Original articles
Path planning for autonomous underwater vehicle based on an enhanced water wave optimization algorithm

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Abstract

The water wave optimization (WWO) algorithm is inspired by shallow water wave theory and mainly simulates propagation, refraction and breaking to obtain the global optimal solution in the search space. Due to its premature convergence and low optimization efficiency, the basic WWO has a slow convergence speed and low calculation accuracy. To improve the overall optimization performance of the basic WWO, an enhanced WWO based on the elite opposition-based learning strategy and the simplex method (ESWWO) is proposed to solve the function optimization problem and path planning problem for an autonomous underwater vehicle (AUV). The elite opposition-based learning strategy increases the diversity of the population and enhances the global search ability to avoid falling into the local optimum. The simplex method has a fast search speed and strong local search ability to obtain a very accurate solution. The ESWWO algorithm can not only achieve complementary advantages to improve the optimization efficiency of the basic WWO but can also balance exploration and exploitation to obtain the global optimal solution. For the function optimization problem, the ESWWO has strong stability and robustness, and the fitness values of the ESWWO are better than those of other algorithms. For the AUV path planning problem, the ESWWO can avoid threat areas with a minimum fuel cost to obtain the optimal path. The experimental results show that the overall optimization performance of the ESWWO algorithm is superior to that of other algorithms, and thus, ESWWO is an effective and feasible method for solving the function optimization problem and AUV path planning problem.

Introduction

The oceans contain abundant marine biological resources, mineral resources and energy, which make them important assets for the sustainable development of mankind. Research and the rational use of the ocean have important guiding significance for human economic and social development. Autonomous underwater vehicle (AUV) technology provides a powerful tool for humans to explore the ocean. With the development of underwater robots towards autonomy, intelligence and remoteness, our demand for intelligent control and autonomous navigation technologies are increasing. AUV path planning is not only one of the key technologies to realize automation and intelligent navigation but is also an important link in whether a robot can accurately, safely and completely complete underwater tasks. The purpose of path planning is to make the AUV complete the tasks specified by the upper-level instructions faster and better and obtain an optimal or suboptimal path from the starting point to the target point according to some optimization criteria (such as the shortest path minimum energy consumption, etc.). Meanwhile, path planning can allow an AUV to avoid threat areas and reach the target point. Since the deep sea environment may have many unpredictable dangers and may be relatively difficult to approach, in actual underwater operations, an AUV can operate independently and complete many tasks without manual intervention, such as the following: marine hydrographic surveying and mine detection, military investigation and rescue, undersea inspection and data collection, ocean exploration and anti-submarine operations, drilling support and subsea construction, and underwater equipment laying and maintenance. The metaheuristic optimization algorithm is of great significance for the realization of safe navigation, concealed navigation and fast navigation for AUVs. Therefore, some novel metaheuristic algorithms have been proposed to solve the AUV path planning problem, including artificial bee colony (ABC) [7], cuckoo search (CS) [3], the dragonfly algorithm (DA) [15], moth–flame optimization (MFO) [14], particle swarm optimization (PSO) [2], the bat algorithm (BA) [27], the flower pollination algorithm (FPA) [28], etc.

Zheng designed a water wave optimization algorithm to solve the function optimization problem and perform high-speed train scheduling, and the results showed that the proposed algorithm had a strong global search ability for obtaining the optimal solution [33]. Zhang et al. proposed an improved WWO algorithm, which included the SCA algorithm and introduced an elite opposition-based learning strategy, to solve the function optimization problem [30]. Wu et al. introduced the elite opposition-based WWO, which included the elite opposition-based learning strategy, the local neighborhood search strategy and an improved propagation operator, for global optimization, and this method improved the convergence speed and calculation accuracy [25]. Zhang et al. applied a wind-driven WWO algorithm to solve the function optimization and engineering design problems, and the results showed that the proposed algorithm balanced exploration and exploitation to find the global optimal solution [31]. Hematabadi et al. presented the chaotic modified WWO to solve the multi-objective optimal bidding strategy problem, and the results showed that the method obtained a faster convergence speed and a better near-optimal solution than the unmodified WWO [4]. Shao et al. used a discrete WWO algorithm to solve the no-wait flow shop scheduling problem, and the results verified the effectiveness and feasibility of the method [18]. Shao et al. created a novel multi-objective discrete WWO to solve the multi-objective blocking flow-shop scheduling problem, and the results showed that the method minimized both the makespan and total flow time [19]. Jin et al. proposed a WWO to solve satellite stability, and the experimental results verified the effectiveness of the method [6]. Ibrahim et al. used a binary WWO to solve the feature selection problem, and the results showed that the proposed algorithm found a minimal subset of features that yielded the maximum classification accuracy [5]. Zhao et al. presented a hybrid discrete WWO to solve the no-idle flowshop scheduling problem, and the results showed that the proposed method was effective and feasible [32]. Zheng et al. tried to solve the combinatorial optimization problem using WWO, and the results of the proposed approach provided insights [34]. Zhou et al. proposed a WWO to determine the parameters of the PID controller for an AVR system, and the results showed that the proposed algorithm was more efficient​ and robust in improving the step response than other algorithm [37]. Zhou et al. applied a WWO to solve the optimal reactive power dispatch problem, and the results showed that the proposed algorithm had better overall performance at reducing the real power losses than other algorithms [36].

Zhu et al. introduced an integrated biologically-inspired self-organizing map to solve the task assignment and path planning of an AUV system, and the results showed that the proposed algorithm was effective and feasible for 3D underwater environments with obstacles [39]. Mahmoudzadeh et al. applied evolutionary algorithms to solve the path planning problem for an AUV rendezvous in a dynamic cluttered undersea environment and to generate the optimal or sub-optimal path [13]. Zeng et al. proposed the QPSO algorithm to optimize the trajectory of an AUV with ocean currents, and the results showed that the algorithm obtained the optimal path [29]. Khan et al. presented an AUV-assisted energy-efficient clustering method for a homogeneous UWSN in the Internet of Underwater Thing. In the method, the AUV not only collected data but also performed dynamic cluster head selection to achieve efficient loads [8]. Wang et al. explored the application of mixed integer nonlinear programming models to solve the trajectory planning problem for an AUV in the presence of currents and obstacles [22]. Wu proposed coordinated path planning for an unmanned aerial–aquatic vehicle and an AUV in an underwater target strike mission, and the results showed that the method could find the theoretically-optimal solution [24]. Sansmuntadas et al. discussed a path planning algorithm for underactuated vehicles with limited fields of view, and the experimental results verified the effectiveness of the algorithm [17]. Taheri et al. designed a randomized kinodynamic path planning algorithm for an AUV to obtain a feasible path from the starting point to the target point [21]. Lin et al. proposed a PSO-based dynamic routing algorithm that applied the stereo vision detection technique to the development of the underwater inspection task [11]. Zhuang et al. proposed a two-stage cooperative path planner for multiple AUVs operating in a dynamic ocean environment, and the results showed that the proposed algorithm could avoid collisions successfully and efficiently [40]. Zhou et al. presented an improved flower pollination algorithm to solve the UUV path planning problem, and the results showed that the proposed algorithm was more effective and feasible than the alternatives [35]. Teng et al. proposed an AUV localization and path planning algorithm to solve the terrain-aided navigation problem, and results showed that the proposed algorithm provided accurate TAN location results [12]. Yan et al. presented an AUV adaptive sampling path planning method based on online model prediction to conduct rapid observation of a coastal marine environment [26]. Sun et al. discussed a deep deterministic policy gradient to realize path following control of AUVs, and the results showed that the proposed method obtained the global optimal solution [20]. Lim et al. proposed selectively hybridized particle swarm optimization algorithms to perform constrained path planning of an AUV, and the results showed that the proposed algorithm generated the optimum path [10]. Barua et al. described algorithms for the guidance and control of an AUV for a specific identification mission in which the goal was to traverse an object of interest on the sea floor several times over a given geometric path [1]. Li et al. presented an AUV optimal path planning method for seabed terrain matching navigation to avoid certain areas, and the results showed that the proposed algorithm demonstrated high matching precision for each matched area [9].

WWO inspired by shallow wave theory mimics propagation, refraction and breaking to effectively search a solution space [33]. To improve the overall optimization performance of WWO, the elite opposition-based learning strategy [16] and the simplex method [38] are introduced into WWO to improve its convergence speed and calculation accuracy. The proposed algorithm is applied to solve the function optimization problem and AUV path planning problem. The experimental results show that the proposed algorithm can effectively balance exploration and exploitation to obtain the global optimal solution.

The remainder of this article is divided into the following sections: Section 2 introduces the WWO algorithm. Section 3 describes the ESWWO algorithm. Simulation tests and results analysis for the benchmark functions are described in Section 4. The ESWWO algorithm for solving the AUV path planning problem is presented in Section 5. Finally, Section 6 discusses the conclusions and future studies.

Section snippets

WWO

WWO mimics wave motion by performing propagation, refraction and breaking to obtain the optimal solution [33]. Each wave has two important properties: the wave height h and the wavelength λ. The optimization process progresses from deep water to shallow water. As the number of iterations increases, the wave height h becomes higher, the wavelength λ becomes shorter, and the fitness value becomes larger. The waveform is shown in Fig. 1 and the correspondence between the problem space and

ESWWO

It is easy for the basic WWO to prematurely converge and fall into the local optimum. To improve the convergence speed and calculation accuracy, the elite opposition-based learning strategy and the simplex method are combined with WWO. We propose ESWWO, which effectively balances the global search ability and the local search ability to obtain the optimal solution.

Experimental setup

The numerical experiment is set up on a computer with an Intel Core i7-8750H 2.2 GHz CPU, a GTX1060, and 8 GB of memory running Windows 10.

Benchmark functions

The 21 benchmark functions are applied to verify the feasibility and effectiveness of ESWWO. Table 4 gives some information about the functions. f1f7 are unimodal functions, f8f12 are multimodal functions, and f13f21 are fixed-dimension multimodal functions.

For all algorithms, the parameters are representative empirical values and are derived from the

Mathematical model

ESWWO is applied to solve the AUV path planning problem to verify the feasibility and effectiveness of the algorithm. The purpose of optimization is to obtain the optimal or near-optimal path. The transformation of the coordinate system is given in Fig. 46.

To accelerate the search speed and improve the calculation accuracy, the coordinate system Oxy needs to be converted into the coordinate system Oxy. For Oxy, the direction from the starting point to the target point is the positive

Conclusions and future studies

In this paper, an enhanced WWO based on the elite opposition-based learning strategy and the simplex method is used to solve the function optimization problem and AUV path planning problem. The purpose of the optimization is to find the global optimal solution and the shortest path. The elite opposition-based learning strategy expands the search range and increases the diversity of the population to enhance the global search ability of WWO. The simplex method accelerates the convergence speed

Acknowledgments

This work was partially funded by the National Nature Science Foundation of China under grant No. 51679057, and partly supported by the Province Science Fund for Distinguished Young Scholars No. J2016JQ0052. The authors would like to thank the editor and anonymous reviewers for the helpful comments and suggestions.

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