Active Scanning Method for AUVs Using Entropy Maps Utilized with Underwater Sonar Measurements

1. INTRODUCTION

The exploration capabilities of autonomous underwater vehicles (AUVs) in unknown environments are important for ocean research, environmental monitoring, and resource exploration. To enable these capabilities, it is necessary to provide robots with highly reliable maps using technologies such as simultaneous localization and mapping (SLAM). In addition, in unknown underwater environments where teleoperation is limited, robots must autonomously generate active paths to build a map.

Robust mapping and autonomous exploration methodologies for mobile robots have been studied extensively. In particular, SLAM has been widely investigated and proven to be effective for many mobile robot sensing platforms [1-3]. In [4] and [5], a method was introduced to represent maps using entropy, a concept from information theory that expresses uncertainty. This approach enables robots to plan optimal paths autonomously and explore unknown environments. However, these studies have generally been validated on ground robot platforms that utilize optical cameras or LiDARs, which are effective on the ground. It has been experimentally verified that such sensors are not suitable for underwater environments because of their high turbidity and signal attenuation rate [6,7].

Owing to such harsh underwater sensing environments, AUVs often rely on acoustic-based sensors, such as forwardlooking and profiling sonars, to acquire nearby information. Image sonar is a widely used sensor for underwater exploration that measures the features (time-of-flight and intensities) of sonar reflections by projecting multiple sonar beams and receiving the reflected signals. It then provides feature measurements in 2-dimensional (2D) images. However, sonar measurements have low signal-to-noise ratios (SNR), and their elevation information is lost owing to the 2D image generation mechanism of image sonar [8,9]. Therefore, a method that considers these limitations is required when applying image sonar to underwater mapping. [10] and [11] proposed a space-carving-based underwater mapping technique, and [12] introduced a method for restoring the shapes of underwater objects by combining an image sonar with a rotational instrument. However, these methods require multiple sonar images and the AUV to remain stationary or follow ideal paths, which are difficult to achieve using real AUVs. [13] and [14] proposed methods for generating 3D point clouds using forward-moving AUVs. However, owing to the limitations of the field-of-view (FoV) of the sensor, it is not possible to reconstruct the overall shape of objects that exceed the FoV using a single scan. To address this issue, [15] proposed a method for reconstructing underwater objects using sonar images obtained from different scan paths while optimally selecting consecutive scanning directions. However, this approach relies on 2D sonar image data to generate the next scan path and align the scanned information, resulting in less accurate reconstruction results when applied to objects with unstructured shapes.

To overcome these limitations, this study proposes a two-stage underwater scanning method for AUVs for efficient underwater mapping (Fig. 1). In the first stage, the robot follows a predefined scanning path and generates a probabilistic 3-dimensional (3D) volumetric map using the 2D image sonar data acquired during the process. In the second stage, the probabilistic map is represented based on entropy, and a successive path that can scan the most uncertain region is generated and followed. Simulation results show that the proposed method provides efficient AUV scan paths to achieve accurate 3D reconstruction of seabed topography and underwater objects. The proposed method enables the autonomous exploration of AUVs in unknown underwater environments.

Fig. 1.

Proposed scanning method based on entropy evaluation of a 3D occupancy voxel map.

2. Method

The pipeline of the proposed method is illustrated in Fig. 2, where the two-stage process is divided into seven distinct steps. The process begins with the generation of an initial volumetric map from sonar data collected as the AUV follows a predefined scan path. This volumetric map is then converted into an entropy map to identify the region with the highest uncertainty. Using this information, the successive scanning attitudes and paths that minimize map uncertainty are determined. The entire process is iterated until the fifth stage, as shown in Fig. 2, where an entropy summation check is performed. The detailed implementation and explanation of each step are provided in the following subsections.

Fig. 2.

Pipeline of proposed scanning method.

2.1 3D Volumetric Mapping Using Sonar Images

Volumetric mapping is a method for probabilistically estimating a map based on AUV attitude and sensor data in an environment with uncertainty. The environment is represented as a collection of volumetric elements such as grids and voxels. In this study, we used a 3D occupancy voxel map for underwater navigation, in which the occupancy probability of each voxel was updated with each new observation. The AUV's attitude is represented by the state vector X=[x_r y_r z_r Φ_r θ_r ψ_r]^T, and the observation data Z is a sonar image represented as a 2D matrix. The entire map M is a set of voxels m₁,m₂,...,m_n each representing an occupancy state. Voxel m_i is represented by a state vector [xⁱ_m yⁱ_m zⁱ_m]^T, and the occupancy probability of the voxel is represented by p(m_i) . Assuming that each voxel is independent, the probability of the entire map M is defined as

$\[ p\left(M\right)=\prod _{i=1}^n p\left(m_i\right). \]$

(1)

The map is updated based on the observations Z_t and AUV attitude X_t over time t. The probability that voxel m_i is occupied, p(m_i ∣ Z_1:t,X_1:t), is calculated as follows:

$\[ \begin{array}{l}\begin{array}{c}n\left(t\right)=\frac{P\left(t\right)V\left(t\right)}{RT\left(t\right)}=\frac{P\left(t\right)\left[V_A+V_H\left(t\right)\right]}{RT\left(t\right)}=\frac{P_0[1+\beta (t\left)\right]\left[V_A+V_H\left(t\right)\right]}{R{T}_0[1+\alpha (t\left)\right]}\\ \cong \frac{P_0}{R{T}_0}\left[V_A+V_H\left(t\right)+V\left(t\right)\left(\beta \right(t)-\alpha (t\left)\right)\right]\\ =n_A\left(t\right)+n_H\left(t\right),\end{array}\\ \begin{array}{c}with n_A\left(t\right)=\frac{P_0}{R{T}_0}{V}_A,\\ n_H\left(t\right)=\frac{P_0}{R{T}_0}\left[V_H\left(t\right)+V\left(t\right)\left(\beta \right(t)-\alpha (t\left)\right)\right]\\ \alpha \left(t\right)=\frac{T\left(t\right)-T_0}{T_0},\beta \left(t\right)=\frac{P\left(t\right)-P_0}{P_0}\end{array}\end{array} \]$

(2)

Here, η represents the normalization term that ensures that the raw sonar image is analyzed according to predefined criteria, distinguishing between occupied and empty pixels, as shown in Fig. 3 (b). Because of the sonar characteristics, these pixels do not provide elevation information in the 3D world's spherical coordinate system. Therefore, as illustrated in Figs. 3 (c) and (d), all the voxels corresponding to the pixel within the sonar FoV from X_t are searched, and the occupancy probability of each cell is updated using Eq. (2). As the AUV moves along a designated path and updates the map based on multiple sonar images, the approximate shape of the seabed can be obtained, allowing the creation of an initial map.

Fig. 3.

Voxel representation of a sonar image. (a) Raw sonar image, (b) pixel thresholding result, (c) occupied voxels, (d) empty voxels.

3. EXPERIMENTS

The proposed methodology was validated using an ROSbased UUV-Sim [17] environment. The experiments were conducted under two scenarios. Fig. 4 illustrates the experimental environment of each scenario and provides sample sonar images obtained under these settings [18]. Scenario 1 features a terrain with a tetrapod, whereas Scenario 2 involves a shipwreck positioned in the same location. In Scenario 1, the object was fully contained within the FoV of the sonar, whereas in Scenario 2, it was significantly larger than the FoV of the sonar. Detailed information on the environmental settings and sonar configurations for each scenario is listed in Table 1.

Fig. 4.

Simulation settings of two scenarios: (a), (c) simulation environments; (b), (d) sonar image examples.

Table 1.

Simulation Specification

The AUV ‘Cyclops’ [19] used in the experiment is a hovering- type AUV that is equipped with six thrusters for its 4 degrees of freedom control (without roll and pitch control). The AUV estimates its state using the IMU and DVL sensors and maintains its position through PID control based on the estimated states and thruster outputs. To collect the observa- tional data, an image sonar tilted 30° downward toward the seabed was mounted at the bottom of the AUV.

In Scenarios 1 and 2, 20 sample poses were generated, and the predefined path was set as a straight line passing over the center of the object. Using the ground-truth values provided by Gazebo, the robot and sensor poses were assumed to be accurate. The total trajectory for each scenario can be found in the “trajectory” section of Fig. 5 and Fig. 6. In Scenario 1, the object was sized such that it fit entirely within the FoV of the sensor. Consequently, most of the front surface of the object was reconstructed after the initial scan. A significant amount of entropy was formed on the rear side of the object, leading to the generation of X_center for C_max at the center of the rear side. The radius r was determined to be 5 m based on the x-y plane radius of C_max, and the sample poses were generated accordingly. Excluding the initial scan path, two additional scans were performed, with each successive scan path depicted as green paths under the “successive path search” section of Fig. 5. During the third scan, the scan TC determined that all Hⁱ_sum had failed to exceed the TC, and the scanning was terminated.

Fig. 5.

Procedure result of proposed method at scenario 1.

Fig. 6.

Procedure result of the proposed method at Scenario 2.

In Scenario 2, unlike in Scenario 1, the object was larger than the FoV of the sensor, indicating that not all parts of the object were captured in the initial scan. Consequently, a significant entropy was observed on both the rear and side surfaces of the object. Additionally, because of the large size of the object, C_max was generated not at the rear of the object but within its interior. The radius r was determined to be 8 m, resulting in the generation of sample poses over a wider area compared with that in Scenario 1. Excluding the initial scan path, three additional scans were conducted, and these successive scan paths are also depicted as green paths under the “Successive path search” section of Fig. 6. In the fourth scan, all Hⁱ_sum images failed to exceed the TC, and the scan was terminated.

4. RESULTS

The object-reconstruction rate was assessed to evaluate the accuracy of the proposed mapping method. A ground truth voxel map was generated based on the model used in the simulation. The comparison between the volumetric map generated by the proposed method and the ground truth voxel map was conducted using the following metrics, namely precision (P), recall (R), and F_β score.

Here, TP refers to the voxels present in the ground-truth model and that were successfully reconstructed in the mapping results. False positive (FP) represents noise voxels that are not in the ground truth model but are generated in the mapping results. False negative (FN) refers to voxels that exist in the ground-truth model but are missing from the mapping results.

The object reconstruction accuracy of the proposed method was compared with data obtained from two different scanning paths. The mapping process followed the approach outlined in Section 2.1. For the lawnmower path, scanning was conducted from a position where the object was initially not visible in the sonar FoV, thereby ensuring that the entire object passed through the scanning area. For the uniform path, the number of scans matched the number of scans in the proposed method, dividing 360° into equal segments. The heading angle was set to align with the object, creating straight paths passing over its center. The path shapes for the lawnmower and uniform methods are shown in Fig. 7. Tables 2 and 3 present the evaluation results of the reconstructed seabed objects in Scenarios 1 and 2, respectively, comparing the proposed method with the reference paths in terms of precision, recall, and F-scores. It can be observed that the precision values are lower than the recall values. This is because a significant number of voxels were classified as FPs. As shown in Fig. 8, this occurs because of the limitations of the image sonar mechanism, specifically, the lack of elevation information, which results in the generation of voxels at the bottom of the object that are counted as FPs.

Fig. 7.

Comparison of scan paths: (a) lawnmower path, (b) uniform path in scenario 1, (c) uniform path in scenario 2

Table 2.

Performance Comparison of Scanning Methods of Scenario 1

Table 3.

Performance Comparison of Scanning Methods of Scenario 2

Fig. 8.

Comparison of ground truth voxels (green) and the generated voxels (red) using the proposed method.

5. CONCLUSIONS

This study proposes a two-stage scanning method for the efficient 3D reconstruction of unknown seabed topography and underwater objects. In the first stage, a 3D occupancy map was generated using underwater image sonar. In the second stage, the initially generated map was transformed into an entropy map, which was used to generate the next scan path. The data acquired along the new scan paths were used to continuously update the seabed topography and objects. To determine the next scan path, an entropy summation method reflecting the characteristics of the sonar image mechanism was proposed. This method quantitatively defines meaningful scans based on the ratio of the remaining entropy summation to the entropy that can be acquired from the candidate scan poses, allowing the robot to autonomously terminate the scanning process. This study conducted computer simulations of two scenarios, demonstrating that the underwater robot could autonomously generate and follow paths based on the initially created map and update the map iteratively. The reconstruction accuracy of the proposed method was found to be higher than or comparable with that achieved using predefined comparison paths in terms of both the precision and recall of the reconstructed objects.

Acknowledgments

This research was supported by the industry–academia cooperation project LIG NEX1.

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