Hybrid Path Planning Strategy Based on Improved Particle Swarm Optimisation Algorithm Combined with DWA for Unmanned Surface Vehicles

Abstract

Path planning is one of the core issues in the autonomous navigation of an Unmanned Surface Vehicle (USV), as the accuracy of the results directly affects the safety of the USV. Hence, this paper proposes a USV path planning algorithm that integrates an improved Particle Swarm Optimisation (PSO) algorithm with a Dynamic Window Approach (DWA). Firstly, in order to advance the solution accuracy and convergence speed of the PSO algorithm, a nonlinear decreasing inertia weight and adaptive learning factors are introduced. Secondly, in order to solve the problem of long path and path non-smoothness, the fitness function of PSO is modified to consider both path length and path smoothness. Finally, the International Regulations for Preventing Collisions at Sea (COLREGS) are utilised to achieve dynamic obstacle avoidance while complying with maritime practices. Numerical cases verify that the path planned via the proposed algorithm is shorter and smoother, guaranteeing the safety of USV navigation while complying with the COLREGS.

1. Introduction

In recent years, the development of Unmanned Surface Vehicle (USV) technology has been relatively rapid [1,2,3]. The USV is an intelligent vehicle that can navigate autonomously and perform various tasks [4]. It has the advantages of no crew driving, risk reduction and efficiency improvement [5]. The USV also has a wide range of application fields; it plays an important role in underwater monitoring [6], maritime search and rescue [7] and target tracking [8,9,10]. Path planning is a non-negligible problem in autonomous navigation of the USV [11,12].

In recent years, with the improvement in path planning techniques, many efficient and practical path planning methods have emerged. Among them, Model Predictive Control (MPC) [13,14] is a common path planning method, which is characterised by solving an open-loop optimal control problem in a finite time domain to obtain the current control action. The MPC has been widely applied to path planning in uncertain environments [15]. Furthermore, popular local path planning algorithms include the Artificial Potential Field (APF) algorithm [16,17,18], Dynamic Window Algorithm (DWA) [19,20,21], etc. All these local path planning algorithms can plan paths in dynamic environments and enable safe avoidance of dynamic obstacles. However, local path planning algorithms mainly make decisions using the current environmental information. The mainstream global path planning algorithms include the A* algorithm [22,23], Rapidly Exploring Random Trees (RRT) algorithm [24,25,26], Ant Colony Optimisation (ACO) algorithm [27,28,29], etc. They have strong search ability and stability, and they are also used and improved by many scholars. For example, based on the A* algorithm, Gu et al. achieved collision avoidance for USVs by establishing risk and traffic models [30]. He et al. proposed a dynamic anti- collision A-star (DAA-star) algorithm based on the A* algorithm to achieve safe collision avoidance for USVs [31]. Considering the influence of wind, waves and dynamic obstacles, Lyridis et al. designed an improved ACO with a fuzzy logic algorithm, which has high solution precision and convergence speed [32].

Although these algorithms can plan better paths through different improvements, they cannot adapt to dynamic environments. The PSO algorithm is versatile and has global convergence [33,34]. It can take multiple factors into account and find a globally optimal solution in path planning. Therefore, the PSO algorithm is also widely used in path planning with constraints [35,36,37,38]. For example, considering the safety of autonomous underwater vehicles (AUVs), Zuo et al. designed an adaptive multi-population PSO algorithm to achieve safe collision avoidance of AUVs [39]. In addition, the PSO algorithm is well represented in USV path planning [40,41]. Considering the problems of low search accuracy, premature convergence and a local optimal in the PSO algorithm, many scholars have proposed different improvement methods and optimisation strategies [42,43]. For example, Wang et al. introduced opposition-based learning (OBL) and improved the inertia weights in the PSO algorithm so that the premature problem of the PSO algorithm was effectively avoided and a safe navigation path was planned for the USV [44]. Zhong et al. introduced mutations based on the PSO algorithm to enhance the search efficiency [45].

However, the PSO algorithm has low efficiency in some complex environments and cannot flexibly avoid obstacles in real time according to dynamic environments. This paper proposes a hybrid algorithm that combines the improved PSO (ANWPSO) algorithm with the DWA, and the COLREGS are incorporated to ensure navigation safety. The main contributions in this paper are as follows:

(1)

A nonlinear decreasing inertia weight and adaptive learning factors are adopted to effectively enhance the solution precision and the convergence speed of the PSO algorithm.

(2)

The path length and path smoothness are considered in the fitness function of the PSO algorithm to reduce path length and improve path smoothness.

(3)

The ANWPSO algorithm is combined with the DWA to achieve both global path planning and local path planning simultaneously.

(4)

The COLREGS are incorporated to reduce the collision risk of the USV.

The remainder of this paper is organised as follows: Section 2 describes the PSO algorithm, ANWPSO algorithm and the principles of the DWA. Section 3 describes the hybrid algorithm that combines the ANWPSO algorithm with the DWA. Section 4 verifies the superiority of the ANWPSO and the hybrid algorithm through simulation comparisons. Section 5 is the conclusion of the paper.

2. Algorithm Principles and Improvements

2.1. PSO Algorithm

The PSO algorithm finds the optimal solution of a problem by simulating cooperation and information sharing in a bird flock. Suppose the search space of the PSO algorithm is a D-dimensional space and N particles are randomly generated in this space, where each particle has velocity and position attributes.

For the i-th particle, its velocity and position can be represented by Equations (1) and (2):

$$v_i={\left(v_{i1},v_{i2},v_{i3},\cdots ,v_{iD}\right)}^T$$

(1)

$$x_i={\left(x_{i1},x_{i2},x_{i3},\cdots ,x_{iD}\right)}^T$$

(2)

For every iteration, the fitness value of each particle is calculated by the fitness function. Then, each particle depends on the currently known individual best position p_i and group best position p_g to guide its own movement. The individual best position p_i and the group best position p_g are represented by Equations (3) and (4):

$$p_i={\left(p_{i1},p_{i2},p_{i3},\cdots ,p_{iD}\right)}^T$$

(3)

$$p_g={\left(p_{g1},p_{g2},p_{g3},\cdots ,p_{gD}\right)}^T$$

(4)

For every iteration, the particle updates its own velocity according to Equation (5):

$$v_{id}^{k+1}=\omega v_{id}^k+c_1{r}_1\left(p_{id}^k-x_{id}^k\right)+c_2{r}_2\left(p_{gd}^k-x_{id}^k\right)$$

(5)

where k represents the current number of iterations. d represents the d-th dimension. $v_{id}^{k+1}$ represents the velocity and position of the i-th particle in the d-th dimension in the k-th iteration. $p_{id}^k$ represents the individual best position of the i-th particle in the d-th dimension in the k-th iteration. $p_{gd}^k$ represents the group best position of the i-th particle in the d-th dimension in the k-th iteration. $c_1$ is the individual learning factor, $c_2$ is the group learning factor and $\omega$ is the inertia weight. r₁ and r₂ are random numbers within the range of [0, 1].

The particle updates its own position according to Equation (6):

$$x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1}$$

(6)

where $x_{id}^{k+1}$ represents the position of the i-th particle in the d-th dimension in the k-th iteration.

The flowchart of the PSO algorithm is shown in Figure 1, with the following steps:

(1)

Initialize. N particles and their initial velocity and position are randomly generated.

(2)

Calculate the fitness value of each particle. If the fitness value of a particle is less than its own historical optimal solution, the individual best position is updated. If the optimal fitness value among all particles is less than the historical optimal solution of the particle group, the group best position is updated.

(3)

The velocity and position of each particle are updated according to Equations (5) and (6).

(4)

Determine if the iteration is over; if not, repeat steps (2) and (3). If yes, the PSO algorithm runs to the end.

2.2. The ANWPSO Algorithm

Although the PSO algorithm can find the global best solution through cooperation and information sharing between particles, it also has problems such as premature convergence, long planned path and path non-smoothness. In order to overcome these problems and to plan shorter and safer navigation paths for the USV, this paper proposes the ANWPSO algorithm, which is obtained by improving the inertia weight, learning factors and fitness function of the PSO algorithm.

2.2.1. Nonlinear Decreasing Inertia Weight

The inertia weight $\omega$ can balance the capacities of global and local searching. A small value of $\omega$ can increase the speed of local convergence and find the target solution more rapidly, and a large value of $\omega$ is able to enhance the global search capacity and jump out of the local optimal. In order to obtain better global search capacity and to enhance the convergence speed, nonlinear decreasing inertia weight $\omega$ is designed in this paper:

$$\omega ={\omega }_{max}-\left({\omega }_{max}-{\omega }_{min}\right)\left({\displaystyle \frac{2k}{K}}-{\left({\displaystyle \frac{k}{K}}\right)}^2\right)$$

(7)

where ${\omega }_{max}$ is the maximum value of the inertia weight, ${\omega }_{min}$ is the minimum value of the inertia weight, k is the current number of iterations and K is the total number of iterations.

2.2.2. Adaptive Learning Factors

The learning factors c₁ and c₂ reflect cooperation and information sharing among particles. A small learning factor can enhance the global search capability but will reduce the local convergence speed, and a large learning factor can enhance the local convergence capacity, but there will be a local optimal. When c₁ is zero, the particle loses the guidance of the individual cognitive component and no longer considers the effect of the individual best position. It is difficult for particles to converge to the target solution, only through cooperation and information sharing among particles. When c₂ is zero, the particle loses the guidance of the group cognitive component and no longer considers the effect of the group best position, which also makes it difficult for each particle working independently to find the target solution. When both c₁ and c₂ are zero, the particle loses the guidance of the individual and group cognitive components and thus loses the ability to search for the target solution.

Therefore, this paper designs adaptive learning factors. As the number of iterations increases, the learning factors c₁ and c₂ change adaptively with the number of convergence of the particles, specifically, as shown in Equations (8) and (9):

$$c_1={\left({\displaystyle \frac{M}{N}}\right)}^2\left(c_{1max}-c_{1min}\right)+c_{1min}$$

(8)

$$c_2={\left({\displaystyle \frac{M}{N}}\right)}^2\left(c_{2max}-c_{2min}\right)+c_{2min}$$

(9)

where M is the number of particles in the particle population that converge to the optimal solution. $c_{1max}$ and $c_{2max}$ are the maxima of c₁ and c₂, respectively. $c_{1min}$ and $c_{2min}$ are the minima of c₁ and c₂, respectively.

2.2.3. Fitness Function

We consider path length and path smoothness in the fitness function:

$$f={\mu }_1{f}_1+{\mu }_2{f}_2$$

(10)

where f denotes the total fitness value, $f_1$ denotes the path length fitness function and $f_2$ is the path smoothness fitness function. ${\mu }_1$ and ${\mu }_2$ are weighting coefficients and take ${\mu }_1={\mu }_2={\displaystyle \frac{1}{2}}$.

Suppose the generated path of the i-th particle is formed by m nodes, the coordinate of the j-th node is $P_j(x_j,y_j)$ and the coordinate of the (j+1)-th node is $P_{j+1}(x_{j+1},y_{j+1})$. Then, the path length is given in Equation (11):

$$f_1=\sum _{j=1}^{m-1}\sqrt{{(x_{j+1}-x_j)}^2+{(y_{j+1}-y_j)}^2}$$

(11)

It can be seen that the smaller f₁ is, the shorter the length is.

As shown in Figure 2, for the steering angle between the path segments, set the vectors formed by two neighbouring nodes P_j and P_j+1 with their own previous nodes as ${\overrightarrow{V}}_j$ and ${\overrightarrow{V}}_{j+1}$, respectively; then, the steering angle ${\theta }_j$ between the path segments is:

$$cos{\theta }_j={\displaystyle \frac{{\overrightarrow{V}}_j·{\overrightarrow{V}}_{j+1}}{\left|{\overrightarrow{V}}_j\right|·\left|{\overrightarrow{V}}_{j+1}\right|}}$$

(12)

$${\theta }_j={\displaystyle \frac{{180}^{°}}{\pi }}arccos\left({\displaystyle \frac{{\overrightarrow{V}}_j·{\overrightarrow{V}}_{j+1}}{\left|{\overrightarrow{V}}_j\right|·\left|{\overrightarrow{V}}_{j+1}\right|}}\right)$$

(13)

The smoothness value of the path is set according to the change in the steering angle ${\theta }_j$. The details are shown in Equations (14) and (15):

$$f_j=\left\{\begin{array}{cc}0,& {\theta }_j=0^{°}\\ 30,& 0^{°}<{\theta }_j<{90}^{°}\\ 60,& {\theta }_j={90}^{°}\\ 90,& {90}^{°}<{\theta }_j<{180}^{°}\end{array}\right.$$

(14)

$$f_2=\sum _{j=2}^{m-1}{f}_j$$

(15)

In Equation (14), the smaller the steering angle ${\theta }_j$ is, the smaller the smoothness value is, which shows that the path segment is smoother. The total fitness value f is obtained by substituting Equations (11) and (15) into Equation (10). With decreasing f, the planned path is more compliant.

2.3. DWA

The DWA can convert the positional obstacle avoidance question for USVs into an optimisation question with speed constraints, and it seeks the target solution through a dynamic window that varies with the motion of the USV. Then, the algorithm selects the optimal path by predicting the motion trajectories of the USV at various combinations of velocities and evaluating the predicted trajectories using an evaluation function. In the velocity space, the velocity (v,w) of the USV needs to be constrained.

Firstly, the velocity constraints of the USV are shown in Equation (16):

$$V_1=\left\{\left.(v,w)\right|v\in [v_{min},v_{max}],w\in [w_{min},w_{max}]\right\}$$

(16)

where v_max and w_max represent the maximum linear velocity and angular velocity of the USV, respectively. v_min and w_min represent the minimum linear velocity and angular velocity of the USV, respectively.

Secondly, there is a maximum and minimum acceleration constraint on the USV. The details are shown in Equation (17):

$$V_2=\left\{\left(v,w\right)\left|v\in [v_c-a_{\mathrm{v}max}\Delta t,v_c+a_{\mathrm{v}max}\Delta t],w\in [w_c-a_{\mathrm{w}max}\Delta t,w_c+a_{\mathrm{w}max}\Delta t]\right.\right\}$$

(17)

where v_c and w_c represent the current linear velocity and angular velocity of the USV, respectively. $a_{vmax}$ denote the maximum acceleration. $a_{wmax}$ denote the maximum angular acceleration.

Finally, in order for the USV to stop before colliding with obstacles, the speed range of the USV is shown in Equation (18):

$$V_3=\left\{\left(v,w\right)\left|v\in \left[v_{min},\sqrt{2dist\left(v,w\right)a_{\mathrm{v}max}}\right],w\in \left[w_{min},\sqrt{2dist\left(v,w\right)a_{\mathrm{w}max}}\right]\right.\right\}$$

(18)

where dist(v,w) represents the closest distance to the obstacle on the corresponding trajectory at (v,w).

The range of velocity constraints in velocity space is the intersection of $V_1$, $V_2$ and $V_3$, that is, $V=V_1\cap V_2\cap V_3$. The DWA evaluates the simulated trajectories in terms of azimuth, distance from obstacles and navigation speed. Thus, the evaluation function of the DWA is shown in Equation (19):

$$G(v,w)=\sigma \left(\alpha H\right(v,w)+\beta O(v,w)+\gamma V(v,w\left)\right)$$

(19)

where H(v,w), O(v,w) and V(v,w) denote the azimuth evaluation factor, the distance evaluation factor and the speed evaluation factor, respectively. $\sigma$ is the smoothing function. $\alpha$, $\beta$ and $\gamma$ denote the weighting coefficients of H(v,w), O(v,w) and V(v,w), respectively.

Because the evaluation function G(v,w) is maximised, H(v,w) is shown in Equation (20):

$$H(v,w)=\pi -\delta$$

(20)

where $\delta$ represents the angle between the target point and the heading of the USV.

Three evaluation factors are normalised:

$$\sigma H(v,w)=normalize\_H\left(u\right)={\displaystyle \frac{H\left(u\right)}{{\displaystyle \sum _{u=1}^S}H\left(u\right)}}$$

(21)

$$\sigma O(v,w)=normalize\_O\left(u\right)={\displaystyle \frac{O\left(u\right)}{{\displaystyle \sum _{u=1}^S}O\left(u\right)}}$$

(22)

$$\sigma V(v,w)=normalize\_V\left(u\right)={\displaystyle \frac{V\left(u\right)}{{\displaystyle \sum _{u=1}^S}V\left(u\right)}}$$

(23)

where S and u represent the total number of sampling groups at a certain time and the u-th sampling trajectory, respectively.

3. Hybrid Algorithm

3.1. ANWPSO Algorithm Combined with DWA

In this paper, we propose a hybrid algorithm that combines the ANWPSO algorithm and DWA. The flowchart of the hybrid algorithm is illustrated in Figure 3, and the specific steps are given below:

(1)

Establish the simulation environment and initialise parameters.

(2)

Calculate the fitness value f of the particle according to Equation (10).

(3)

Determine whether the fitness value f of the particle is smaller than the fitness value $f_{pi}$ corresponding to the individual best position. If f is smaller than $f_{pi}$, update the individual best position. If f is not smaller than $f_{pi}$, retain the individual best position.

(4)

Determine whether the fitness value f of the particle is smaller than the fitness value $f_{pg}$ corresponding to the group best position. If f is smaller than $f_{pg}$, update the group best position. If f is not smaller than $f_{pg}$, retain the group best position.

(5)

Update the velocity and position of the particle according to Equations (5) and (6).

(6)

Determine whether the iteration is over. If not, return to step (3). If the iteration ends, output the optimal solution and generate the optimal global path.

(7)

Select key nodes in the optimal global path as sub-target points for local path planning.

(8)

Establish velocity space and sample the velocities of the USV.

(9)

Predict trajectories for each group of sampled velocities and evaluate the predicted trajectories according to Equation (19).

(10)

Select the optimal predicted trajectory based on the evaluation results and record the velocity and position corresponding to the optimal trajectory.

(11)

Determine whether the reached sub-target point is the target point. If not, return to step (8). If the sub-target point is the target point, the run ends and outputs the optimal local path.

3.2. COLREGS

To ensure the navigational safety of USV, the COLREGS are incorporated into the hybrid algorithm in this paper. We set constraints on the sampling angular velocity in the DWA in combination with the COLREGS in this paper. Specifically, the sampled angular velocity is set to a positive value when avoiding to the left, and it is set to a negative value when avoiding to the right. Based on these constraints, the sampling angular velocity of the DWA is filtered to achieve an effective combination of the COLREGS and DWA.

We mainly simulate head-on, overtaking and crossing in this paper. For these three encounter situations, the COLREGS are as follows, with specific collision avoidance situations shown in Figure 4.

(1)

Head-on: when two ships encounter on opposite or nearly opposite directions resulting in danger of collision, each ship shall turn to the right and then pass on the left of another ship.

(2)

Overtaking: when a ship pursues another ship from behind, it should make way for another ship and pass on the left of another ship.

(3)

Crossing: when two ships cross, resulting in danger of collision, and if another ship is on the right of one’s own ship, give way to another ship.

It is difficult to distinguish the type of encounter due to the good flexibility of USVs. Therefore, the type of encounter is judged by comparing the heading angles of two ships in this paper. As shown in Figure 5, the two ships form a situation of head-on when the angle range between the two ships is in [0°, 22.5°] and [337.5°, 360°]. The two ships form a situation of crossing when the angle range between the two ships is in [22.5°, 112.5°] and [247.5°, 337.5°]. When the heading angle between the two ships is within [122.5°, 247.5°], the two ships form an overtaking situation.

4. Simulation and Analysis

4.1. Simulation Environment and Parameters

To validate the efficiency of the proposed method, the PSO algorithm, the PSO algorithm with nonlinear decreasing inertia weight (NWPSO), the PSO algorithm with adaptive learning factors (APSO) and the ANWPSO algorithm are simulated and compared, respectively. The parameters of the four algorithms are given in

Table 1. Parameter setting for each algorithm.

Algorithm	Parameter	Value
	Inertia weight $\omega$	0.8
PSO	Individual learning factor c1	2
	Group learning factor c2	2
	Inertia weight $\omega$	0.8
APSO	Individual learning factor c1	Changes according to Equation (13) and the range is 0.4 to 1.4.
	Group learning factor c2	Changes according to Equation (14) and the range is 0.2 to 1.2.
	Inertia weight $\omega$	Nonlinear decreasing according to Equation (11) and the range is 0.4 to 1.2.
NWPSO	Individual learning factor c1	2
	Group learning factor c2	2
	Inertia weight $\omega$	Nonlinear decreasing according to Equation (11) and the range is 0.4 to 1.2.
ANWPSO	Individual learning factor c1	Changes according to Equation (13) and the range is 0.4 to 1.4.
	Group learning factor c2	Changes according to Equation (14) and the range is 0.2 to 1.2.

.

In this paper, a grid method is used for building the simulation map, which divides the navigation map into a series of square grids of the same size. Then, it marks the corresponding square grids according to the location of obstacles. The simulation map is selected to have an area of 100 m × 100 m and is divided into 100 × 100 square grids in this paper. As shown in Figure 6, the actual area of each square grid is 1 m × 1 m. The black and white areas represent obstacles and the water surface, respectively.

4.2. Simulation and Comparison

In this paper, PSO, APSO, NWPSO and ANWPSO are adopted for path planning of USVs, respectively. The performance of the four algorithms is compared and tested in terms of planned path length and path smoothness. The total number of populations for all four algorithms is set to 100 and the maximum number of iterations is 200 in the simulation experiments. The four algorithms are run 20 times, respectively.

From 20-time simulation experiments, the planned shortest paths from the four algorithms are shown in Figure 7. The longest path, shortest path, average path and variance of the four algorithms in these 20-time simulations, respectively, are listed in

Table 2. Comparison of path lengths planned by four algorithms in 20-time simulation experiments.

Algorithm	Longest Path/m	Shortest Path/m	Average Length/m	Variance/m2
ANWPSO	98.22	92.75	95.12	1.96
NWPSO	103.43	95.60	98.69	2.94
APSO	107.21	99.18	103.73	3.68
PSO	112.13	103.04	107.70	5.23

The average length and variance of the path are results of 20-time simulation experiments.

. ANWPSO reduces 5.03%, 8.38% and 12.40% more in the longest paths planned and reduces 2.98%, 6.49% and 9.98% more in the shortest paths than NWPSO, APSO and PSO, respectively. In 20-time simulation experiments, the average path length planned by ANWPSO reduces 3.62%, 8.30% and 11.68% more than the other three algorithms, respectively. Moreover, the performance of the ANWCPSO algorithm is shown to be more stable through the variance value.

The number of path turning points for the four algorithms in 20-time simulation experiments is shown in

Table 3. Comparison of number of path turning points planned by four algorithms in 20-time simulation experiments.

Algorithm	Maximum Number of Turning Points	Minimum Number of Turning Points	Average Number of Turning Points
ANWPSO	5	3	3.95
NWPSO	9	6	7.50
APSO	12	9	9.85
PSO	16	7	12.20

The average of path turning points is the result of 20-time simulation experiments.

. By analysing 20-time simulation results, the maximum and minimum number of turning points planned by ANWPSO are smaller than those of the other three algorithms, and the average number of turning points of the paths planned by ANWPSO is reduced by 47.33%, 59.90% and 67.62% more than that of NWPSO, APSO and PSO, respectively.

Figure 8 shows the corresponding convergence curves for the four algorithms. The fitness value of ANWPSO converges to the optimum at the 15th iteration, while NWPSO, APSO and PSO converge to the optimal fitness value at the 20th, 28th and 51st iterations, respectively. ANWPSO is 25%, 46.43% and 70.59% ahead of schedule compared to the other three algorithms. The optimal fitness values for ANWPSO, NWPSO, APSO and PSO are 91.38, 95.60, 99.18 and 103.04, respectively.

According to the simulation results, the convergence speed of ANWPSO is faster than that of the other three algorithms. And due to the path length and path smoothness being considered in the fitness function of the ANWPSO algorithm, this can effectively shorten the path length and improve the smoothness of the path.

4.3. The Planning Capabilities of the Hybrid Algorithm Based on the COLREGS

To validate the path planning capability of the hybrid algorithm after incorporating the COLREGS in multi-ship encounters, this paper simulates the collision avoidance situation between two ships in head-on, overtaking and crossing. The parameters of the DWA are set as follows: $\alpha$ = 0.4, $\beta$ = 0.2, $\gamma$ = 0.4, the prediction time is 3 s and the sampling time is 0.5 s. The parameters of the USV are shown in

Table 4. Parameters of USV.

Parameter	Value	Parameter	Value
Total mass	21.5 kg	Maximum angular speed	0.5 rad/s
Length	1.40 m	Acceleration range	±1 m/s2
Width	0.65 m	Angular acceleration range	±0.3 rad/s2
Maximum speed	2.0 m/s	Endurance time	2 h

.

(1)

Head-on: As shown in Figure 9, the USV is in the opposite direction of the obstacle ship, and the USV turns to the right according to the COLREGS to avoid collision. After the USV navigates to a safe distance, it will keep navigating along the global path towards the target point.

(2)

Overtaking: As shown in Figure 10, when the USV is overtaking the obstacle ship, the USV turns to the left according to the COLREGS to avoid collision. After the USV navigates to a safe distance, it will keep navigating along the global path towards the target point.

(3)

Crossing: As shown in Figure 11, when the obstacle ship is laterally in front of the starboard of the USV, the USV turns to the right according to the COLREGS to give way to the obstacle ship and passes astern of it. After the USV navigates to a safe distance, it will keep navigating along the global path towards the target point.

In the case of head-on, overtaking and crossing situations, the navigation direction and status of the obstacle ship are both uncertain. The USV may avoid the obstacle ship from the left or right side by using the DWA, and the avoidance direction is random. There is a high risk of collision between the USV and the obstacle ship. By introducing the COLREGS, the USV will avoid in accordance with the prescribed avoidance rules, thereby significantly improving the safety of avoidance.

The heading angle variations of the USV in the three encounter types are shown in Figure 12, Figure 13 and Figure 14, which show the linear and angular velocity variations of the USV in the three encounter types, respectively. Through simulation experiments on the three encounter types, it can be seen that the proposed hybrid algorithm is able to safely avoid the obstacle ship according to the COLREGS, which ensures the navigational safety of the USV in a multi-ship encounter.

5. Discussion

In this paper, a hybrid path planning algorithm is proposed by combining the ANWPSO algorithm and DWA, and the COLREGS are introduced to ensure the navigation safety of USVs in multi-ship encounters. The simulation and comparison of the PSO algorithm, APSO algorithm, NWPSO algorithm and ANWPSO algorithm show that the ANWPSO algorithm can plan shorter and smoother global paths and reduce the number of iterations at the same time. This is due to the fact that the nonlinear decreasing inertia weight and adaptive learning factors are introduced in the PSO algorithm, and the fitness function is improved by considering the path length and path smoothness. This improved method can effectively enhance the performance of the algorithm and plan better paths. Three multi-ship encounter scenarios are simulated to demonstrate that the hybrid algorithm incorporating the COLREGS ensures USVs can safely avoid the obstacle ship. These results show that with the introduction of the COLREGS, USVs can safely avoid collisions in accordance with the rules when encountering an obstacle ship. It effectively reduces the risk of collision and improves navigational safety.

Furthermore, the algorithm proposed in this paper has some limitations. It only considers the collision risk of USVs in multi-ship encounters. We will further consider the effects of uncertain factors such as ocean currents in our future research.

6. Conclusions

In this paper, we propose a hybrid algorithm that combines the ANWPSO algorithm and DWA for path planning of the USV. To overcome the shortcomings of the PSO algorithm and plan a better global path, the ANWPSO algorithm is proposed by incorporating a nonlinear decreasing inertia weight and adaptive learning factors into the PSO algorithm and considering the path length and path smoothness in the fitness function. Secondly, the ANWPSO algorithm is combined with the DWA, and the DWA is utilised to plan the local path of the USV. In addition, the COLREGS are introduced in the hybrid algorithm considering various encounter situations. The simulation comparison with the NWPSO algorithm, APSO algorithm and PSO algorithm shows that the proposed ANWPSO algorithm can effectively accelerate the convergence speed, improve the path smoothness and shorten the path length. The simulation of the three encounter types shows that the proposed hybrid algorithm ensures USVs safely avoid obstacle ships and reduces the collision risk of USVs.

However, the proposed hybrid algorithm ignores the effects of environmental factors such as marine currents, and it has some limitations. We will further consider the influence of environmental factors in future research and perform practical tests to ensure that the proposed method can work safely and reliably in various practical environments.