaal et al. (2016) have proposed a path tracking and collision avoidance method based on Nonlinear MPC (NMPC) with elliptical ship domain, and applied the method to a 3-DOF ship model. After that, a disturbance observer is introduced in the controller to realize the effective control and collision avoidance under uncertain disturbances (Abdelaal et al., 2018).

Stochastic optimization algorithms, such as grey wolf optimization algorithm (GWO) (Yao et al., 2016), ant colony optimization (ACO) algorithm (Bououden et al., 2015), particle swarm optimization (PSO) algorithm (Chen et al., 2018, Wang et al., 2018b), etc, are widely used in complex optimization tasks, e.g., the dynamic programming in MPC. Among them, the PSO algorithm is most commonly used in various optimization problems due to its simple structure and fast convergence.

As a novel stochastic optimization algorithm similar to PSO, beetle antenna search (BAS) algorithm is proposed in 2017 (Jiang and Li, 2018), which has a more concise search strategy based on the foraging behavior of beetles. The effectivenesses of BAS-based algorithms have been validated in various optimization problems (Wang et al., 2018a, Sun et al., 2019, Lin et al., 2018, Lin and Li, 2018). Lin et al. (2018) use the BAS algorithm to solve the PID fine-tuning problem of the double closed-loop DC motor speed regulator. Sun et al. (2019) propose a BAS-based fine-tuning method for the back-propagation neural network (BPNN). Wu et al. (2019) propose a novel fall-back BAS algorithm for collision-free path planning. Due to the concise search strategy, BAS-based algorithms are considered to have great potential in solving optimization problems in MPC.

Although rich achievements have been obtained, there still exists several main drawbacks in existing ship collision avoidance methods:

(1) Most of the path generation methods take fewer considerations of the ship maneuverability, which may lead to a large gap between the actual collision avoidance results and the expectation.

(2) Existing real-time optimization based methods usually use static maneuvering characteristics (e.g., the turning radius and maximum heading change) to set constraints, and realize real-time collision avoidance by a delayed feedback, which cannot foresee the potential collisions.

(3) The premature and local optimum problems in optimization algorithms (e.g., the PSO and BAS) also affects the collision avoidance results.

In addition, the widely used ship hydrodynamic model has plenty of parameters, which also has influences on the real-time performance of collision avoidance. In this study, a simplified 3 degree of freedom (3-DOF) ship model is established and a predictive collision avoidance method is proposed based on MPC and an improved BAS algorithm. The main contributions of this study are briefly summarized as follows:

  • (1)

    A simplified 3-DOF ship model is proposed by ignoring higher-order terms of the Abkowitz model for collision avoidance, which reduces the complexity for prediction and optimization.

  • (2)

    A predictive collision avoidance strategy derived from MPC is proposed to give full considerations of ship maneuverability and real-time ability, which can predict potential collision risks and obtain feedback from the environment simultaneously.

  • (3)

    In order to solve the nonlinear optimization problem in MPC better, the original BAS algorithm is improved in this study based on antenna performances to defect the local optimum problem.

The remainder of this article is organized as follows. In Section 2, a simplified 3-DOF motion model based on Abkowitz model is proposed. In Section 3, a predictive collision avoidance strategy based on the simplified model, COLREGs and predictive control method is designed. In Section 4, an improved BAS algorithm is proposed, and the convergence of the proposed method is analyzed theoretically. In Section 5, ship collision avoidance experiments under typical encounter scenarios are carried out to verify the effectiveness of the proposed method by comparisons with the original BAS algorithm. In Section 7, conclusions and further research are presented.

Section snippets

Simplified 3-DOF ship dynamic model

The 3-DOF motion coordinate system of a underactuated surface vessel is shown in Fig. 1. Here, Ooxoyo is the inertial coordinate system of the vessel, Oxy is the co-rotational coordinate system of the vessel. u,v and r are the velocities in surge (body-fixed x), sway (body-fixed y) and yaw directions, respectively. δ and ψ are the rudder and heading angle of the vessel, respectively. β is the drift angle. Then the 3-DOF hydrodynamic model can be obtained as shown in Eq. (1). m(u̇vrxGr2)=X,m(

Collision avoidance based on predictive control

The proposed simplified model in Eq. (10) is used to predict the future states of the ship motion. Then, the ship collision risks in different encounter scenarios in finite time horizon are calculated based on the predicted states of the own ship and the target ship. Finally, both the safety factor (collision risk) and the economic factor (control changes) are considered comprehensively to form the optimization problem of collision avoidance.

Improved BAS algorithm for collision avoidance

At present, swarm intelligence and evolution algorithms, i.e., genetic algorithm (GA), particle swarm optimization (PSO) and ant colony search algorithm (ACO), have been applied in nonlinear optimization problems successfully. However, the essence of this kind of stochastic optimization methods represented by PSO is using a certain population of species to share the optimal value according to some strategy. When the population size is large, the prediction process in Eq. (18) in each iteration

Simulation experiments

Simulation experiments are carried out in two aspects:

(1) Maneuverability predictions of zig-zag tests and turning test are carried out based on the widely used KVLCC2 ship model and the proposed simplified 3-DOF hydrodynamic model for accuracy verification;

(2) Typical encounter scenarios (head-on, crossing, over-taking, etc.) are set up, and the collision avoidance simulations are conducted to verify the effectiveness of the proposed predictive collision avoidance method based on the improved

Summary

In summary, a simplified 3-DOF ship dynamic model is introduced and a predictive collision avoidance method is proposed based on model predictive control and an improved beetle antenna search (BAS) algorithm. The ship dynamic model is simplified by ignoring several higher-order terms in the Taylor extensions of the force and moment in Abkowitz model. Then a predictive collision avoidance strategy is proposed by applying the model predictive control method with the simplified ship model and

Conclusions and future works

The main works of this paper are concluded as follows:

(1) With respect to the simplified ship dynamic model, the zigzag tests and turning tests results show that the predictions of the proposed simplified 3-DOF model are accurate compared with the complete model, which indicates the effectiveness of the simplified model.

(2) With respect to the proposed improved BAS algorithm, the results in benchmark function tests and ship collision avoidance tests show that the improved BAS algorithm

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This research is supported by the Fundamental Research Funds for the Central Universities (No. 2019-YB-022), the High Technology Ship Project of Ministry of Industry and Information Technology (No. 2016050001), the Key Project of Science and Technology of Wuhan (201701021010132), the Open Project Program of Fujian University Engineering Research Center of Marine Intelligent Ship Equipment, Minjiang University, and financially supported by the Double First-rate Project of WUT (Wuhan university

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