Path Planning of Deep-Sea Landing Vehicle Based on the Safety Energy-Dynamic Window Approach Algorithm

Abstract

To ensure the safety and energy efficiency of autonomous sampling operations for a deep-sea landing vehicle (DSLV), the Safety Energy-Dynamic Window Approach (SE-DWA) algorithm was proposed. The safety assessment sub-function formed from the warning obstacle zone and safety factor addresses the safety issue arising from the excessive range measurement error of forward-looking sonar. The trajectory comparison evaluation sub-function with the effect of reducing energy consumption achieves a reduction in path length by causing the predicted trajectory to deviate from the historical trajectory when encountering “U”-shaped obstacles. The pseudo-power evaluation sub-function with further energy consumption reduction ensures optimal linear and angular velocities by minimizing variables when encountering unknown obstacles. The simulation results demonstrate that compared with the Minimum Energy Consumption-DWA algorithm, the SE-DWA algorithm improves the minimum distance to an actual obstacle zone by 68% while reducing energy consumption by 11%. Both the SE-DWA algorithm and the Maximum Safety-DWA (MS-DWA) algorithm ensure operational safety with minimal distance to the actual obstacle zone, yet the SE-DWA algorithm achieves a 24% decrease in energy consumption. In conclusion, the path planned by the SE-DWA algorithm ensures not only safety but also energy consumption reduction during autonomous sampling operations by a DSLV in the deep sea.

1. Introduction

The abundance of marine resources has attracted global attention as resources, energy, and space available on land are gradually diminishing [1,2]. The Deep-Sea Landing Vehicle (DSLV) is an autonomous deep-sea equipment capable of long-term, large-scale, and short-distance refinement operations in the deep-sea environment [3,4]. There is a huge challenge for DSLV to complete autonomous sampling operations because the forward-looking sonar has a large ranging error caused by-deep sea noise and the battery power of the DSLV is limited. Therefore, planning a safe and energy-efficient path holds significant importance for DSLV in autonomous sampling operations.

Path planning is categorized into global path planning and local path planning. Global path planning relies on accurate global maps to efficiently achieve collision-free and shortest path planning [5,6]. Local path planning is real-time path planning in unknown environments based on data collected by relevant sensors such as LiDAR and forward-looking sonar, with higher requirements for path safety, smoothness, and traceability [7,8,9]. The Dynamic Window Approach (DWA) algorithm, one of the classical algorithms for two-dimensional local path planning, generates trajectories and assigns scores through feasible velocity combinations to directly determine the optimal velocity [10,11]. The algorithm considers the robot’s physical constraints, environmental factors, and current state comprehensively without requiring path following.

Xin et al. [12] proposed an Enhanced DWA algorithm that takes the distance function as the weight of the target-oriented coefficient, which effectively optimizes the stability of the mobile robot during operation with lower angular velocity dispersion and less energy consumption. However, this algorithm has a longer runtime compared with the DWA algorithm. While using this algorithm for autonomous sampling operations can reduce energy consumption in the propulsion system, it may increase energy consumption in other systems such as positioning and communication. Additionally, it does not account for safety concerns in the deep-sea environment.

Wang et al. [13] proposed an ACO-DWA algorithm that addresses the issue of poor obstacle avoidance performance for robots in high-density obstacle environments and unknown obstacle static environments. This algorithm effectively addresses safety concerns for DSLVs in the deep-sea environment. However, it lacks an energy-related evaluation sub-function, leading to an inability to reduce the DSLV’s energy consumption during autonomous sampling operations.

Masato Kobayashi et al. [14] proposed the DWV (Dynamic Window Approach with Virtual Manipulators) algorithm, which enhances the robot’s success rate in reaching the target point by generating more predictive trajectories in narrow or dynamic environments. While this algorithm can ensure a certain degree of energy reduction by reducing the path length, the safety of DSLV is not guaranteed when applying this algorithm for autonomous sampling operations.

Figure 1 illustrates the deep-sea autonomous sampling operations for DSLV. The application of the DWA algorithm for autonomous sampling operations in the deep sea has two deficiencies. (1) The safety of the DSLV is considerably compromised when encountering ground obstacles such as underwater ridges in unknown deep-sea environments. This compromise is mainly due to the degradation of the accuracy of forward sonar ranging caused by deep-sea noise. The detected obstacle volume may be smaller than the actual volume due to the decrease in accuracy [15,16]. (2) The limited energy of DSLV will be depleted more quickly due to the absence of energy consumption-related evaluation sub-functions in the DWA algorithm [3].

To address the above issues, improvements and additional evaluation sub-functions have been introduced to ensure the safety and reduce energy consumption during autonomous sampling operations. The safety assessment sub-function, formed of warning obstacle zones and safety factors, addresses safety concerns arising from the decreased accuracy of forward-looking sonar due to underwater noise and other factors. The trajectory comparison evaluation sub-function reduces energy consumption by decreasing the path length when encountering “U”-shaped obstacles. The pseudo-power evaluation sub-function reduces energy consumption by optimizing linear and angular velocities when encountering unknown deep-sea obstacles.

The subsequent sections of this paper are outlined as follows: Section 2 presents the kinematic modelling of the DSLV. Section 3 introduces the fundamental principles of the SE-DWA algorithm and the flows of applying it to the DSLV for deep-sea autonomous sampling operations. Section 4 determines the coefficients of the SE-DWA algorithm’s evaluation functions and compares them with the DWA algorithm in terms of safety and energy consumption under a deep-sea environmental map. Section 5 concludes the findings of this article.

2. Kinematic Modelling of DSLV

Flat abyssal plain areas are commonly chosen to enhance the success rate of autonomous sampling operations for DSLV [17]. The problem is simplified to a two-dimensional plane for algorithmic research, as the terrain changes in these areas are minor and negligible.

The DSLV developed in this paper utilizes a dual-motor rear-wheel drive system, controlled differentially to manage its forward, backward and steering movements. The schematic diagram of bilateral motor drive of DSLV is shown in Figure 2.

The DSLV kinematic modelling diagram is shown in Figure 3. In the Cartesian coordinate system O-XY, let $x_{(t)}$ and $y_{(t)}$ represent the horizontal and vertical coordinates of the geometric center of the DSLV, respectively, and $\theta$ denotes the heading angle. The project team reinforced the track structure’s tensioner brackets to withstand the impact of landing on the seabed during the design phase of the DSLV. Furthermore, the DSLV maintains a slow crawling speed when operating on a flat sandy bottom. For analysis purposes, it can be assumed that the DSLV’s center of mass aligns with the geometric center. Consequently, the linear and angular velocities of its center of mass are as follows:

$$\left\{\begin{array}{l}v=\omega R=\frac{v_o+v_i}{2}\hfill \\ \omega =\frac{v_o-v_i}{B}\hfill \end{array}\right.$$

(1)

where the expressions for $v_o$ and $v_i$ are as follows:

$$\left\{\begin{array}{l}{v}_o=(1-s_1)·r_1·{\omega }_1\hfill \\ v_i=(1-s_2)·r_1·{\omega }_2\hfill \end{array}\right.$$

(2)

where $R$ represents the steering radius; $v_o$ and $v_i$ denote the linear velocities of the left and right tracks, respectively; $B$ indicates the center distance between the left and right tracks; $s_1$ and $s_2$ refer to the slip rates of the left and right tracks, respectively; $r_1$ stands for the radius of the left and right track drive wheels; and ${\omega }_1$ and ${\omega }_2$ represent the angular velocities of the left and right track drive wheels, respectively.

By combining Equation (1) and Figure 3, the position coordinates of the DSLV at moment $t$ can be obtained as $(x(t),y(t),\phi (t))$, as shown in Equation (3), and the position coordinates corresponding to moment $t+1$ can be obtained as $(x(t+1),y(t+1),\phi (t+1))$, as shown in Equation (4).

$$\left\{\begin{array}{l}x(t)=v·\cos \theta ·t\hfill \\ y(t)=v·\sin \theta ·t\hfill \\ \phi (t)=\omega ·t\hfill \end{array}\right.$$

(3)

$$\left\{\begin{array}{l}x(t+1)=x(t)+{\displaystyle {\int }_t^{t+1}(v·\cos \theta ·t)}dt\hfill \\ y(t+1)=y(t)+{\displaystyle {\int }_t^{t+1}(v·\sin \theta ·t)}dt\hfill \\ \phi (t+1)=\phi (t)+{\displaystyle {\int }_t^{t+1}(\omega )}dt\hfill \end{array}\right.$$

(4)

The DSLV autonomous sampling control module model is shown in Figure 4.

3. The SE-DWA Algorithm

3.1. Velocity Constraints

The speed window of the SE-DWA algorithm is illustrated in Figure 5. It is constrained by speed limit ($E_v$), safety limits ($E_o$), and the acceleration and deceleration limits of the motor drive ($E_a$) [18]. The expression ($E_{all}$) for the velocity window of the SE-DWA algorithm is as follows:

$$E_{all}=E_v\cap E_o\cap E_a$$

(5)

(1)

Speed limit

The maximum and minimum speed limits for DSLV are as follows:

$$E_v=\{(v,\omega )|v\in [0,v_{max}],\omega \in [{\omega }_{min},{\omega }_{max}]\}$$

(6)

where $v_{max}$ represent the maximum linear velocities, and ${\omega }_{min}$ and ${\omega }_{max}$ represent the minimum and maximum angular velocities.

(2)

Security restriction

The DSLV limits the speed window to avoid collisions with obstacles, and the limited speed window is as follows:

$$E_o=\left\{\begin{array}{l}\{(v,\omega )|v\le \sqrt{2·dis{t}_{obs}(v,\omega )·\dot{v}}\cap \omega \le \sqrt{2·dis{t}_{obs}(v,\omega )·\dot{\omega }}\}\hspace{1em}{L}_{dist}>2{\sigma }_{max}^{sonar}\hfill \\ \{(v,\omega )|v\le \sqrt{2·dis{t}_{warn}(v,\omega )·\dot{v}}\cap \omega \le \sqrt{2·dis{t}_{warn}(v,\omega )·\dot{\omega }}\} 0<L_{dist}\le 2{\sigma }_{max}^{sonar}\hfill \end{array}\right.$$

(7)

where $dis{t}_{obs}(v,\omega )$ represents the distance on the trajectory corresponding to the velocity combination to the nearest obstacle zone; $dis{t}_{warn}(v,\omega )$ represents the distance on the trajectory corresponding to the velocity combination to the nearest warning obstacle zone; $L_{dist}$ represents the distance between the edges of the two nearest obstacle zone; and ${\sigma }_{max}^{sonar}$ represents the maximum error value of the forward sonar ranging distance.

(3)

Reachable speed limit

The range of DSLV speed combinations in a sampling period is as follows:

$$E_a=\{(v,\omega )|v\in [v_0-\dot{v}·\Delta t,v_0+\dot{v}·\Delta t],\omega \in [{\omega }_0-\dot{\omega }·\Delta t,{\omega }_0+\dot{\omega }·\Delta t]\}$$

(8)

where $v_0$ and ${\omega }_0$ represent the current linear and angular velocities of the DSLV; $\dot{v}$ and $\dot{\omega }$ represent the maximum linear accelerations and angular accelerations of the DSLV; and $\Delta t$ represents the sampling period.

3.2. Evaluation Function

3.2.1. Safety Evaluation Sub-Function

The DWA algorithm requires real-time acquisition of obstacle positions as a component of its local path-planning approach. However, the precision of forward sonar ranging data in the deep-sea environment is lower and the errors are larger compared with LiDAR ranging data on land [16,19]. The inability to guarantee the safety of autonomous sampling operations on the seafloor emphasizes the need to address this issue. In this section, the obstacle avoidance evaluation sub-function within the DWA algorithm will be enhanced and will be named the safety evaluation sub-function.

The safety evaluation sub-function calculates its cost based on the distance between the predicted trajectory and obstacles, multiplied by the safety coefficient corresponding to the warning obstacle zone. Figure 6 illustrates the method for computing this cost, using the example of cost calculation for the i-th predicted trajectory and j-th obstacle. To prevent a sharp increase in cost due to a high number of obstacles in the local map, a threshold radius $R_{safe}$ is established, with the geometric center of the DSLV as the point of origin. When the j-th obstacle located within this circle, the cost associated with the i-th predicted trajectory encountering the j-th obstacle is as follows:

$$cos{t}_{ij}^{safe}=\eta L_{ij}^{safe}$$

(9)

where $\eta$ represents the safety coefficient and $L_{ij}^{safe}$ represents the distance from the endpoint of predicted trajectory i to the center of the j-th obstacle. Their respective values are as follows:

$$\eta =\left\{\begin{array}{l}0.8 0<L_{ij}^{obsmin}\le {\sigma }_{max}^{sonar}/2\hfill \\ 0.9 {\sigma }_{max}^{sonar}/2<L_{ij}^{obsmin}\le {\sigma }_{max}^{sonar}\hfill \\ 1.0 {\sigma }_{max}^{sonar}<L_{ij}^{obsmin}\hfill \end{array}\right.$$

(10)

$$L_{ij}^{safe}=(\sqrt{{(x_j-x_i)}^2}+\sqrt{{(y_j-y_i)}^2})$$

(11)

where $L_{ij}^{obsmin}$ represents the closest distance from the endpoint of predicted trajectory i to the edge of the j-th obstacle; $x_i$ and $y_i$ represent the x and y coordinates of the endpoint of predicted trajectory i, respectively; and $x_j$ and $y_j$ represent the x and y coordinates of the center of the j-th obstacle, respectively.

The expression for the safety evaluation sub-function of predicted trajectory i within the current sampling cycle is as follows:

$$safe{(v,\omega )}_i=\frac{1}{j_{max}}{\displaystyle \sum _{j=1}^{j_{max}}cos{t}_{ij}^{safe}}$$

(12)

where $j_{max}$ represents the number of obstacles within a radius of $R_{safe}$.

The construction of the obstacle zone, actual obstacle zone, and warning obstacle zone is illustrated in Figure 7. In the figure, $\lambda =rand\left[-{\sigma }_{max}^{sonar},{\sigma }_{max}^{sonar}\right]$. Both the obstacle zone and the actual obstacle zone are impassable areas. The obstacle zone is a known area, while the actual obstacle zone is unknown. Both the DWA algorithm and the SE-DWA algorithm plan paths based on the obstacle zone. However, a certain distance from the actual obstacle zone is required to ensure the safety of DSLV’s autonomous sampling operations. In trajectory one, obstacles are enlarged by the DSLV’s width, resulting in a shorter path length but lower safety. The algorithm corresponding to trajectory one will be referred to as the Minimum Energy Consumption-DWA (MEC-DWA) algorithm. In trajectory two, obstacles are expanded by the DSLV’s width and ${\sigma }_{max}^{sonar}$, resulting in a longer path length but higher safety. The algorithm corresponding to trajectory two will be referred to as the Maximum Safety-DWA (MS-DWA) algorithm.

Figure 8 illustrates the mechanism of the safety evaluation sub-function. In trajectory one, obstacles are expanded only by the DSLV’s width. The volume of the actual obstacle zone can easily exceed the obstacle zone, leading to safety concerns. However, trajectory two involves obstacles that are expanded by both the DSLV’s width and ${\sigma }_{max}^{sonar}$. Although the volume of the actual obstacle zone cannot exceed the obstacle zone, the excessive inflation requires DSLV to crawl a longer distance to reach the target point. In trajectory three, despite expanding the obstacles only by the DSLV’s width, the presence of the warning obstacle zone and the safety evaluation sub-function lead to a different choice. Under the same linear and angular velocities, when compared with the DWA algorithm, it selects position 2 instead of position 1. This decision keeps it away from the actual obstacle zone, ensuring the safety of the DSLV.

3.2.2. Trajectory Comparison Evaluation Sub-Function

The seafloor is filled with irregular obstacles, making it prone to the formation of a “U”-shaped obstacle environment [20]. The DWA algorithm, due to the scoring mechanism of its evaluation functions, may end up crawling a longer distance while attempting to find an exit from the “U”-shaped obstacle environment. In some cases, it might even become stuck without finding a way out. To address this issue, this section introduces a new trajectory comparison evaluation sub-function.

The trajectory comparison evaluation sub-function entails evaluating the proximity of predicted trajectories to the grid cells occupied by historical trajectories, which contributes to the calculation of the cost value used for scoring. Figure 9 illustrates the method for computing the cost value of the trajectory comparison evaluation sub-function. The shaded area represents grid cells within a radius of $R_{locus}$ around the historical trajectory. Taking the calculation of predicted trajectory m and historical trajectory n as an example, a threshold radius of $R_{locus}$ is established with the DSLV’s geometric center as the origin. When historical trajectory n falls within the circle, the corresponding cost value for predicted trajectory m in relation to historical trajectory n is as shown below:

$$cos{t}_{mn}^{locus}=(R_{locus}-L_{mn}^{locus})·\left|\right|\frac{v-v_0}{v_{max}}\left|\right|$$

(13)

where $L_{mn}^{locus}$ represents the distance from the endpoint of the predicted trajectory m to the grid cell where the historical trajectory n is located, and $v$ and $v_{max}$, respectively, denote the current linear velocity at the endpoint of the predicted trajectory m and the maximum linear velocity achievable within the current velocity window. (The addition of velocity terms aims to prevent a sharp increase in the cost values for the surrounding grid cells when the vehicle travels at low speeds.)

The expression for the trajectory comparison evaluation sub-function of the predicted trajectory m is as follows:

$$locus(v,\omega )=\frac{1}{n_{max}}{\displaystyle \sum _{n=1}^{n_{max}}cos{t}_{mn}^{locus}}$$

(14)

where $n_{max}$ represents the number of grid cells within a radius of $R_{locus}$ that contain historical trajectories.

Figure 10 illustrates the mechanism of the trajectory comparison evaluation sub-function. Trajectories four and five are generated by the DWA algorithm and the SE-DWA algorithm, respectively. When faced with a ‘U’-shaped obstacle environment, trajectory five is more favorable than trajectory four because of its ability to escape local optima. When scoring is conducted using the evaluation function of the DWA algorithm, satisfying both conditions ${\theta }_1<{\theta }_2$ and $d_1<d_2$, the two trajectories will receive similar scores, making it challenging to determine their relative superiority. However, with the inclusion of the trajectory comparison evaluation sub-function, the cost of grid cells within the purple circle for trajectory four is lower compared with that for trajectory five. As a result, trajectory five receives a higher score, allowing the DSLV to identify the exit of the ‘U’-shaped obstacle environment.

3.2.3. Pseudo-Power Evaluation Sub-Function

The trajectory comparison evaluation sub-function aims to decrease energy consumption by minimizing the distance crawled by the DSLV. According to the reference literature, the DSLV maintains optimal velocity during crawling to minimize variations in the linear and angular velocities, which can reduce energy consumption to a certain extent [21,22]. Therefore, the constructed pseudo-power evaluation sub-function is as follows:

$$energy(v,\omega )=1-\frac{v·\dot{v}+\omega ·\dot{\omega }}{v_{\max }·{\dot{v}}_{\max }+{\omega }_{\max }·{\dot{\omega }}_{\max }}$$

(15)

where $\dot{v}$ and $\dot{\omega }$ represent linear and angular accelerations, respectively, and ${\dot{v}}_{max}$ and ${\dot{\omega }}_{max}$ represent the maximum linear velocity and the maximum angular acceleration, respectively.

3.3. Evaluation Function of the SE-DWA Algorithm

To satisfy the dynamic constraint conditions of the DSLV, the evaluation sub-functions need to undergo a smoothing process, specifically normalization. The calculation formula is shown as follows:

$$\left\{\begin{array}{c}head{(v,\omega )}_k^{smooth}=\frac{head{(v,\omega )}_k}{{\displaystyle \sum _{k=1}^{K}head{(v,\omega )}_k}}\\ safe{(v,\omega )}_k^{smooth}=\frac{safe{(v,\omega )}_k}{{\displaystyle \sum _{k=1}^K\sec {(v,\omega )}_k}}\\ vel{(v,\omega )}_k^{smooth}=\frac{vel{(v,\omega )}_k}{{\displaystyle \sum _{k=1}^{K}vel{(v,\omega )}_k}}\\ locus{(v,\omega )}_k^{smooth}=\frac{locus{(v,\omega )}_k}{{\displaystyle \sum _{k=1}^{K}locus{(v,\omega )}_k}}\\ energy{(v,\omega )}_k^{smooth}=\frac{energy{(v,\omega )}_k}{{\displaystyle \sum _{k=1}^{K}energy{(v,\omega )}_k}}\end{array}\right.$$

(16)

where $K$ represents the total number of predicted trajectories; $k$ represents the current predicted trajectory under evaluation; $head(v,\omega )$ represents the navigation evaluation sub-function, which indicates the complement angle between the velocity direction and the target point; $safe(v,\omega )$ represents the safety evaluation sub-function; $vel(v,\omega )$ represents the velocity evaluation sub-function, which indicates the speed magnitude in the trajectory; $locus(v,\omega )$ represents the trajectory comparison evaluation sub-function; and $energy(v,\omega )$ represents the pseudo-power evaluation sub-function.

The final evaluation function of the SE-DWA algorithm is as follows:

$$\begin{array}{ll}G(v,\omega )=& {\gamma }_{1}head{(v,\omega )}_k^{smooth}+{\gamma }_{2}safe{(v,\omega )}_k^{smooth}+{\gamma }_{3}vel{(v,\omega )}_k^{smooth}\\ & +{\gamma }_{4}locus{(v,\omega )}_k^{smooth}+{\gamma }_{5}energy{(v,\omega )}_k^{smooth}\end{array}$$

(17)

where ${\gamma }_1$, ${\gamma }_2$, ${\gamma }_3$, ${\gamma }_4$, and ${\gamma }_5$ represent the weights of the five evaluation sub-functions, respectively.

3.4. Application of the SE-DWA Algorithm in DSLV

The process diagram of DSLV applying the SE-DWA algorithm is depicted in Figure 11, with the following main steps. (1) Initialization: the deep-sea environment data acquired using sensors such as forward sonar are used to construct a map using the grid-based method. Subsequently, the destination point is established. (2) The SE-DWA algorithm: after acquiring a DSLV’s state parameters, the SE-DWA algorithm’s evaluation function is employed to determine the optimal predicted trajectory for the sampling period. (3) Real-time environmental detection: sensors continuously monitor the surrounding environment. When a potential collision with an actual obstacle zone or a local optimum is detected, adjustments in heading angle are executed. (4) Destination detection: at the end of each sampling period, a check is performed to verify whether the DSLV has reached the target point. If the target point has been reached, the path planning for this cycle is concluded. Otherwise, steps (2) and (3) are reiterated until the target point is attained.

4. Simulation Experiment

4.1. Determination of Evaluation Function Coefficients

The SE-DWA algorithm comprises five evaluation sub-functions associated with four weights. These weights are designated as the navigation weight, safety weight, velocity weight, and energy consumption weight. The navigation weight corresponds to the navigation evaluation sub-function, which is used to control the DSLV’s motion direction. The safety weight corresponds to the safety evaluation sub-function, which is employed to prevent collisions between the DSLV and obstacles. The velocity weight pertains to the velocity evaluation sub-function, governing the DSLV’s maximum linear velocity. The energy consumption weight is associated with both the trajectory comparison evaluation sub-function and the pseudo-power sub-function. It serves the purpose of reducing path length and ensuring optimal velocity, respectively, thus lowering energy consumption.

The coefficients for the navigation evaluation sub-function, safety evaluation sub-function, and velocity evaluation sub-function in the SE-DWA algorithm are referenced from the coefficients set in the DWA algorithm [18]. To determine the coefficients for the trajectory comparison evaluation sub-function and the pseudo-power evaluation sub-function, simulation experiments are conducted in the simulated deep-sea environmental map ($80 \mathrm{m} \times 80 \mathrm{m}$) shown in Figure 12. In the figure, S(2,2) and G(78,78) represent the starting point and the goal point, respectively. Assuming that DSLV behaves as a point mass, obstacles were constructed as shown in Figure 7 to form obstacle zones, actual obstacle zones, and warning obstacle zones. The algorithm was validated using Matlab 2018a. The software was run on a 64-bit operating system with an Intel(R) Core(TM) i5-5200 CPU processor.

To determine the ratio between the coefficients of the safety evaluation sub-function, trajectory comparison evaluation sub-function, and pseudo-power evaluation sub-function, a coefficient ratio ($ratio={\gamma }_2/({\gamma }_4+{\gamma }_5)$) was set from 0 to 2 in increments of 0.1 for ten path-planning experiments. During these experiments, the closest distance to an actual obstacle zone and the average energy consumption when moving to the target point were recorded. Finally, the relationship between the coefficient ratio and the closest distance to obstacles and energy consumption is illustrated in Figure 13.

From Figure 13, it can be observed that the closest distance to the actual obstacle zone increased from 0.5 m to 3 m when the coefficient ratio ranged from 0.5 to 1.5, indicating a significant improvement in safety distance. However, in the range of 1.5 to 2.0, the value remained relatively stable at around 3 m, indicating little change in safety distance. As for energy consumption, it gradually increased within the coefficient ratio of 0.6 to 1.5, while a noticeable upward trend was observed in the range of 1.5 to 2.0. To strike a balance between energy consumption and safety considerations, the coefficient ratio of 1.5 was selected, corresponding to a ratio of 3:2 for the coefficients. As a result, the final coefficient ratios for the safety evaluation sub-function, trajectory comparison evaluation sub-function, and pseudo-power evaluation sub-function were determined to be in the ratio of 3:1:1.

4.2. Simulated Experiments in the Deep-Sea Environment

To validate the effectiveness of applying the SE-DWA algorithm to autonomous sampling operations in the deep sea, a simulation-based verification is conducted in the underwater environment depicted in Figure 12. The simulation parameters for the DSLV are outlined in

Table 1. Simulation parameters for the DSLV.

${\mathit{v}}_{\mathit{m}\mathit{a}\mathit{x}}$	${\mathit{\omega }}_{\mathit{m}\mathit{a}\mathit{x}}$	${\mathit{\omega }}_{\mathit{m}\mathit{i}\mathit{n}}$	${\dot{\mathit{v}}}_{\mathit{m}\mathit{a}\mathit{x}}$	${\dot{\mathit{\omega }}}_{\mathit{m}\mathit{a}\mathit{x}}$	${\mathit{s}}_1,{\mathit{s}}_2$
0.2 m/s	0.4 $\mathrm{rad}/\mathrm{s}$	−0.4 $\mathrm{rad}/\mathrm{s}$	0.1 ${\mathrm{m}/\mathrm{s}}^2$	0.15	0.85~1.0

, where the DSLV slip rate ($s_1$ and $s_2$) is referenced from the literature [23]. The simulation parameters for both the DWA algorithm and the SE-DWA algorithm are detailed in

Table 2. Simulation parameters for the DWA algorithm.

${\mathit{\alpha }}_1$	${\mathit{\alpha }}_2$	${\mathit{\alpha }}_3$	${\mathit{t}}_{\mathit{p}\mathit{r}\mathit{e}}$	${\mathit{R}}_1$	${\mathit{R}}_2$
0.1	0.3	0.2	5 s	1 m	2 m

and

Table 3. Simulation parameters for the SE-DWA algorithm.

${\mathit{\gamma }}_1$	${\mathit{\gamma }}_2$	${\mathit{\gamma }}_3$	${\mathit{\gamma }}_4$	${\mathit{\gamma }}_5$	${\mathit{t}}_{\mathit{p}\mathit{r}\mathit{e}}$	${\mathit{R}}_1$	${\mathit{R}}_3$	${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{x}}^{\mathit{s}\mathit{o}\mathit{n}\mathit{a}\mathit{r}}$	${\mathit{R}}_{\mathit{s}\mathit{a}\mathit{f}\mathit{e}}$	${\mathit{R}}_{\mathit{l}\mathit{o}\mathit{c}\mathit{u}\mathit{s}}$
0.1	0.3	0.2	0.1	0.1	5 s	1 m	0.5 m	2 m	30 m	25 m

, respectively. In these tables, $t_{pre}$ refers to prediction time, $R_1$ represents the inflation of the DSLV’s body width, $R_2$ denotes the inflation maximum error, $R_3$ signifies the safety distance, and ${\sigma }_{max}^{sonar}$ is referenced from the literature [16,24].

Constructing the environmental map in Figure 10 based on the scheme in Figure 7, three approaches—namely the MEC-DWA algorithm, the MS-DWA algorithm, and the SE-DWA algorithm—are employed for 50 simulation experiments. The distinction between the MEC-DWA algorithm and the MS-DWA algorithm resides solely in their size-to-obstacle expansion. They exemplify two extremes concerning safety and energy consumption. The paths produced by the MEC-DWA algorithm demonstrate the lowest attainable energy consumption within the realm of DWA algorithms, albeit at the expense of the safety performance. Conversely, the paths generated by the MS-DWA algorithm attain the highest level of safety among DWA algorithms but do so at the cost of the highest energy consumption.

The comparison of distances to actual obstacle zones and energy consumption for these 50 simulations is illustrated in Figure 14 and Figure 15. The statistical results, including the average values for the simulation data, are presented in

Table 4. Average of 50 simulation data.

Algorithm	Minimum Distance to Actual Obstacle Zone	Average Minimum Distance to Actual Obstacle Zone	Energy Consumption	Path Length
The MEC-DWA algorithm	0.547 m	3.505 m	26,880.3 J	134.752 m
The MS-DWA algorithm	2.113 m	6.231 m	31,651.7 J	160.051 m
The SE-DWA algorithm	1.715 m	5.534 m	24,049.4 J	124.981 m

.

Based on Figure 14 and Table 4, it is evident that both the SE-DWA and MS-DWA algorithms have planned paths with a minimum distance from actual obstacle zones that exceeds 1.5 times the width of the DSLV (1 m). This distance provides a substantial safety margin to accommodate imperfect sensing systems, control errors, or other sources of uncertainty. In contrast, the paths generated by the MEC-DWA algorithm result in a minimum distance from actual obstacle zones that is less than the width of the vehicle. In such a scenario, the risk of collision between the DSLV and obstacles significantly increases due to factors such as sensor inaccuracies.

To validate the safety of the planned paths, besides checking if the minimum distance from actual obstacle zones meets the requirements, a safety assessment can also be employed. Safety assessment ($s_d$) is represented as the ratio of the minimum distance from actual obstacle zones to the average minimum distance from actual obstacle zones. For the paths generated by the SE-DWA algorithm and the MS-DWA algorithm, $s_d$ is 0.339 and 0.310, respectively. This indicates that the DSLV is relatively distant from obstacles, resulting in a lower collision risk. Conversely, for the paths generated by the MEC-DWA algorithm, $s_d$ is 0.156. This indicates that the DSLV is relatively closer to obstacles, resulting in a higher collision risk. The safety assessment for paths generated by the SE-DWA algorithm and the MS-DWA algorithm shows little difference, which confirms the validity of the SE-DWA algorithm’s safety evaluation sub-function.

According to Table 4, it is evident that the path length for the SE-DWA algorithm is the shortest, showing a 21.9% reduction compared with the path length of the MS-DWA algorithm. When compared with the energy-efficient MEC-DWA algorithm, it also demonstrates a 7.2% reduction. At the same velocity, less time and energy are consumed when crawling to the target point. The trajectory comparison evaluation sub-function of the SE-DWA algorithm has been validated.

Based on Figure 15 and Table 4, it is evident that the SE-DWA algorithm plans paths with the lowest energy consumption. The unit energy consumption is the ratio of energy consumption to path length, indicating shorter travel times and lower energy consumption for the same path length. The unit energy consumption corresponding to the MEC-DWA algorithm, MS-DWA algorithm, and SE-DWA algorithm is 199.47, 197.76, and 192.42, respectively. The pseudo-power evaluation sub-function of the SE-DWA algorithm has been validated.

For the specific analysis, the path-planning results of the three approaches from one of the fifty trials were selected for examination. The path-planning results for the DWA algorithm and the SE-DWA algorithm are depicted in Figure 16 and Figure 17, respectively. The variations in linear and angular velocities for the DWA algorithm and the SE-DWA algorithm are displayed in Figure 18 and Figure 19, respectively. The energy consumption profiles for all three approaches are illustrated in Figure 20.

Based on the results from Figure 16 and Table 4, it is evident that the path generated by the MEC-DWA algorithm contains three turning points. These turning points indicate instances where the DSLV detects an impending collision with the actual obstacle zone, triggering emergency braking and adjustments to the heading angle. The minimum distance from the generated path to the actual obstacle zone is 0.547 m, which is smaller than the DSLV’s vehicle width. This result does not ensure the autonomous sampling safety of the DSLV.

The path planned by the MS-DWA algorithm maintains a minimum distance of 2.113 m from the actual obstacle zones. This distance is significantly greater than the 0.547 m maintained by the MEC-DWA algorithm. Due to the larger inflation, the DSLV is required to travel a greater distance to reach the target point when encountering narrow areas. As a result, the path length increases by 18.7% compared with that of the MEC-DWA algorithm.

Based on the outcomes presented in Figure 17 and Table 4, it is evident that the SE-DWA algorithm generates a path with a minimum distance of 1.715 m from the actual obstacle zone, which is greater than the width of a DSLV’s width. This ensures the safety of a DSLV’s autonomous sampling operations. It validates the effectiveness of the added safety evaluation sub-function and the warning obstacle zone. The path length is reduced by 7.8% compared with that of the MEC-DWA algorithm and further reduced by 21.9% compared with that of the MS-DWA algorithm. This confirms the effectiveness of the trajectory comparison evaluation sub-function.

As evident from Figure 18 and Figure 19, it is clear that when comparing the SE-DWA algorithm with the DWA algorithm, there are smaller variations in both the linear and angular velocities. This ensures that the DSLV remains at an optimal speed, contributing to a reduction in energy consumption to some extent. This finding validates the effectiveness of the pseudo-power evaluation sub-function. Simultaneously, Figure 17 and Figure 19 reveal that the path-planning times for the DWA algorithm are 1010 s and 830 s, respectively. In contrast, the SE-DWA algorithm completes path planning in only 700 s. This efficiency is a result of shorter path lengths and optimal velocities, further confirming the effectiveness of the trajectory comparison evaluation sub-function and the pseudo-power evaluation sub-function.

From Figure 20 and Table 4, it is evident that the SE-DWA algorithm has the lowest energy consumption per meter. Compared with the MEC-DWA algorithm, the energy consumption is reduced by 10.5%. When compared with the MS-DWA algorithm, the energy consumption is reduced by 24%.

5. Conclusions

We have proposed the SE-DWA algorithm to address safety and energy consumption challenges faced by DSLVs during autonomous sampling operations in the deep-sea environment. Based on the dynamic window derived from the analysis of a DSLV’s kinematics, we have devised three crucial sub-functions: safety evaluation sub-function, trajectory comparison evaluation sub-function, and pseudo-power evaluation sub-function. The safety evaluation sub-function tackles safety issues arising from reduced accuracy of forward-looking sonar due to underwater noise and other factors. The trajectory comparison evaluation sub-function reduces energy consumption by decreasing the path length when encountering “U”-shaped obstacles. The pseudo-power evaluation sub-function optimizes linear velocity and angular velocity to reduce energy consumption when encountering unknown deep-sea obstacles. Eventually, we conducted simulation experiments using deep-sea environmental maps. The simulation results demonstrate that the path planned by the SE-DWA algorithm compared with that from the DWA algorithm not only ensures enhanced safety performance but also results in at least an 11% reduction in energy consumption. The SE-DWA algorithm aligns better with the requirements of DSLVs for autonomous sampling in the deep-sea environment.

In the safety evaluation sub-function of the SE-DWA algorithm, the value used to construct the warning obstacle zone is currently set as the maximum forward-looking sonar error, which is a fixed value. When this value can be adaptively adjusted in the future, path security will be further enhanced and energy consumption will be further reduced. In the future, the focus will be on applying the SE-DWA algorithm to DSLVs’ autonomous sampling operations at a depth of 4500 m in the deep sea to validate its feasibility and effectiveness in real-world environments.