For decades, CCPP has undergone extensive research, and many algorithms have emerged, such as the bio-inspired neural network (BNN) approach, the Boustrophedon Cellular Decomposition (BCD) method, and the deep reinforcement learning approach (DRL). Luo and Yang (2008) developed the bio-inspired neural network (BNN) method to navigate robots to perform CCPP while avoiding obstacles within dynamic environments in real time (Zhu et al., 2017). The robot is attracted to unscanned areas and repelled by the accomplished areas or obstacles based on the neuron activity in the BNN given by the shunting equation (Yang and Luo, 2004; Li et al., 2018). Without any prior knowledge about the environment, the next position of the robot depends on the current position of the robot and neuron activity associated with its current position (Luo et al., 2016). However, it is time- and energy-consuming for the vehicles and requires high computing resources to process fine-resolution mapping (Sun et al., 2018). Unlike the BNN approach, the boundary representation method that defines the workspace is adopted by the Boustrophedon Cellular Decomposition (BCD) method and the deep reinforcement learning approach (DRL). The BCD method is proposed by Acar and Choset (2002), which decomposes the environment into many line scan partitions and is explored through a back-and-forth path (BFP) in the same direction. The BCD is an effective CCPP method with more diverse, non-polygonal obstacles in workspace. In trapezoidal decomposition as a cell, it is covered in back-and-forth patterns. For a complex configuration space with irregular-shaped obstacles, BCD needs to construct a graph that represents the adjacency connections of the cells in the boustrophedon decomposition. Therefore, a deep leaning-based method may promote it to a more efficient CCPP method (Sünderhauf et al., 2018; Valiente et al., 2020; Rawashdeh et al., 2021). Similarly, Nasirian et al. (2021) utilized traditional graph theory to segment the workspace and proposed a deep reinforcement learning approach to solve the CCPP problem in the complex workspace. However, the most common shape of the workspace is represented by polygons. As irregular areas of non-convex polygons, they can still be decomposed into multiple convex polygons (Li et al., 2011). Thus, the representation of polygons is also adopted in this study to express most workspace that needs to be explored. Such a method simplifies the complex environments and solves the covering irregularity for vehicles (Quin et al., 2021).

Faster R-CNN originated from R-CNN, and Fast CNN uses a unified neural network (NN) for object detection shown in Figure 4A. The faster R-CNN avoids using selective search, which accelerates region selection and further reduces computational costs. The faster R-CNN detector is mainly composed of a region proposal network (RPN), which generates region proposals, and a network that uses these generated feature patches (FP) for object detection. The region of interest (ROI) pooling layer is used to resize the feature patch (RFP), finally concatenated with a set of fully connected (FC) layers in our study. The two fully connected NN layers are utilized to refine the location of the bounding box and classify the objects. Faster R-CNN effectively uses the bounding box in our studies to identify and locate vehicles and obstacles in the images. This is also applied to the map obtained from farms, search, and rescue scenes to distinguish the vehicles, machines, and human beings on the image.

Although the above-mentioned CCPP approaches have achieved remarkable results, such approaches may still be sub-optimal when the starting and target positions required by the vehicle are included in the path. Especially for multiple sub-region exploration tasks shown in Figure 1A, the task is considered continuous to explore the four sub-regions, and the starting point of the next sub-region to be explored is the target point of the last sub-region as shown by the red circles in Figure 1. The selection of intermediate target points for multiple polygonal exploration areas is still an open problem because it needs to consider the shape and relative position of each sub-region, as well as the entrance and exit of the exploration area (Graves and Chakraborty, 2018). For simplicity, the entrances of the next sub-region are selected as target points here. The connection path length from the starting point to the target point should be considered, as shown in the blue lines in Figure 1B. In this case, ignoring the connection path may increase the complete path length of the overall exploration task (Xie et al., 2019). Thus, it is vital to consider the starting and target points of the vehicle, including the exploration task, and obtain a shorter path that effectively utilizes the limited onboard resources. Another challenging problem that arises in CCPP is obstacle avoidance (An et al., 2018; Wang et al., 2021). Based on the excellent optimization and search capabilities of nature-inspired algorithms, researchers have recently explored many nature-inspired computational approaches to solve vehicle collision-free navigation problems (Deng et al., 2016; Ewerton et al., 2019; Lei et al., 2019, 2021; Segato et al., 2019). For instance, a hybrid fireworks algorithm with LIDAR-based local navigation was developed by Lei et al. (2020a), capable of generating short collision-free trajectories in unstructured environments. Zhou et al. (2019) developed a modified firefly algorithm with the self-adaptive step factor to avoid the premature and improve the operational efficiency of autonomous vehicles. Lei et al. (2020b) proposed a graph-based model integrated with ant colony optimization (ACO) to navigate the robot under the robot’s kinematics constraints. Xiong et al. (2021) further improved ACO using the time Taboo strategy to improve the algorithm convergence speed and global search ability in a dynamic environment. Cèsar-Tondreau et al. (2021) proposed a human-demonstrated navigation system, which integrates the behavioral cloning model into an off-the-shelf navigation stack.

This study proposes a progressive three-layer framework for the CCPP navigation of autonomous vehicles. Initially, in the first layer, a new type of deep learning-based complete coverage path generation method is developed to generate complete coverage trajectories without considering obstacles. A feature learning-enabled fully convolutional deep neural network (FCNN) model is developed to identify the edges of the workspace to be explored, in combination with the starting and target positions of the vehicle to estimate waypoints given an occupancy grid map and generate the CCPP paths. The generated paths are references to guide the vehicle in the following layers to reset and continue CCPP with obstacle avoidance once traversing in the vicinity of obstacles, which improves the computational efficiency of vehicle re-planning.

In the second layer, the obstacles in the environment are considered in this stage. A nature-inspired path planning method is proposed to perform autonomous navigation of vehicles in the environment. Particularly, the vehicle deeply re-plans when it traverses in the vicinity of obstacles. In this study, the Bat algorithm is utilized to plan a collision-free trajectory in light of the size and shape of the obstacles. Once the vehicle completes the re-planning near the obstacles, a new re-joint mechanism is developed to enable the vehicle to re-join complete coverage trajectories. Additionally, an environment-based obstacle approximation and fusion paradigm is developed using image processing of feature extraction. Based on the proposed obstacle approximation and fusion method and the nature-inspired path planning method integrated with the re-joint mechanism, the autonomous vehicle takes less computational effort for optimal path planning on the map populated with obstacles.

Furthermore, a reactive local navigator in the third layer is developed to dynamically update the path and map in real time, so as to avoid moving obstacles and unknown obstacles in the dynamical environment. It dynamically adjusts the speed and direction based on onboard LIDAR sensors to navigate autonomous vehicles locally, thereby benefiting obstacle avoidance and safety assurance.

Overall, the framework composed of three layers advances accurately and is efficiently based on the environmental information layer by layer. Specifically, in the first layer, only the satellite images are needed to provide the size and shape of the searching area and the vehicle’s initial and final positions. In the second layer, the images obtained from the unmanned aerial vehicle (UAV) are required to gather detailed information of the obstacles in the environment, such as minecarts, planters, and vehicles. The third layer is based on onboard LIDAR sensors, used for real-time local reactive navigation of autonomous vehicles, avoiding moving obstacles, and building maps simultaneously. The contributions of this study are summarized as follows:

1) A hierarchical framework is proposed for the autonomous vehicle CCPP navigation in real-time environments;

The rest of this study is organized as follows: in Section 2, the deep learning-based complete coverage path generation method is addressed. The second layer with regard to the nature-inspired algorithm and re-joint mechanism is explained in Section 3. Section 4 shows the reactive local navigator based on LIDAR sensors, which is the third layer in our proposed framework. Simulation and comparison studies are presented in Section 5. Several important properties of the presented framework are summarized in Section 6.

In this section, the required assumptions are described for the proposed method. The region to be explored is assumed in a 2D environment, and the configuration space ℧ for autonomous vehicle Δ is formulated as ℧ ⊆ R 2 . For this study, the boundary of the area to be explored is first obtained based on image processing. There are many existing studies on edge detection (Poma et al., 2020; Nasirian et al., 2021), proving its practicability and reliability (Wagner and Oppelt, 2020). Hence, this study omitted this step and the workspace is directly analyzed. Each region is described by a standard form of convex polygon, ζ = { V , E } , V = { 1,2 , … , n } , E = { ( 1,2 ) , … , ( n , 1 ) } , where V is a set of vertices in clockwise order and E a set of edges. The vehicle’s exploration range (for the task of seeding, cleaning, rescuing, etc.) is a circle with a diameter of d. The vehicle starting position is denoted as P s and the end position is denoted as P e . The CCPP path is denoted as ω = { F 1 , F 2 , … , F n } , while the full CCPP path is Ω = { P s , ω , P e } . There are infinite potential solutions for covering an area known as an NP-hard problem (Arkin et al., 2000). Therefore, a variety of search patterns have been developed, such as star, zigzag, spiral, or BFP. The BFP path is utilized to establish the complete coverage path with advantages of low spatial complexity to be tracked easily by the autonomous vehicle.

Previous research has mainly focused on the CCPP exploration in the workspace to be explored while ignoring the vehicle’s starting and end positions in real-world scenarios. However, based on energy optimization and constraint considerations, the entire trajectories need to be considered. Therefore, for multiple edges of the polygons, the starting and end points of the vehicle should be combined to determine the vehicle’s search direction. Meanwhile, in light of the properties of the BFP-based CCPP trajectories, the optimal trajectory lines are parallel to one of the edges of the area (Torres et al., 2016). The procedure of the search direction is developed in Algorithm 1, and the process details are discussed in the following sections. The algorithm requires searching the set of opposite vertex pairs η, such as vertices (i, j) in Figure 2A. One of the vertexes, such as i, finds its adjacent vertex i _adj , and the BFP is formed in parallel to the line i , i a d j ̄ with the gap distance based on the vehicle exploration range d. In this case, the search direction θ is perpendicular to i , i a d j ̄ toward the j. The function Dist (i, j) calculates L R , the total length of the BFP trajectory in the workspace. L R = ∑ s = 1 n x F s + 1 − x F s 2 + y F s + 1 − y F s 2 (1)

Then, the starting and end points of the autonomous vehicle are enclosed in the total length L to obtain the optimal CCPP path Ω. Notably, the optimal BFP-based CCPP trajectory is first obtained in light of the edge of the explored polygon before combining it with the start and end points to obtain the minimum total length. Thus, the search direction θ of the BFP is obtained in the range of [ − π, π] represented by dashed lines with autonomous vehicle BFP segmentation lines, as shown in Figure 2B.

Algorithm 1

Pseudo-code for search direction.

Through the obtained BFP path segmentation line, we take the points that are intersections of the segmentation line and the workspace edge as a regression problem, and a fully convolutional deep neural network is utilized to estimate the positions of different points. In light of the turning radius of the vehicle, as shown in Figure 3B, the global CCPP trajectories are predicted by the neural network (NN) from the input image. The input image with resolution M × N is first divided into an I _M × I _N grid map (Figure 3A). The grid map I _M × I _N is h times smaller than the input image. Each grid contains h × h pixels, and the confidence probability C ( s ) denotes the confidence of the points in the grid s. C ( s ) tends to zero when no point in the grid s while the confidence probability C ( s ) > T ( c ) represents the possible points in the grid s, where T ( c ) denotes the confidence threshold. In each grid, the location of the final CCPP trajectory point is further refined by δ _m and δ _n in accordance with the vehicle turning radius.

The fully convolutional neural network (FCN) designed by an input tensor X ( i ) is gradually convolved by a stack of n residual reduction modules as shown in Figure 3C. Each module is composed of a series of two-dimensional convolutional layers, with Mish as the activation function, and the channel and spatial attention layer, allowing the network to highlight more relevant features. In addition, each module ends with a convolutional layer with stride 2 to reduce the spatial dimension of the input tensor. After n residual reduction modules, the two dimensions of the first dimension are reduced to a factor h + 1. Therefore, we insert a transposed convolutional layer with a stride of 2 to obtain a two-dimensional output tensor of I _M × I _N (refer to Figure 3). Add a remaining connection of the output tensor from the n − 1 block to include important spatial information in the tensor before the last layer. Finally, similar to a single-stage target detection network, the output tensor Y ( i ) and the shape I _M × I _N × 3 are calculated by 1 × 1 convolution operation, and the sigmoid and tanh are utilized as the activation of the first and last two channels, respectively. Thus, the confidence probability C ( s ) obtained by sigmoid predicts the existence of possible waypoints. In contrast, the tanh function is limited between −1 and +1, and the two coordinate compensations δ _m and δ _n of each unit are calculated.

In the field of autonomous vehicles, map information is highly important, especially for global path planning, which determines the accuracy of the trajectory. However, for complex environments, such as disaster sites, many obstacles are scattered or gathered in various places, which bring safety and computational difficulties to the path planning of autonomous vehicles. When acquiring the disaster area or agricultural field map through drones, we need to retrieve map information to obtain specific locations of obstacles and approximate and merge a large number of obstacles into several large convex obstacles, thereby improving the efficiency of search and exploration tasks. Especially at the disaster site, the rescue time is limited, and it is important to quickly locate and approximate obstacles in the complex environment. Therefore, this section proposes an effective method for obstacle detection, obstacle approximation, and fusion.

In order to compare the proposed model with others, we compare the proposed CCPP method with the well-known Boustrophedon Cellular Decomposition (BCD) method (Acar and Choset, 2002). In this section, the map is a satellite image from the North Farm of Mississippi State University as shown in Figure 8. The starting and target points are randomly selected. Different shapes of the targeted areas are selected to perform coverage searches. The edges of the targeted areas as three scenarios are highlighted in yellow, blue, and green in Figure 8. The starting and target points are represented by squares and stars, respectively. The exploration range d of the autonomous vehicle is set as 5 m. The shape of the targeted areas, the starting and target positions of the autonomous vehicle are considered. Then, the directions of the vehicle’s search of the proposed CCPP in these three scenarios are achieved in Figures 9A–C, respectively.

In three scenarios, the proposed CCPP method has a shorter path length regardless of the coverage path within the targeted areas, the path connecting the starting and target points, and the final total path. The trajectories of the proposed CCPP method are shown in Figures 9A–C, respectively. The trajectories of the BCD method are shown in Figures 9D–F, respectively. The comparative studies are summarized in Table 1.

The average precision (AP) metric is utilized to evaluate the training results. A total of 3000 synthetic images with a resolution of 800 × 800 are utilized for training and h = 8. Then, the network is evaluated with 1000 synthetic images. The network is trained with 200 epochs using Adam optimizer. The learning rate is equal to 3e-4, and the batch size is 16. A tunning point prediction is within the selected area as a true positive (TP), while more predictions fall within the selected range. Only one is counted as TP and all others as false positive (FP). All ground-truths not covered by a prediction are counted as false negatives (FN). Because different confidence thresholds can obtain different recall and precision values and the AP calculation is obtained by the common definition of recall and precision, we change the threshold value from 0 to 1 with step size 0.1. Multiple results obtained by modifying the threshold show that recall and precision are inversely proportional. The final confidence threshold is set as 0.9. At a distance range of 8 pixels, the average precision equals 0.9735.

Consequently, through the deep learning method, the turning points of the autonomous vehicle are generated, and the final CCPP paths are obtained, as shown in Figures 10A,B. The neural network training and testing procedure are similar to the Deepway model (Mazzia et al., 2021). However, the Deepway model relies only on identifying row-based crops to manually sort the order of waypoints that generates the final CCPP result. It remarkably limits the usage scenarios of the model and requires additional labor time to sort the waypoints. Our proposed model extends the range of usage to random environments with arbitrary shape search areas and considers the relative positions of the autonomous vehicle to obtain the optimal CCPP path, as shown in Figure 10.

In this section, simulation studies are carried out to validate the second and third layers of the proposed framework, utilized for CCPP re-joint and obstacle avoidance in environments with stationary and dynamic obstacles. Due to the relatively large environment, in order to better show the re-joining path of the autonomous vehicle, a part of the map is truncated. More detailed information of the images is obtained from the drones, as shown in Figure 11A, in which haystacks and trucks are detected as obstacles. Obstacles are then approximated and merged into a grid-based map. The CCPP with obstacle avoidance function uses the CCPP path obtained in the first layer as a reference to decrease the computational effort. The proposed obstacle avoidance method based on the BA algorithm will only be triggered when an obstacle is presented in front of the vehicle. The grid of the current position is taken as the starting point, and the next grid of the CCPP reference path unoccupied by obstacles is regarded as the target point to plan a collision-free trajectory. The proposed method is unnecessarily to recalculate for the complete map, which can flexibly adapt to the alterations of obstacles in the map. The CCPP trajectory of static obstacle avoidance is shown in Figure 11B. When there are unknown and moving obstacles in the environment, such as the trucks in Figure 11, the autonomous vehicles can still rely on the onboard LIDAR to dynamically avoid obstacles and return to the original coverage path to search the entire environment. Two specific operations of the autonomous vehicle avoiding moving trucks are shown in Figure 12. The autonomous vehicle, the first truck, and the second truck are represented by dark blue circles, yellow rectangles, and light blue rectangles, respectively. The autonomous vehicle performs dynamic avoidance twice for the first truck. The vehicle successfully avoids obstacles and returns to the planned CCPP trajectory. The second truck first stops at the original position before the vehicle avoids obstacles according to the obstacle avoidance path planned by the second layer of the framework. During the returning process, the truck starts to move, and the vehicle can still avoid obstacles to the updated truck position. These results prove that the proposed CCPP framework is effective and efficient in coverage navigation under real-world applications.