An Efficient Autonomous Exploration Framework for Unmanned Surface Vehicles in Unknown Waters

Abstract

The detection of unknown waters has been studied and applied in various fields, such as national defense, military operations, engineering surveying and mapping, and scene reconstruction. To improve exploration efficiency in unknown waters, this paper proposes a framework for autonomous exploration using unmanned surface vehicles (USVs). This framework, comprising a multi-stage exploration strategy and a hierarchical navigation strategy, is designed to mitigate the inherent restrictions between the exploration target point and exploration direction in USV operations. These two strategies are optimized for the exploration target point and feasible navigation route to address the problem of the USV’s limited mobility during exploration. Rapidly exploring random tree (RRT) and boundary detection methods are used in the local layer to find the boundary in front of and behind the USV, and the gain of the target point is optimized. The hierarchical navigation method is implemented in the global layer to plan appropriate navigation paths. The proposed method is tested in simulations in several virtual environments and contrasted with the conventional methods currently in use. The findings indicate that our strategy covers more ground more effectively than other methods (our method achieved an exploration efficiency ranging from 4.9 to 5.3 $m^2$/s, whereas traditional methods ranged from 2.3 to 3.9 $m^2$/s, which demonstrates that our approach can improve exploration efficiency by up to 200% compared to traditional methods), spending less time exploring while significantly reducing collision probability.

1. Introduction

Autonomous exploration usually uses sensor data acquired from the environment with prior knowledge to independently perform path planning and environmental exploration in an unknown environment with minimal path cost and working time. It is crucial for accomplishing target search and rescue activities and is widely utilized in environmental investigation, scene reconstruction, and other domains [1,2]. The complex geometry and structure of the environment can still make it difficult.

Given the extensive attention in diverse disciplines, numerous techniques have been developed to address the problem of autonomous exploration, including boundary-based and random sampling-based methods. The frontier-based exploration method determines that the next target of the agent must be the boundary point between the explored and unexplored areas. Based on randomly sampled observation points, the method does not take the boundary as the target point of exploration, nor does it traverse all nodes in order. Instead, it employs a random sampling strategy to identify the subsequent location in the environment where it can gather the most data. Frontier-based approaches typically employ image processing [3] to identify boundary data [4,5] and carry out boundary detection on the entire global map following each map update. In the early phase of exploration, boundary extraction is relatively fast. However, the computational resources used for boundary extraction will grow geometrically with this incremental expansion and will spend a lot of time waiting for data processing, leading to frequent delays in work. Moreover, the access sequence of boundary points [6,7,8,9] will also greatly affect the efficiency of environmental exploration. Using an observation point method that relies on random sampling is called greedy. This method involves exploratory actions that maximize the return of an unknown area and obtain the next or several immediate target points. As a result, the path created is frequently inefficient, and the need frequently travels back and forth, continually visiting the same area. Moreover, for agents with non-differential speed and insufficient steering ability, a large number of invalid paths will be generated, which greatly reduces exploration efficiency.

In recent years, scholars have combined these two exploration methods to obtain the next best target point by evaluating the unknown gain contained in the boundary target point. Rapidly expanding random tree (RRT) is the most common method [10] for extracting boundary target points. This technique uses the random properties of RRT growth, randomly scattering points in the known map region, causing the random tree to grow along the direction of the random points, eventually covering the exploration area and extending to the boundary of the environment. Recording the location of the treetop is used as the boundary target point. This method does not need to construct the environment map accurately and has good results in two-dimensional and three-dimensional environments, so it has been widely used [11]. RRT, however, is also a fundamentally greedy strategy. It does not consider the entirety of the set continuity and only evaluates all boundary nodes individually. If the exploration process only chooses the boundary point with the greatest unknown gain as the target point, it might turn to other regions with greater benefits for exploration when a particular region is not fully explored, leading to an invalid backtracking phenomenon and reducing exploration efficiency. Additionally, the random growth of trees often results in the frequent omission of the corners of the map, which are likely to contain the greatest orthogonality in any factorial representation of the environment.

In this paper, we propose a more efficient exploration and navigation planning framework. The two exploration methods have limitations for the sake of the characteristics that USV cannot rotate when moving, and it is not easy to adjust the heading angle repeatedly in the course of navigation. The frame is shown in Figure 1. The exploration algorithm takes the incremental map produced by simultaneous localization and mapping (SLAM) and extracts the target points, sending both the global and local target points to the path-planning module. The path-planning module plans an optimal path covering both local and global target points and incrementally expands the map through sensor data during navigation to the target point. This framework focuses on maintaining the local map rather than global maps. In order to improve the timeliness of detection, the USV acquires surrounding boundary information with minimal computational cost and plans a reasonable navigation path through hierarchical navigation. Compared with existing research, the main contributions of this paper are summarized as follows:

(1)

Our exploration framework adopts a multi-stage exploration strategy in comparison with the current exploration methods, and it introduces the concepts of the global layer and local layer during the exploration process. The multi-phase exploration strategy is implemented in the local layer. The exploration strategy based on RRT and the frontier detection method based on the image are used to obtain the local boundary observation points. In the global layer, the global optimal observation point is dynamically selected as the end point of global backtracking, and repeated access to multiple regions is constrained by the gain function to minimize invalid backtracking behavior.

(2)

We introduce a hierarchical navigation strategy compared to traditional navigation. In the backtracking phase, we allocate local and global boundary observation points at the same time, using the global boundary observation points as the endpoints for the current navigation plan. This can reduce the repeated forward and backward movement of the USV when adjusting its course during exploration.

The rest of this paper is organized as follows. Section 2 provides the related work on autonomous exploration and how our approach can further contribute, and Section 3 defines the problems considered. The solution is described in detail in Section 4 and evaluated in Section 5 with simulations. Finally, Section 6 summarizes and concludes the work of this paper.

2. Problem Formulation

Autonomous exploration methods have significantly evolved in recent years and may be broadly separated into two categories: conventional methods and methods based on machine learning. Among the former methods, the frontier-based method [12,13,14] and the method based on randomly sampled observation points [15,16,17,18,19,20,21] are the mainstream approaches applicable to most scenarios. These select the next target point using acquired map information. The fundamental idea behind machine learning-based methods [22,23,24,25,26] is to govern decision-making through autonomous learning during the exploration phase. However, these methods face significant challenges in practical deployment. One major issue is the difficulty in transferring models trained in controlled environments to more complex, real-world settings. As a result, most experiments with machine learning-based methods are still confined to straightforward indoor environments.

The frontier-based exploration method is one of the earliest developed methods for autonomous exploration. It drives the agent to explore by using boundary points, which contain information about unknown regions, as the target. The method described in [12] involves moving towards boundary points to maximize the collection of environmental information. This method does not consider obstacle information and selects the boundary point with the shortest Euclidean distance as the target point. While this approach cannot ensure the safety of boundary points and often results in repeated visits, it has provided foundational insights for subsequent research. Later improvements introduced various methods to enhance the gain function and path cost [5,27,28,29] to obtain the optimal boundary points. However, this method is prone to local optimization issues and can lead to inefficient backtracking when encountering local minima. Consequently, the exploration efficiency in complex environments remains limited. In another approach, the concept of a traveling salesperson (TSP) is presented [6,7,8]. By sorting all the boundaries reasonably, an optimal exploration path that covers the map to a greater extent and consumes less time can be obtained. However, with the increase in the exploration area, the calculation amount will expand rapidly.

In contrast to the boundary approach, the method based on random sampling of observation points employs random sampling points as direct target sites in free space and does not need to analyze and process all boundaries in the map. After the rapidly exploring random graph (RRG) was proposed [30], RRG has been widely used because it does not require geometric division of the search area, has a high coverage rate and a wide search space range, and is biased toward unexplored areas. In reference [17], RRG is utilized for underground exploration, and RRG is used to effectively identify and optimize exploration paths in local narrow spaces to eliminate mobility limitations caused by multibranched and tunnel-like networks. With reference to [16,17], a random graph [18] is employed as a method of random sampling. The map is continuously built using the ray-tracing method, and an interruption mechanism is introduced to decouple the node gain and draw the agent to the unexplored area to complete the exploration. RRT [31] can also achieve randomness. The receding horizon “next–best–view” planner (RH-NBVP) [15] use of RRT in three-dimensional space expansion generates RRT to find the unknown space that can be passed through. Through the gain function, the most plentiful branch, which has the richest unknown information, is then chosen to explore the unknown space. This method can effectively explore a single area. However, this method is unsuitable for exploring larger environments due to its inherent tendency to overlook areas that have not been thoroughly explored. Reference [32] uses RRT to guide the robot to detect dangerous gas leakage and draw the gas concentration range map. Reference [10] introduces the exploration framework of hierarchical RRT, generates random trees in global and local space, respectively, obtains boundary information through the growth of random trees, and selects the best target points according to boundary revenue. Compared to the boundary detection method based on image processing, this method is more flexible. However, after reaching each observation point, the local spatial RRT tree is reset, leading to the deletion and regeneration of many influential nodes, resulting in computational waste. Moreover, the global tree grows simultaneously with the local tree, which may result in invalid backtracking of the agent, which abandons the local node and goes to the global node with a relatively high gain. Due to the limits of both methods, reference [33] combines frontier-based and random sampling-based exploration methods, using the improved RRT as the path planning algorithm for the UAV. However, this approach can cause discontinuities in the exploration path and reduce exploration efficiency. In the dual-stage viewpoint planner (DSVP) [34], the dynamic pruning random tree strategy is introduced during the local exploration stage to prune nodes that are outside of the local plan, allowing the tree to grow better along the frontier direction. A relocation strategy is proposed in the global exploration phase, which uses the global map to quickly locate the global observation points and keep the nodes generated by RRT in the exploration process to achieve the goal of fast backtracking. In this method, local exploration is the main task at present. When the local exploration is complete, it will be guided to a global unknown area for further exploration, which greatly improves the timeliness of exploration. But inevitably, in the relocation phase, there will be a pause caused by calculating the optimal global target point. To navigate to the selected global boundary point, the non-optimal viable path created by RRT is used, resulting in an invalid path cost and requiring a lot of time.

The contribution of this paper lies in proposing an efficient exploration framework that eliminates ineffective backtracking through a multistage exploration strategy. Additionally, a hierarchical navigation strategy is employed to minimize unnecessary forward and backward adjustments of the USV, achieving the maximum movement expectation in the lowest amount of exploration time. We tested the proposed exploration framework under the Robot Operating System (ROS) and compared it with Image-Based, RRT [10], and their combination method DSVP [34]. The results show that, for low-speed navigation, our results are better than the exploration efficiency of other methods in terms of completing the coverage of the whole environment and can be adapted to relatively high-speed navigation after subsequent improvement.

3. Problem Description

The problem considered within this work consists of exploring a bounded space $V\subset {\mathbb{R}}^3$. There are three kinds of regions on the bounded space V known as the free region $V_{free}$, the unknown region $V_{unknown}$, and the occupied obstacle region $V_{occu}$. When working, the USV relies on sensor information and $V_{known}$ to realize its positioning and explore and map $V_{unknown}$.

Assumption 1.

USVs will be explored in a two-dimensional environment. Therefore, it is better to transform the above area into a two-dimensional grid map for exploration.

The problem can be defined as follows:

Question 1: Given the unknown environment, how can the proposed multiphase exploration strategy be used to acquire observation points and complete the overall environmental exploration?

Question 2: Given the USV’s motion characteristics, how can we use the proposed hierarchical navigation strategy to plan efficient navigation routes?

4. Methodology

Our exploration framework takes inspiration from DSVP and divides the strategy into three phases. In the exploration stage, we use dynamically expanded RRT to create a random tree and use Image-Based boundary detection methods to jointly obtain boundary observation points in the local layer for clustering to integrate adjacent and invalid observation points. We also obtain the best local observation points from the gain function. When the USV moves to the assigned local observation point in the pruning phase, the random tree will be pruned instead of reset. In the effective backtracking phase, when there is no unknown region in the local layer, the USV will backtrack to the best global boundary observation point and continue to complete the exploration. In this phase, the USV will implement the hierarchical navigation strategy. The hierarchical navigation strategy involves planning a dynamic and feasible path covering the current local layer and global layer observation points given the premise of considering the kinematic model of the USV. During the work, the USV has converted among three phases to explore the environment.

4.1. Multiphase Exploration Strategy

4.1.1. Exploration Phase

The exploration phase is used to extend $V_{known}$. We use dynamic extended RRT and a frontier detection method based on image segmentation to generate observation points around the USV. Figure 2a shows the process of the exploration phase, with the USV as the geometric center and the blue dashed region $\mathcal{L}\subset {\mathbb{R}}^3$ defined as the local layer. In the process of exploration, RRT and frontier detection methods based on image segmentation are used for partition detection.

Define the upper half of the local layer ${\mathcal{L}}_{\mathcal{T}}\subset \mathcal{L}$ and create a dynamic random tree with the current position of the USV ${\mathcal{P}}_{\mathcal{B}}$ as the root. The nodes generated by each iteration of the random tree after meeting the boundary are the local observation points $X_{\mathcal{L}}^{\mathcal{R}}$ in the upper half of the region. RRT is selected for high search space coverage and, in concert with the pruning stage, the growing parts can be retained each time, reducing the calculation cost. Moreover, due to the motion characteristics of the USV, it is not easy to reach the target point behind itself in the local layer. Therefore, RRT is only used to detect the upper half of the region, and priority is given to assigning observation points to the USV first.

Since the growth range of RRT is specified, the growing branches can better go along the direction of the USV, which is conducive to the acquisition of boundary points. Also, because the limited growth range is specified, the possibility of dropping corners is significantly reduced. In the lower part of the local layer ${\mathcal{L}}_{\mathcal{B}}\subset \mathcal{L}$, the Canny edge detection method is used, which is consistent with the traditional boundary detection method. Given the grid map and limited exploration area, in this case, it does not take up more memory and has more efficient boundary extraction, and the center of the extracted boundary is selected as the local observation point $X_{\mathcal{L}}^{\mathcal{F}}$ in the lower half of the region.

In the exploration stage, the relationship of each parameter is described as follows:

$$\left\{\begin{array}{c}{X}_{\mathcal{L}}={\displaystyle \sum _{i=1}^h}{X_{\mathcal{L}}^{\mathcal{R}}}_i+{\displaystyle \sum _{j=1}^k}{X_{\mathcal{L}}^{\mathcal{F}}}_j\hfill \\ s.t.{X_{\mathcal{L}}^{\mathcal{R}}}_i,{X_{\mathcal{L}}^{\mathcal{F}}}_j\in \{{\mathcal{L}}_{\mathcal{T}},{\mathcal{L}}_{\mathcal{B}},FOV\left(S_l\right),\mathcal{L}\},\hfill \end{array}\right.$$

(1)

$$\left\{\begin{array}{c}R\left(X_{\mathcal{L}}^i\right)=\lambda T(X_{\mathcal{L}}^i,{\mathcal{P}}_{\mathcal{B}})I\left(X_{\mathcal{L}}^i\right)-N(X_{\mathcal{L}}^i,{\mathcal{P}}_{\mathcal{B}})\hfill \\ s.t.i\in \{\mathcal{R},\mathcal{F}\},\hfill \end{array}\right.$$

(2)

$$T(X_{\mathcal{L}}^i,{\mathcal{P}}_{\mathcal{B}})=\left\{\begin{array}{c}1+T_{gain},if\psi \le {\displaystyle \frac{\pi }{6}}\hfill \\ 1-T_{gain},if{\displaystyle \frac{\pi }{6}}<\psi \le {\displaystyle \frac{\pi }{2}}\hfill \\ 0,if\psi <{\displaystyle \frac{\pi }{2}},\hfill \end{array}\right.$$

(3)

$$T_{gain}=\left\{\begin{array}{c}{\lambda }_{1}sin\psi ,if\psi \le {\displaystyle \frac{\pi }{36}}\hfill \\ cos\psi ,if{\displaystyle \frac{\pi }{36}}<\psi \le {\displaystyle \frac{\pi }{12}}\hfill \\ {\lambda }_{2}sin\psi ,if{\displaystyle \frac{\pi }{12}}<\psi \le {\displaystyle \frac{\pi }{6}}.\hfill \end{array}\right.$$

(4)

In Equation (1), $X_{\mathcal{L}}$ is defined as the set of local observation points obtained in the exploration phase. The subscripts of $X_{\mathcal{L}}^{\mathcal{R}}$ and $X_{\mathcal{L}}^{\mathcal{F}}$, which are obtained by RRT and the edge detection method, represent the order of generating corresponding observation points, and the local observation points are restricted to the local layer. Further, $FOV\left(S_l\right)$ is the effective field of view of the sensor, and its coverage is smaller than the planning area of the local layer $\mathcal{L}$, while the acquisition process of observation points will be effectively carried out within the scope of $FOV\left(S_l\right)\cup \mathcal{L}$. As a result, the unknown boundary area will be closer to the visual constraint range of $\mathcal{L}$, and the unknown area in $\mathcal{L}$ will be acquired more purposefully. Considering the motion characteristics of the USV with limited turning, in the exploration phase, directions are preferentially allocated to the observation points $X_{\mathcal{L}}^{\mathcal{R}}$ in the current exploration, while $X_{\mathcal{L}}^{\mathcal{F}}$ is distributed behind the USV, so priority is not given. All observation points that have not been visited are imported into the global target point set $X_{\mathcal{G}}$ with delay and lag. Equations (2)–(4) show the gain function used to calculate each local observation point, which is similar to the method used in [10]. On this basis, the steering gain is added, which is more suitable for the exploration characteristics of the USV.

In Equation (2), $X_{\mathcal{L}}^i=X_{\mathcal{L}}^{\mathcal{R}}\cup X_{\mathcal{L}}^{\mathcal{F}}$ is used to denote all observation points in the local range, and the weight $\lambda$ is used to make the gain $T·I$ have a similar order of magnitude as the navigation cost N. Additionally, $I\left(X_{\mathcal{L}}^i\right)$ represents the information gain at the observation point, whose size is related to the selection of the sensor, and it is expressed in the form of the unknown area covered. As shown in Figure 3, the red circular area is defined as the effective field of view of the sensor, and the sum of the yellow and pink areas is defined as the unknown area, which is different from the traditional use of only the yellow area and abandons the small occupied area of the grid. By increasing the information gain, the influence of navigation costs can be reduced, and the USV can go to the local observation point farther away. The information gained from the observation point is expressed as the sum of the yellow and pink areas. Further, $N(X_{\mathcal{L}}^i,{\mathcal{P}}_{\mathcal{B}})$ represents the navigation cost of the USV from the current position ${\mathcal{P}}_{\mathcal{B}}$ to the observation point $X_{\mathcal{L}}^i$. Here, the feasible path generated by obstacle occlusion is not considered but is only represented by Euclidean distance. Also, $T(X_{\mathcal{L}}^i,{\mathcal{P}}_{\mathcal{B}})$ represents the steering gain brought by the observation point $X_{\mathcal{L}}^i$, whose specific magnitude is given by Equations (3) and (4). In Equation (3), $\psi$ represents the radian between the target point and the direction of the USV. Further, $T_{gain}$ is the steering gain coefficient, and its magnitude is related to $\psi$. In Equation (4), ${\psi }_1$ and ${\psi }_2$ represent the steering weight coefficient, which is the order of magnitude used for balance calculation. Here, considering that a large steering angle may have a certain impact on navigation, the selection should meet ${\psi }_1>10{\psi }_2$ to ensure the priority of small angle selection. It can be seen from the selection of $T(X_{\mathcal{L}}^i,{\mathcal{P}}_{\mathcal{B}})$ and $T_{gain}$ that, by the size of $\psi$, the steering gain and the steering weight coefficient are calculated, and the USV is encouraged to go to the observation point with a small angle in the current direction; that is, there is a small amplitude of steering during the voyage, which can cover the map more effectively. After obtaining the best observation point, the USV enters the pruning phase when it moves to point B in Figure 2b after one iteration.

4.1.2. Pruning Phase

The main purpose of pruning is to remove useless RRT nodes from the local layer. The so-called useless nodes are the nodes that are occluded and outside the upper half of the current local layer. As shown in Figure 2b, firstly, the physical structure of the random tree is updated, and the root is converted from A to B. Secondly, all nodes and branches that are blocked by obstacles and outside the upper part of the current local layer are deleted, such as the light blue nodes and branches in the figure. Finally, the empty node without branches is connected to the current root, B. During the pruning process, new local observation points, namely the orange nodes in the graph, are randomly sampled and added to the local observation point set. Meanwhile, local observation points $X_{\mathcal{L}}^{\mathcal{G}}$ that are not in the current local layer are transformed into global observation points and added to the global observation point set $X_{\mathcal{G}}$. Note that $X_{\mathcal{L}}^{\mathcal{G}}$ does not consist only of the $X_{\mathcal{L}}^{\mathcal{F}}$ legacy, but also of $X_{\mathcal{L}}^{\mathcal{R}}$, which is not selected and whose surroundings are not detected during the exploration phase. In the pruning phase, because part of each growth iteration is retained, it will use a smaller amount of computation than the method of regenerating a new local random tree. In addition, the boundary detection algorithm based on image segmentation is collocated. In the process of exploration, the previous phase of ${\mathcal{L}}_{\mathcal{T}}$ will take part in the composition of the current moment ${\mathcal{L}}_{\mathcal{B}}$. This will largely avoid missing unexplored corners due to the random nature of tree growth.

Algorithm 1 defines the detailed process of the pruning phase. The local layer is updated at a constant frequency. At each update, all $X_{\mathcal{L}}$ values are checked, and the local observation points $X_{\mathcal{L}}^{\mathcal{G}}$, which were dropped into the global layer during the exploration phase, are imported into $X_{\mathcal{G}}$. This procedure corresponds to lines 3 through 8 in Algorithm 1. Then, $P_{\mathcal{B}}$ is transformed into the root node $V_{init}$, and all RRT nodes in $\mathcal{L}$ are checked. All nodes V and branches E that are not in ${\mathcal{L}}_{\mathcal{T}}$ are pruned, and the nodes that are not pruned are directly connected to the root node. In terms of code implementation, we designed a $Con$ function to connect nodes.    

Algorithm 1: Pruning Phase

4.1.3. Effective Backtracking Phase

Backtracking is inevitable during exploration, but we can avoid invalid backtracking. So-called invalid backtracking refers to the act of repeatedly moving back and forth between a few regional explorations, which greatly reduces exploration efficiency. The backtracking that occurs when the current subarea is fully explored before entering another subarea can be an effective backtrace.

In the exploration process, when there is no unknown boundary information in ${\mathcal{L}}_{\mathcal{T}}$, that is, $X_{\mathcal{L}}^{\mathcal{R}}=⌀$, it will change from the local exploration phase to the effective backtracking phase of the global layer. In this phase, the local image observation point $X_{\mathcal{L}}^{\mathcal{F}}$, the global layer information $\mathcal{G}\subset {\mathbb{R}}^3$, and the global observation point set information $X_{\mathcal{G}}$ are used, and the hierarchical navigation strategy is combined to complete the effective backtracking. Here, $X_{\mathcal{L}}^{\mathcal{F}}$, which is not converted to $X_{\mathcal{L}}^{\mathcal{G}}$, consists of $X_{\mathcal{L}}\in {\mathcal{L}}_{\mathcal{B}}$, left over from the exploration phase. Further, $\mathcal{G}$ is an incremental map obtained from the beginning of exploration until now, which is mainly used to plan the navigation path of the USV in the backtracking phase. Also, $X_{\mathcal{G}}$ is composed of $X_{\mathcal{L}}^{\mathcal{G}}$ left over from each iteration. In the iteration process, the global observation point with the nearest distance and the least backtracking cost is selected from $X_{\mathcal{G}}$ as the navigation target point, and a reasonable path is planned through the hierarchical navigation strategy to complete effective backtracking. Here, the selection of the best global observation point follows the generated time order. The time order is determined by marking the time angle index for the global target point $X_{\mathcal{G}}^i\subset X_{\mathcal{G}}$. Each backtracking will search from the observation point generated the previous time in $X_{\mathcal{G}}$. In the backtracking phase, the USV sailed in the area of the known, but it may be gathering information to extend other boundary conditions. The planning of the course may use $FOV\left(S_l\right)$ to cover the unknown boundary, so it needs to update the list of the global observation point $X_{\mathcal{G}}$. If $X_{\mathcal{G}}=⌀$ appears, the exploration work has been completed and the exploration will end.

4.2. Hierarchical Navigation Strategy

Under the premise of considering the kinematics model of the USV, the hierarchical navigation strategy plans the navigation path of the USV at the local layer and the global layer, respectively, by assigning local observation points and global observation points simultaneously. The main purpose of this method is to plan a reasonable turning route in the local layer so that the USV can change course efficiently and plan sparse paths in the global layer for the USV to follow and complete effective backtracking, thereby complete environmental exploration faster. The triggering of the hierarchical navigation strategy should satisfy:

$$\begin{array}{c}\hfill \left\{\begin{array}{c}BestPoint X_{\mathcal{L}}^i={X_{\mathcal{L}}^{\mathcal{R}}}_i\hfill \\ s.t.{\displaystyle \sum _{{\displaystyle \genfrac{}{}{0pt}{}{i=1}{i\ne j}}}^h}{X_{\mathcal{L}}^{\mathcal{R}}}_i=⌀\hfill \end{array}\right..\end{array}$$

(5)

In the equation, $BestPoint{X}_{\mathcal{L}}^i$ is the local RRT node with the maximum gain R in the ${\mathcal{L}}_{\mathcal{T}}$ layer in the exploration phase and is the target point of the next voyage of the USV in the exploration process. The second formula indicates that there are no other unknown boundary points ${X_{\mathcal{L}}^{\mathcal{R}}}_i=⌀$ except $BestPoint{X}_{\mathcal{L}}^b$ in the current ${\mathcal{L}}_{\mathcal{T}}$ layer. This makes the USV sail to $BestPoint{X}_{\mathcal{L}}^i$; the local exploration phase is completed and transformed into the backtracking phase. In the traditional backtracking phase, the USV usually needs to repeatedly advance and retreat to adjust its course to the next observation point, which greatly reduces exploration efficiency and can even cause dangerous collisions. This situation can be avoided by using this hierarchical navigation strategy under the premise of considering the kinematic model of the USV.

4.2.1. Local Navigation Planning

In the local layer planning, the planned path $T_{\mathcal{L}}$ should have two constraints.

Firstly, it meets the requirement that the USV can adjust its course by planning a path with a reasonable turning radius to complete the subsequent planning after sailing to $X_{\mathcal{L}}^b$, completing the local exploration stage, and realizing dynamic obstacle avoidance at this stage.

Second, the $X_{\mathcal{L}}^{\mathcal{F}}$ information needs to be dynamically detected during local layer planning, and the subsequent decision of the USV will depend on $X_{\mathcal{L}}^{\mathcal{F}}$. When $X_{\mathcal{L}}^{\mathcal{F}}\ne ⌀$ in the local layer, the $FOV\left(S_l\right)$ of the USV in $T_{\mathcal{L}}$ should cover the remaining $X_{\mathcal{L}}^{\mathcal{F}}$ as much as possible, which is consistent with the representation in lines 9 to 11 of Algorithm 2. Algorithm 3, referenced in Algorithm 2, will be detailed later in the text. And when the $X_{\mathcal{L}}^b$ exploration is completed, local planning will be carried out to go to $X_{\mathcal{L}}^{\mathcal{F}}$ instead of going to the global best observation point.

Algorithm 2: Exploration Phase

As shown in Figure 4, the cyan rectangle represents the coverage area of the local layer. In $\mathcal{L}$, the position of the USV at the current moment is $P_{\mathcal{B}}$, and $X_{\mathcal{L}}^{\mathcal{R}}$ is the only observation point in the upper half of the local region obtained and clustered by RRT. The planned local path between $P_{\mathcal{B}}$ and $X_{\mathcal{L}}^{\mathcal{R}}$ refers to the Dubins navigation planning. Also, $P_{\mathcal{B}}$ and $X_{\mathcal{L}}^{\mathcal{R}}$ are taken as the initial and final points of navigation planning, and the course of points $X_{\mathcal{L}}^{\mathcal{R}}$ is specified as the maximum sideslip angle point. The selection of the $P_{\mathcal{B}}$ point turning here is related to the global optimal observation point $X_{\mathcal{G}}^b$. Generally, in order to optimize the $T_{\mathcal{L}}$, the same side of $X_{\mathcal{G}}^b$ is used as the turning direction by default, and the set radius, as the radius of the light pink circle shown in Figure 4, is used as the minimum turning radius to solve the Dubins navigation planning problem. After arriving at point $X_{\mathcal{L}}^{\mathcal{R}}$, because the local target point set is updated and detected at this stage, the USV will make different decisions based on whether $X_{\mathcal{L}}^{\mathcal{F}}$ exists.

When $X_{\mathcal{L}}^{\mathcal{F}}\ne ⌀$, the local path planning should make the USV at view point ${\mathcal{V}}_p$ in $T_{\mathcal{L}}$ satisfy the conditions as follows:

$$\begin{array}{c}{\mathcal{V}}_p\in T_{\mathcal{L}},\end{array}$$

(6)

$$\begin{array}{c}\forall X_{\mathcal{L}}^{\mathcal{F}}s.t.\exists {\mathcal{V}}_p{X}_{\mathcal{L}}^{\mathcal{F}}iscoveredbyFOV\left(S_l\right)at{\mathcal{V}}_p.\end{array}$$

(7)

Equations (6) and (7) require $T_{\mathcal{L}}$ to pass through the sampled viewpoint ${\mathcal{V}}_p$; that is, the randomly generated ${\mathcal{V}}_p$ is a point on the feasible path, and for any $X_{\mathcal{L}}^{\mathcal{F}}$, there exists a ${\mathcal{V}}_p$ so that the USV can observe at least one $X_{\mathcal{L}}^{\mathcal{F}}$ when passing by this point. It should be noted that the selection of Equation (7) may lead to the possibility that multiple viewpoints observe the same $X_{\mathcal{L}}^{\mathcal{F}}$ at the same time, which may cause the planning $T_{\mathcal{L}}$ to be non-optimal. But in general, the complexity of the water environment is not comparable to the complexity of the indoor environment, so there are no multiple $X_{\mathcal{L}}^{\mathcal{F}}$ values. Therefore, although $T_{\mathcal{L}}$ is not optimal, it can achieve the desired effect. After sailing to the ${\mathcal{V}}_p$, the local boundary detection will continue in the exploration phase, which is consistent with the representation in lines 4 to 9 of Algorithm 3. The track of the resulting $T_{\mathcal{L}}$ as a whole is shown by the red line in Figure 4.

When $X_{\mathcal{L}}^{\mathcal{F}}=⌀$, the planned path should meet the requirements of global backtracking. At this time, $T_{\mathcal{L}}$ is related to $X_{\mathcal{G}}^b$ and $V_b$. In Figure 4, the light green dot $X_{\mathcal{G}}^b$ is defined as the global best observation point, and the green dot $V_b$ is defined as the boundary point at the intersection of the global path planning and $\mathcal{L}$. At this stage, the USV will not perform local boundary detection but only use $V_b$ as the final target point to perform local stage backtracking, and its curve is shown by the dotted red line.

Algorithm 3: The Strategy of Hierarchical Navigation

4.2.2. Global Navigation Planning

In the global layer planning process, we assume that the motion model of the USV is an integrity constraint, and the USV is abstracted into a point without considering its orientation. Since the navigation is in a known environment, only the optimal track $T_{\mathcal{G}}$ from the current position $P_{\mathcal{B}}$ to $X_{\mathcal{G}}^b$ is planned, as shown in the dark green line in Figure 4. This is similar to the usual global planning algorithm. Therefore, here we only use A-Star, a depth-first global path planning algorithm, to generate rough planning for the global layer, while the specific navigation planning has been solved in the planning stage of the local layer. The overall navigation process has been expressed in detail in Algorithm 3.

The workflow of the entire framework is shown in Figure 5. The USV collects environmental information through LiDAR to update the point cloud data. The map module obtains the attitude data of the motion sensor, updates the local and global maps, and extracts and selects the exploration target points. Through the algorithm decision, the selected optimal target point is sent to the path planning module for navigation planning and, in this process, new sensor data are received and new maps are expanded. Then, it starts a new process loop.

5. Simulation

In this section, we conduct environmental exploration simulations in the virtual world of the Gazebo 9 simulation engine [35]. For comparing exploration algorithms, we used an ideal water surface environment without physical plug-ins such as wind, waves, and currents, which will be the focus of subsequent research. The physical characteristics and sensor configurations of the simulated USV [36] are consistent with those in the real world. Unlike ground vehicles that use wheeled odometers to directly obtain mileage information, our USV model employs an extended Kalman filter (EKF) to fuse IMU and GNSS data. This fusion generates odometer (Odom) messages that contain the estimated position and attitude information of the USV in space, which is used for localization through the robot localization package that incorporated EKF and GNSS information. The USV model is shown in Figure 6. The algorithm runs on the Ubuntu 18.04 operating system based on the ROS Melodic distribution, using a laptop computer with an Intel Core i7-4720HQ CPU (2.6 GHz) and 12 GB RAM to compare the performance of each exploration method.

5.1. Simulation Environment

Three water surface environments with different layouts and sizes were created for simulation, and the performance of the proposed exploration framework was verified by each of the three environments.

Table 1. Simulation environment characteristics.

	Large-Scale	Convoluted	Narrow Corridors	Cluttered Obstacles
SEE		✓	✓	✓
LME	✓	✓	✓	✓
HBE	✓

lists the characteristics of the simulation environment, and the specific map is shown in Figure 7.

• Simple Enclosed Environment (SEE) (35 m × 40 m): Contains simple layouts and relatively narrow enclosures designed to examine the effectiveness of a hierarchical navigation strategy, as shown in Figure 7a.
• Large Maze Environment (LME) (120 m × 60 m): Includes long narrow corridors and complex spatial layers. The performance of the exploration strategy is tested by checking whether invalid backtracking is generated, as shown in Figure 7b.
• Harbor Basin Environment (HBE) (105 m × 85 m): The harbor basin of the Lingshui Campus of Dalian Maritime University is selected as the simulation environment and drawn at 1:2, aiming at the performance of the complete detection and exploration framework, as shown in Figure 7c.

5.2. Simulation Test Evaluation

Our simulation stipulates that the USV sails at a speed of 2 knots (≈1.03 m/s); a circular area with a radius of 20 m represents the effective field of vision of the sensor $FOV\left(S_l\right)$; the local layer $\mathcal{L}$ is set as a circular area with a radius of 25 m; and the resolution of the map is set as 0.2 m. In the simulation, we compare two typical exploration methods and their fusion versions to our method (i.e., four methods). The two typical methods use the open source code of the applicable operating system version, and the fusion version has its unique 3D framework, which we wrote according to our understanding of relevant articles.

• Image-Based: The Canny edge detection algorithm is used to extract the boundary observation points and search for the boundary points with the highest gain.
• RRT: The randomness of global and local RRT trees is used to search for the best boundary observation point across space.
• DSVP: The combination of the above two methods. This method adds an Image-Based edge detection algorithm to the global map to reduce backtracking generation and improve exploration efficiency.

Each method was run five times at three random locations for a total of 15 times. If the USV almost stopped moving or arrived at a time limit, the exploration was defined as complete, and the operation was finished. Here we define the time limit as a period after stopping movement (120 s for SEE and 300 s for LME and HBE). The selected results are the three best trajectories of each random point, as shown in Figure 8 (from left to right are: Ours, DSVP, Image-Based, and RRT, respectively), and the evaluation indexes (length of navigation path and exploration area) are the average values of these three times. Figure 8a shows the best trajectory of SEE, where the triangle marks the initial position of exploration. In this simulation, the other three methods are explored with the original navigation algorithm instead of using the hierarchical navigation strategy. The path width at the top left of the map is slightly larger than the turning radius of the USV, and the wall at the top and left of the map forms an impassable narrow path. As can be seen from Figure 8a, except for our method, other methods change course by retreating or even hitting obstacles. Moreover, RRT has obvious ineffective backtracking because it has limitations in acquiring target points, especially for USVs with limited movement.

Figure 9a,b compare the average travel distance and the average detection area of all the methods. Our method completes the environmental exploration after a voyage of 105.9 m in 267.7 s. It can be seen that Image-Based and RRT almost cannot work in the later stage of exploration and cannot cover the whole space every time. This is because the planned path is constrained by the environment, resulting in a smaller average detection area than our method. Because the DSVP is limited by navigation, its exploration effect is also somewhat lacking compared with ours. In addition, the three optimal exploration times and the average exploration time of the above methods are shown in

Table 2. Exploration time of four methods in the SEE scene.

Method	Exploration Time			Average Time
	Yellow	Green	Black
Ours	207.4 s	267.7 s	235.6s	236.9 s
DSVP	395.4 s	274.2 s	390.0 s	353.2 s
Image-Based	375.3 s	382.2 s	439.5 s	399.0 s
RRT	384.8 s	420.3 s	395.2 s	400.1 s

.

Figure 8b,c show the optimal trajectories of LME and HBE. To reduce the risk of collision with obstacles in the simulation, Dubins local route planning is added to all the planning aspects of the exploration tests. From the best trajectories of DSVP, Image-Based, and RRT in the figure, it can be seen that these methods will produce a certain degree of invalid backtracking, and most of them will produce a large degree of turning in the navigation trajectory. Our method completed the exploration in LME and HBE with 332.45 m in 1182.7 s and 428.9 m in 1508.0 s, respectively. Figure 10 and Figure 11 compare the evaluation indexes of all methods. According to the results, the average sailing speed is not different from other methods, but the exploration can be completed in the shortest time. When the environment is large, our exploration strategy is better than other methods, and the average running time is the smallest. Corresponding

Table 3. Exploration time of four methods in the LME scene.

Method	Exploration Time			Average Time
	Yellow	Green	Black
Ours	1104.4 s	1182.7 s	812.8 s	1033.3 s
DSVP	1436.4 s	1307.8 s	1083.9 s	1276.0 s
Image-Based	1469.5 s	1356.6 s	1102.8 s	1309.6 s
RRT	2198.2 s	1519.0 s	1610.1 s	1775.7 s

and

Table 4. Exploration time of four methods in the HBE scene.

Method	Exploration Time			Average Time
	Yellow	Green	Black
Ours	1508.0 s	1419.7 s	1379.6 s	1435.8 s
DSVP	2117.3 s	1859.5 s	1649.3 s	1875.4 s
Image-Based	2091.7 s	1756.5 s	2665.4 s	2171.2 s
RRT	2463.7 s	3104.3 s	2129.2 s	2565.7 s

record the three best exploration times and the average exploration time.

In our comparison, we use two primary metrics to evaluate exploration efficiency: $\delta$ ($m^2$/s) and $r_{\delta }$. The metric $\delta$ ($m^2$/s) represents the average exploration efficiency of an algorithm, defined as the average area explored per second during the exploration process. The metric $r_{\delta }$ indicates the relative efficiency compared to our proposed strategy.

Table 5. Comparison of exploration efficiency.

	Ours		DSVP		Image-Based		RRT
	$\mathsf{\delta }$	${\mathit{r}}_{\mathsf{\delta }}$	$\mathsf{\delta }$	${\mathit{r}}_{\mathsf{\delta }}$	$\mathsf{\delta }$	${\mathit{r}}_{\mathsf{\delta }}$	$\mathsf{\delta }$	${\mathit{r}}_{\mathsf{\delta }}$
SEE	5.0	1	3.3	0.66	2.9	0.58	2.8	0.56
LME	4.9	1	3.9	0.80	3.8	0.78	2.6	0.53
HBE	5.3	1	3.5	0.66	2.6	0.49	2.3	0.43

compares the exploration efficiency of four methods using these metrics. It can be seen that, in the same virtual environment, our method significantly improves exploration efficiency and reduces exploration time compared to the other methods.

6. Conclusions

Aiming at the problem of water surface environment exploration, we propose an exploration framework that includes a multistage exploration strategy and hierarchical navigation strategy. The transition among the exploration, pruning, and practical backtracking phases thoroughly explores the entire environment by introducing the concepts of global and local layers. In the local layer, RRT and boundary detection algorithms detect the boundary before and after the USV’s voyage. The gain of the target point is optimized to reduce the inherent constraint that the target point is different from the exploration direction. In the global layer, the hierarchical navigation strategy is introduced to plan reasonable navigation routes to improve the timeliness of exploration and guide the environment to continue to expand. Finally, we compare the proposed method with three other methods in three large simulation environments (including SEE, LME, and HBE) to verify the effectiveness and robustness of the proposed method. The results show that our method takes less time and covers the area faster than other methods. However, the low-cost 2D LiDAR used in the simulation itself cannot provide the details required for accurate obstacle detection in the real surface environment, and the simulated maritime scene does not include environmental factors such as waves and currents. In the future, we will use these problems as our research direction and, on this basis, consider the impact of near-shallow water shorelines on USV operations as well as the impact of dynamic obstacles on environmental detection, and we will conduct test experiments in real scenes.