# Chemical servoing with hexapod robot for gas source localization and YOLO-based visual defect detection

Guillaume Morin-Duponchelle, Benoit Zerr, Ahmed Nait Chabane

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Guillaume Morin-Duponchelle, Benoit Zerr, Ahmed Nait Chabane. Chemical servoing with hexapod robot for gas source localization and YOLO-based visual defect detection. International Journal of Intelligent Robotics and Applications, In press, Focused Section on Robotics Enabled Inspection, 10.1007/s41315-025-00464-0. hal-05078255

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# Chemical Servoing with Hexapod Robot for Gas Source Localization and YOLO-based Visual Defect Detection

Guillaume Morin-Duponchelle$^{a, b}$, Ahmed Nait Chabane$^a$ and Benoit Zerr$^b$

$^a$CESI LINEACT, 24 rue Le paquebot, Saint Nazaire, 44600, France; $^b$ENSTA Bretagne, 1 rue François Verny, Brest, 29806, France

## ARTICLE HISTORY

Compiled May 26, 2025

## Preprint Notice

### Preprint version.

This manuscript is the original version (preprint) submitted to the *International Journal of Intelligent Robotics and Applications* (IJIRA). **It has not been peer-reviewed, revised, or accepted at this stage.** For the final published version, please refer to:

https://doi.org/10.1007/s41315-025-00464-0

## ABSTRACT

Robotic systems have the ability to perform industrial inspection tasks through the integration of visual and chemical servoing functions. A commonly used system is the image-based servoing system. This study presents an innovative approach that merges chemical servoing with visual defect detection in industrial settings using a hexapod robot. The main goal is to develop a hexapod robot capable of detecting and approaching a gas source through chemical servoing, and subsequently analyzing the source using a pretrained YOLOv5m model, a one-stage CNN detector architecture. The effectiveness of the proposed methodology is showcased through simulations that compare different chemical servoing algorithms and image defect detection techniques for gas source identification. In addition, a prototype of the hexapod robot is presented.

## KEYWORDS

Hexapod robot; Chemical servoing; Visual detection; YOLO; Convolutional Neural Network (CNN); industrial inspection

## 1. Introduction

The use of mobile robots for industrial inspection has been an essential strategy for maneuvering through complex, restricted, or dangerous settings. These robots replace humans in scenarios where safety is compromised, such as exposure to chemicals or radiation. They also handle tasks that are too dangerous for direct human intervention, such as maintaining high-voltage power lines. Industries such as offshore operations,
chemical processing, and power generation (including nuclear and thermal plants) ben-
efit significantly from the deployment of these robots [? ]. Benefits include increased
consistency in reaching remote or confined areas, increased dependability in perform-
ing specific duties, and a more comprehensive and uniform examination, all leading to
reduced inspection downtime.

In the field of robotics, considerable focus has been directed towards nonholonomic
robots, characterized by distinct movement limitations. These robots have been the
subject of extensive investigation due to their straightforward system architecture, pre-
cise odometry facilitated by encoders, and the abundance of control strategies at hand.
However, there is still a research gap in the domain of legged robots, particularly in
the context of visual servoing, and even more so in relation to insect-like models [1].
The particular design of the robot indicates that it was specifically created for a par-
ticular function. In this instance, the robot’s structure is meant to address the common
difficulties faced in terrestrial and industrial enclosed spaces. This underscores the ap-
propriateness of legged robots for such limited industrial environments. For example,
the authors of [2] propose a hexapod robot developed to inspect aircraft components
using a deep learning technique.

Chemical sensing has long been overlooked within the robotics community due to
the technical challenges associated with the implementation of artificial olfaction on
robotic platforms [3]. In the existing literature, very few studies address the challenge
of localizing the gas source using a hexapod robot equipped with sensors. In their work
[4], the authors introduce an approach that uses a genetic algorithm and a self-organizing
map to locate CO2 gas with a hexapod robot.

The objective of this research is to develop a hexapod robot capable of detecting
gas sources and analyzing defects that cause gas emissions. The methodology involves
implementing a chemical servoing technique to pinpoint the gas sources, followed by the
use of a pretrained region-based approach with convolutional neural network (RCNN) to
classify the defects as being of industrial origin. This study shows promise in improving
the safety and efficiency of industrial operations. Early detection and classification of
industrial gas leaks can prevent accidents, reduce operational interruptions, and improve
worker safety.

The following sections will explore into the relevant literature in this field, the
methodology employed for the robot’s design and implementation, the results and analy-
sis of the experiments conducted, and conclude by summarizing the findings and propos-
ing future research directions.

## 2. Related Work

### 2.1. *Image-Based Visual Servoing*

Visual servoing is a field that uses computer vision data to generate real-time control
signals to guide mechanical motion [5]. It combines image processing, computer vision,
and control theory [6,7]. This methodology can be divided into two components: visual
and motion. First, measurements are extracted from images, visual characteristics are
analyzed, and they are incorporated into the control system. The discrepancy between
the current and desired values of these visual features is then used to regulate the
robot's velocity. Image-Based Visual Servoing (IBVS) operates the end effector in a
closed loop. The camera is attached to the mobile frame and tracks the relative position
of the target. The features of the object could include its coordinates, lines, color [8],
color combinations [9], or QR codes [10]. A control algorithm assesses the error in the
observed attributes without determining the pose of the target object [11].

Recent studies have highlighted the proficiency of Image-Based Visual Servoing (IBVS) in detecting cracks and imperfections in various materials, including concrete structures and metallic surfaces [12]. IBVS improves the alignment of robots with captured images, allowing precise location and detailed examination of suspicious areas [13]. However, while IBVS is promising for crack and fault detection, it is not the optimal solution to identify gas sources, which requires different techniques. Furthermore, there are notable limitations to IBVS [14]. Its effectiveness decreases when dealing with significant rotations, causing the object to move out of the camera's field of view, hindering detection. This is known as the off-screen effect. IBVS may also face challenges in navigating complex environments or adapting to sudden changes, affecting its reliability and real-time operation. Additionally, constraints such as limited computational resources and processing speeds in mobile robots can affect IBVS performance [15]. In the context of gas source detection and tracking, chemical sensors, which can directly detect the presence and concentration of gases, are more suitable for industrial inspections. The integration of IBVS with these sensors could lead to a comprehensive inspection system that uses the strengths of both techniques.

## 2.2. Chemical Servoing and Gas Source Localization

Heavy industries are susceptible to accidents with severe consequences for local and regional populations. These incidents often result from inadequate maintenance, non-compliance during development, or human error [16]. To address this problem, continuous monitoring of air quality and inspections of industrial infrastructure is crucial.

Various established techniques for chemical measurements enable the generation of chemical maps [17]. For example, leaks of methane, ethylene and propylene can be detected accurately using infrared camera systems [18]. Terahertz imaging systems provide capabilities for non-destructive inspection and chemical analysis [19]. Gas chromatography (GC) and ion mobility spectrometry (IMS) are capable of identifying specific chemical substances [20]. However, despite their precision and comprehensive data coverage, these methods are often costly, require significant computational resources, lack portability, and are slow to operate.

As a result of the risks associated with conducting real gas experiments, Gas Dispersion Simulation (GDS) plays a crucial role in predicting challenges and improving research and development in robotics. When simulating gas dispersion, factors such as spatial dimensions [21], dispersion modeling techniques [22], and gas concentration levels [23] must be taken into account. Basic GDS models are commonly classified as box models (which simulate uniform gas concentrations within boxes) [23], Gaussian models [24], and analytical models [22]. More sophisticated approaches include models based on Lagrangian, Eulerian, and computational fluid dynamics (CFD). These models simulate gas dispersion by tracking the random movement of numerous particles influenced by airflow and turbulence patterns. The Eulerian model, which uses a fixed 3D Cartesian grid as a reference frame, unlike Lagrange models, which use a moving frame, provides more accurate results. However, a significant limit is the substantial computational burden that increases with increasing particle count [25,26]. CFD-based models address three-dimensional equations related to wind, temperature, humidity, and gas concentrations. These models are used for simulations that demand high spatial and temporal precision, explicitly considering physical obstructions such as buildings and
<table><caption>Table 1.: Comparison of Gas Dispersion Simulators for robotics applications. In the presented table, MOX Metal Oxide Sensors, PID Photo Ionization Detectors, CAD Computer Aided Design, CFD Computational Fluid Dynamics.</caption><thead><tr><th>Category</th><th>Lagrangian</th><th>Eulerian</th><th>Hybrid</th><th>Hybrid</th><th>Lagrangian</th></tr></thead><tbody><tr><td>Simulator</td><td>PlumeSim</td><td>Orebro</td><td>GADEN</td><td>WRF-Chem</td><td>HYSPLIT</td></tr><tr><td>Robotic Integration</td><td>Yes</td><td>Yes</td><td>Yes</td><td>-</td><td>-</td></tr><tr><td>Environment</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Type</td><td>2D</td><td>3D</td><td>3D</td><td>3D</td><td>3D</td></tr><tr><td>Dimensionality</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Obstacles</td><td>None</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Input Format</td><td>Manual</td><td>Occupancy Files</td><td>CAD</td><td>Emission and Weather Files</td><td>Meteorological data</td></tr><tr><td>Wind Simulation</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>CFD Support</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td></tr><tr><td>Gas Dispersion</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Model</td><td>CFD</td><td>Filament</td><td>Filament</td><td>Full Chemical</td><td>Lagrangian puff/particle</td></tr><tr><td>Gas Sources</td><td>Single</td><td>Single</td><td>Multiple</td><td>Multiple</td><td>Single or multiple</td></tr><tr><td>Chemical Type</td><td>Independent</td><td>Gravity/Buoyancy</td><td>Gravity/Buoyancy</td><td>Full Chemical Mechanisms</td><td>User-defined or simplified</td></tr><tr><td>Sensor Emulators</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Chemical Sensors</td><td>MOX</td><td>MOX</td><td>MOX, PID</td><td>Varied as needed</td><td>User-defined</td></tr><tr><td>Anemometer</td><td>-</td><td>-</td><td>Ultrasonic</td><td>Internal/External Models</td><td>User-defined</td></tr><tr><td>References</td><td>[29-31]</td><td>[32-34]</td><td>[27,35]</td><td>[36,37]</td><td>[38-40]</td></tr></tbody></table>

walls [27].

Different GDS implementations have been examined in academic sources, such as Ansys [?] and OpenFoam [28] software. Although these tools can create complex dispersion models, they lack the ability to simultaneously integrate robotic platforms and gas-sensing emulation. On the contrary, Plumesim [29] succeeded in combining robotic functions with the simulation of gas dispersion based on Gaussian plumes. However, the foundational simulation theory of Plumesim does not accommodate complex gas scenarios or detailed plume dispersion. Various GDS software packages, such as GADEN, OREBRO, and HYSPLIT, are designed to meet a wide range of simulation requirements, particularly relevant to robotics applications. GADEN provides a wide range of functionalities for 3D gas dispersion simulation, encompassing the management of obstacles and the selection among various dispersion models. A comparative study shown in Table 1 from the literature emphasizes essential features for robotic applications. These include abilities for robotic integration, environmental modeling, wind simulation, gas dispersion modeling techniques, and backing for sensor imitation.

## 2.3. Leak detection in industrial applications

Traditional methods for detecting leaks, such as manual inspections and ultrasound testing, are often time-consuming, costly, and require specialized skills. These limitations underscore the necessity for more efficient, precise, and cost-effective leak detection solutions. Deep learning has emerged as a promising alternative that addresses these challenges and offers significant advancements in leak detection capabilities.

Supervised learning is a commonly employed approach for leak detection using deep
learning techniques. In supervised learning, a model is trained on a dataset where images or videos containing leaks are annotated. The model then learns to associate the input data with the corresponding leak annotations. Convolutional neural networks (CNNs) are a popular type of supervised learning model for leak detection. CNNs can extract detailed features from images and videos and are robust to variations in lighting, noise, and background disturbances.

One-stage detectors such as YOLO are favored for leak detection because of their speed and efficiency. YOLO directly predicts bounding boxes and class probabilities for objects in images or videos, eliminating the need for region proposals. This feature makes YOLO suitable for real-time applications. The simple architecture of YOLO facilitates its implementation and deployment in industrial settings. The YOLO model has evolved through several iterations, each bringing improvements. Although YOLOv1 and YOLOv2 were the first to achieve real-time object detection, they had accuracy limitations. YOLOv3 improved accuracy without compromising speed. For example, in a study by Zhao X et al. [41], YOLOv3 was used to detect leaks in gas pipelines. Similarly, YOLOv4 was designed to strike a balance between accuracy, speed, and resource use. YOLOv5 introduces further enhancements in accuracy and training.

On the contrary, while one-stage detectors are faster, they generally offer lower accuracy compared to two-stage detectors like Faster R-CNN. Faster R-CNN operates by first generating a set of region proposals and then determining the presence of a leak in each proposal. In essence, the application of deep learning has demonstrated its efficacy in detecting leaks within industrial environments. Deep learning models provide exceptional accuracy, robustness, scalability, and adaptability, making them suitable for a wide range of leak detection applications. Among these models, YOLO stands out as a particularly suitable choice for leak detection due to its speed, precision, and simplicity. Research has shown that YOLO can achieve accuracy levels similar to those of state-of-the-art leak detection techniques, while significantly outperforming them in terms of speed. In this study, we opt to use YOLOv5 for the detection of gas leaks.

## 3. Methodology

This research addresses the challenge of detecting and reaching Points of Interest (POIs) in an environment using a hexapod robot. The choice was made to use a hexapod robot that walks at three degrees of freedom per leg to address the problem of detecting POIs. POIs can be visual (e.g., defects on a surface) or chemical (e.g., gas leaks). The proposed approach integrates various modules to allow the robot to navigate and reach POIs autonomously. The modules that make up the proposed methodology include:

* **Robot Architecture and Control:** The role is to control the robot's leg and motion. The standard input data for this approach include the robot's configuration for control, laser sensor data for position determination, and a map of the environment for navigation. The servomotors provide information on the robot's condition and make modifications to the motor controller.

* **Chemical Servoing:** Chemical servoing retrieves data from chemical sensors to determine the concentration of gas and the direction of air flow. The desired output data are the position of the robot relative to the map, the position of chemical percepts translated into navigation points, and the achievement of these percepts where the robot's position should be as close as possible to the position of the gas source location.
* **Visual detection of defects:** Specific input data for visual servoing include visual sensor data, an RGB video stream, and a depth video stream. The desired output data are the robot's position relative to the map, the position of visual percepts translated into navigation points, and the achievement of these percepts where the robot's position should be as close as possible to the position of the percepts.

* **Navigation:** Navigation enables the robot to autonomously navigate through an environment using navigation points within a designated map frame of reference. In our methodology, navigation plays a crucial role in enabling the robot to 1) determine its position in relation to the surroundings (such as obstacles and passable areas), 2) interpret various data from the map, and 3) mark POIs on the map.

* **Odometry** The stability of the hexapod robot's position is critical in various situations. It is essential for the robot's odometry to accurately update its position as it navigates through its surroundings. Inaccurate odometry can lead to the robot deviating from its intended position due to a cumulative error (referred to as the "drifting effect") or being relocated to an arbitrary position on the map (known as the "kidnapping effect"). To address this, a 2D laser sensor (RPLidar) is used to align two laser scans and determine the robot's position within its environment. This approach has been implemented to improve the Monte Carlo localization algorithm (AMCL) [42]. Nevertheless, a limitation of this algorithm is its inability to handle abrupt changes in the robot's pose, resulting in localization failures and the robot being displaced randomly within its environment. The proposed model relies on sending commands to the robot to predict its position, with these commands specifying both translation and rotation in the robot's local reference frame.

The schematic in Figure 1 illustrates a comprehensive outline of the proposed methodology for chemical servoing and visual detection of defects using a hexapod robot.

## 3.1. Hexapod Robot Kinematic and control

### 3.1.1. Hexapod Robot Controller

The control architecture of a hexapod robot is crucial to achieving stable and efficient locomotion. The robot's pose and gait must be controlled in real time based on its morphology, which includes the dimensions of the segments, minimum and maximum angles, and other factors. The controller serves as the cornerstone, establishing the link between the navigation module and the actuators (servomotors).

The control architecture for the hexapod robot consists of three main components:

(1) Pose controller: This controller adjusts the positions of the legs at their extremities (end effectors) based on different static poses (rest, standing, etc.).

(2) Gait controller: This controller generates gaits that allow the robot to move by a sequence of different poses, and, therefore, a sequence of different application points of the end effectors.

(3) Motor controller: This controller interfaces between the hardware (servomotors) and the hexapod controller (angle control information). It serves as an interface for communication, acts as a driver, and allows motor information to be sent back to the hexapod controller. The motor controller depends on the servomotor
<figure><img src="image_2.png" /><figcaption>Figure 1.: Comprehensive outline of the proposed methodology for chemical servoing and visual detection of defects using a hexapod robot.</figcaption></figure>

manufacturer and the software suite they provide.

Using forward and inverse kinematics, the control framework can accurately manage the position and movement pattern of the hexapod robot, allowing it to perform various tasks and maneuver through complex surroundings. Figure 2 shows the complete control structure of the Hexapod robot.

### 3.1.2. Kinematic Model Representation

To effectively manage the hexapod robot, it is essential to determine the position of each end effector (located at the tip of each leg) in relation to the rotational angles for each degree of freedom. For this purpose, both forward and inverse kinematics are used. The kinematic model is integrated as a component of the OpenSHC controller [43] through the application of Denavit-Hartenberg (DH) parameters [44]. The determination of end effector positions and joint angles involves the use of forward kinematics (FK) and inverse kinematics (IK) computations. The body frame can be defined as $(Ob, Xb, Yb, Zb)$, with the body orientation denoted as $(O_{roll}, O_{pitch}, O_{yaw})$. The displacement is characterized in terms of $(x, y, z)$. Robot odometry with respect to a reference map frame $(O_m, X_m, Y_m, Z_m)$ is rooted in a local system. The coordinate frames are established as follows: x (forward), y (left), and z (up). The leg frame is used to translate the intended movement of the robot body using forward and inverse kinematics methodologies.

#### Forward kinematics

The position of the end effector is calculated based on the joint angles, which is crucial to simulate the motion of the robot and visualizing its configuration. Taking into account the angle parameter, the goal is to reach a specific destination of the end effector, identified as the endpoint $P_{endeff} = (x_{endeff}, y_{endeff})$. This task is required for all six legs of our hexapod robot. The DH notation is commonly used for solving forward kinematics, allowing for the representation of a robot's joints with varying degrees of
<figure><img src="image_3.png" /><figcaption>Figure 2.: Architecture of a hexapod robot controller.</figcaption></figure>

freedom. The stiffness of a robot is represented through the DH framework, where the parameters $\theta_i$, $d_i$, $a_i$, and $\alpha_i$ are defined. The number of joints ($i = 0, 1, 2, ..., n$) is considered degrees of freedom, as shown in Figure 3. A link $i$ can move with respect to the link ($i-1$). The axis $i$ is determined by a line in the space around which the link $i$ rotates or moves relative to the link ($i-1$). The $a$ link is described by two parameters that explain the relative orientation of two axes in space. $a_i$, the common perpendicular distance, indicates the distance between two consecutive axes $i-1$ and $i$, acting as a shared perpendicular distance between $z_i$ and $z_{i-1}$, which signifies translation along the x-axis. This line remains distinct and unique unless the two axes are parallel, as illustrated in Figure 3.

Then, transformations based on translation and rotation matrixes modeling the different effectors are applied. The equation of the homogeneous transform is given by:

$$H_{i,i+1} = Rot_{z,\theta_i} \times Trans_{z,d_i} \times Trans_{x,a_i} \times Rot_{x,\alpha_i} \quad (1)$$

$$H_{i,i+1} = \begin{bmatrix} \cos\theta_i & -\sin\theta_i\cos\alpha_i & \sin\theta_i\sin\alpha_i & a_i\cos\theta_i \\ \sin\theta_i & \cos\theta_i\cos\alpha_i & -\cos\theta_i\sin\alpha_i & a_i\sin\theta_i \\ 0 & \sin\alpha_i & \cos\alpha_i & d_i \\ 0 & 0 & 0 & 1 \end{bmatrix} \quad (2)$$

We used the notation "sin" and "cos" to represent the sine and cosine functions. In the notation $H_{i+1}$, the reference frame ($o_i x_i y_i z_i$) is described in equation 1 and the transformed frame in equation 2. Similarly, the transformation matrix for the DH parameter $\theta_i$ is given by equation 3, $d_i$ by equation 4, $a_i$ by equation 5, $\alpha_i$ by equation 6:
<figure><img src="image_4.png" /><figcaption>Figure 3.: Denavit Hartenberg parameters representation from [45].</figcaption></figure>

$$ Rot_{z,\theta_i} = \begin{bmatrix} \cos\theta_i & -\sin\theta_i & 0 & 0 \\ \sin\theta_i & \cos\theta_i & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \qquad (3) $$

$$ Trans_{z,d_i} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & d_i \\ 0 & 0 & 0 & 1 \end{bmatrix} \qquad (4) $$

$$ Trans_{x,a_i} = \begin{bmatrix} 1 & 0 & 0 & a_i \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \qquad (5) $$

$$ Rot_{x,\alpha_i} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos\alpha_i & -\sin\alpha_i & 0 \\ 0 & \sin\alpha_i & \cos\alpha_i & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \qquad (6) $$

In the case where q1, q2, q3 represent the joints of the coxa, femur, and tibia, we obtain the following.

$$ H_e^1 = H_2^1(q1) \times H_3^2(q2) \times H_e^3(q3) \qquad (7) $$

Inverse kinematics
Inverse kinematics calculates the joint angles required to reach a desired position of the end effector. This is essential for controlling the robot's movement and for achieving specific tasks.

The desired change in joint angle $\Delta\theta$ for a given incremental change in end effector position $\Delta\vec{s}$ is calculated using the Jacobian matrix $J$ and the Levenberg-Marquardt method, also known as the damped least squares method [46]. The complete derivation is provided by Equations 8, 9, and 10, resulting in the ultimate Equation 12.

The change in joint angles is determined by using the Jacobian to compute the end effector's position. The Jacobian matrix $J$ is defined as:

$$J(\theta) = \left( \frac{\partial \vec{s}_i}{\partial \theta_j} \right)_{i,j} \qquad (8)$$

where $\vec{s}_i$ represents the end effector of the link and $\theta_j$ represents the joint parameter. Subsequently, the calculation of the Jacobian's linear velocity can be performed:

$$\frac{\partial \vec{s}_i}{\partial \theta_j} = \vec{v}_j \times (\vec{s}_i - \vec{p}_j) \qquad (9)$$

The relationship between the end effector's position change and the joint angles change is given by:

$$\Delta\vec{s} \approx J\Delta\theta \qquad (10)$$

where $\Delta\theta$ can be solved using the Levenberg-Marquardt method:

$$\Delta\theta \approx J^T(JJ^T + \lambda^2 I)^{-1}\Delta\vec{s} \qquad (11)$$

Using a compact notation and approximation, the final result is:

$$\Delta\theta = J^T(JJ^T + \lambda^2 I)^{-1}\Delta\vec{s} = Z\Delta\vec{s} \qquad (12)$$

$\Delta\theta$ represents the change in joint position during the stance phase.

$J$ represents the Jacobian matrix of the robot.

$J^T$ represents the transpose of the Jacobian matrix.

$\lambda$ is a positive real parameter.

$I$ represents the identity matrix.

$Z$ is a matrix defined as $Z = J^T(JJ^T + \lambda^2 I)^{-1}$.

The forward and inverse kinematics solutions help establish the connection between the angles of various leg segments, linking them to the robot's base as a point of reference (mobile base). After obtaining the coordinates of the end-effector, it becomes essential to define the workspace of the different legs and implement a scheduling approach to facilitate movement, known as the gait.

### 3.1.3. Hexapod Robot Navigation

Navigation is essential for enabling a robot to autonomously navigate through an environment using predefined navigation points within a "map" frame. In our methodology, navigation plays a crucial role in enabling the robot to: 1) orient itself with respect to
<figure><img src="image_5.png" /><figcaption>Figure 4.: Proposed approach for hexapod robot navigation.</figcaption></figure>

the surroundings, including obstacles and passable areas, 2) interpret various map data, and 3) pinpoint areas of interest on the map. The navigation component encompasses aspects such as odometry, integration with the hexapod controller, and translation of navigation points into speed directives. Key input data required for this process include the localization algorithm (AMCL), odometry information, sensor transformations (in Cartesian coordinates), 2D laser sensor readings, and the map itself. Both local and global cost functions are used to assess occupied, free, and unexplored spaces. The global planner uses these costs to devise a long-term navigation plan, while the local planner uses them to generate short-term navigation strategies. Recovery behaviors come into play when the robot becomes disoriented within the map or encounters obstacles, such as rotating in place. The trajectory algorithm calculates the most efficient path between the robot and the target navigation point. Figure 4 illustrates our navigation approach, which consists of four main components: the trajectory algorithm, local and global planning (taking into account the characteristics of the robot), and local and global cost functions (associated with the levels of congestion of the robot).

## 3.2. Odometry and Localization

Odometry pertains to the ability of a robot to determine its location and direction. Estimating the orientation of a hexapod robot presents a challenge due to the complex movements of the legs that facilitate its motion. Unlike wheeled robots, a hexapod robot calculates its odometry using a target velocity derived from the body velocity, as detailed in the Kinematics Model Section 3.1.2. Our robot undergoes testing with various odometry techniques: Extended Kalman Filter (EKF) for pose estimation, which integrates and refines all odometry data; odometry obtained from the resultant velocity; and scan matching, which updates the robot's localization by comparing two consecutive frames of laser data. The EKF data of the pose estimation (using the IMU) and the controller odometry (desired speed) drift quickly due to the accumulated error. The laser scan matching is the most appropriate method for obtaining accurate odometry
in our case.

### 3.3. Chemical Servoing

This section presents the integration of a chemical sensor-based control approach, a simulation environment, and a gas source-seeking algorithm. The chemical control system enables the robot to plan its navigation based on the presence of a gas plume in its environment. The robot should autonomously move towards the gas source. Since the gases targeted by the selected sensors are harmful, it is premature to implement the experiment in a real robot. To overcome this issue, the chemical control system was developed in simulation. The simulation environment includes a gas dispersion model. For the tests, we used the environments provided by the GADEN simulator [27], but it is possible to generate the air flux of an environment based on a personalized environment based on his 3D model and an interface of Computational Fluid Dynamics (CFD) simulation.

The first part is the preprocessing; the 3D environment model (in mesh format, 3D) is used to calculate the flux dynamics and generate a base of air flux data. The simulator will then generate the gas panache based on the data of the air flux calculated for the environment and the parameters of the gas sources. The dispersion of the gas is then recovered in the simulation environment in the loop. The capacitors are also simulations in the environment and permit one to perform a test on acquisition with different possible noise detector facts. In this article, four distinct approaches for localizing gas sources are tested: Grid, spiral surge, spiral cast, and particle filter. Each technique comes with its own advantages and drawbacks, making them appropriate for various situations. A comparative analysis of gas source search methods based on six criteria is illustrated in Table 2: Exploration (efficiency in locating gas sources), Coverage (approximation of environmental exploration and mapping), Estimation (precision in determining gas source position), Complexity (level of implementation and operational complexity), Energy usage and Applicability (suitability for diverse environments and circumstances).

<table><caption>Table 2.: Comparison of Gas Source Seeking Algorithms</caption><thead><tr><td>Algorithm</td><td>Exploration</td><td>Coverage</td><td>Estimation</td><td>Complexity</td><td>Energy</td><td>Applications</td></tr></thead><tbody><tr><td>Grid [47]</td><td>Low</td><td>Low</td><td>Non-probabilistic</td><td>Low</td><td>Low</td><td>Static env. mapping</td></tr><tr><td>Surge Spiral [48]</td><td>Fast</td><td>Medium</td><td>Non-probabilistic</td><td>Med.</td><td>Med.</td><td>Dynamic env. exploration</td></tr><tr><td>Surge Cast [49]</td><td>Medium</td><td>Med.-high</td><td>Non-probabilistic</td><td>Med.</td><td>Med.</td><td>Complex env. with obstacles</td></tr><tr><td>Particle Filter [50]</td><td>Probabilistic</td><td>High</td><td>Adaptive</td><td>High</td><td>High</td><td>Precise source localization</td></tr></tbody></table>

The selection of a method for searching for gas sources is influenced by several factors. The evaluation of different algorithms according to the specific needs of the application is essential. Table 2 can be used as an initial guide to choose the most appropriate algorithm. The comparative results of the four algorithms are discussed in Section 4.1. The algorithm proposed for chemical servoing is depicted in Figure 5.
<figure><img src="image_6.png" /><figcaption>Figure 5.: Algorithm proposed for chemical servoing.</figcaption></figure>

# 4. Simulations and Results

In this section, a comparison is made between different chemical control algorithms in a simulated environment. Subsequently, an evaluation of image anomaly detection with R-CNN is conducted using metrics.

## 4.1. Chemical Servoing results

This section presents the results of two simulated experiments carried out within a robot operating system (ROS) environment. The first experiment focuses on the integration of gas sensors with ROS, while the second investigates gas movement in confined spaces. RViz, which stands for Robot Visualization, serves as a visualization framework used to offer visual feedback in both experiments. The first experiment takes place in a 10x6-meter area with a single obstacle to showcase the possibility of modeling gas movement and maneuvering a hexapod robot. In Figure 6, we can observe the simulation of a gas emission from the green square located at the top of the environment. The red square represents an air flow that acts as an air inlet to displace gas within the room. The blue lines indicate the laser data collected by the robot to locate itself and track the gas flow. The second experiment takes place in a maze. Our objective is to demonstrate the ability to navigate through a maze and reach the source, even if the simulation cycle reaches the end of the particle simulation data loop. The goal is to validate the recovery system that aims to trace the chemical precept (the plume) and resume its search, as shown in Figure 7. This environment is a case of an environment constrained by the presence of a 1-meter-wide corridor.

Chemical servoing is evaluated by employing various search algorithms to locate the gas source. These algorithms include: Grid, Surge-Cast, Spiral, Surge-Spiral, and Particle filter methods. The evaluation takes place within the ROS and RViz framework, carried out in the setting depicted in Figure 6.

The study began with the evaluation of the efficiency of different algorithms in reaching the gas source. Initially, the focus was on testing the effectiveness of various algorithms in identifying the gas source. It was followed by 10 trials to assess the reliability of the approach. The objective was to identify the algorithm that demonstrates the fastest convergence. The average time taken by each algorithm to reach the gas source is presented in Figure 8. Examination of the time taken to execute various algorithms shows notable differences. The Grid algorithm proves to be the most effective, completing the task in just 3 minutes and 37 seconds. In contrast, the particle filter algorithm lags behind, taking more than 10 minutes to reach the gas source. The other algorithms, such as Surge Cast, Spiral, and Surge Spiral, fall somewhere in between these two extremes
<figure><img src="image_7.png" /><figcaption>Figure 6.: Simulation of Robot Motion Capture with the GADEN Package for Gas Source Localization in a 10x6 Meter Environment with a single obstacle. (a) Screen capture of the robot's movement at the beginning of the gas source search mission. (b) Capture of the robot's movement as it approaches the gas source. (c) and (d) close-up screenshots of the robot's movement</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7.: Simulation of Robot Motion Capture with the GADEN Package for Gas Source Localization in a 10x6 Meter Maze Environment with a 1-Meter-Wide Corridor. (a) Global view of the maze used for the simulation. (b) Top view of the robot's movement in the map.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 8.: Analyzing the duration required to reach the gas source using various algorithms: Grid, Surge Cast, Spiral, and Particle Filter.</figcaption></figure>

and require more than twice the time taken by the Grid algorithm. The outcomes of
the different algorithm simulations can be viewed via these video links:

(1) Grid algorithm See Video.

(2) Surge cast algorithm: See Video.

(3) Particle filter algorithm: See Video.

(4) Spiral algorithm: See Video.

The precision of gas source detection by the robot was evaluated in the 10 tests carried out using the Grid algorithm. As illustrated in Figure 9, it can be observed that in trials 1 to 4, as well as trials 8 and 10, the absolute errors on the X and Y axes stay consistent within approximately 10 cm of the target. This is in line with the safety distance maintained between the robot and the target, indicating a high level of accuracy. However, the absolute errors in trials 7 and 9 are significantly higher, measuring 2.81 meters (trial 7) and 1.62 meters (trial 9) along the X-axis, and 0.7 meters (trial 7) and 0.16 meters (trial 9) along the Y-axis. In Trials 7 and 9, the robot initiated the trial from a position 2 meters to the left of the original starting point. Consequently, the flow direction was reversed, causing the robot to move farther away from the source. Thus, the robot faced challenges in reaching the gas plume because of the considerable distance between it and the plume.

## 4.2. Visual Defect Detection results

This section discusses the results of training and assessment of the YOLO v5 model to identify defects on metal surfaces. The effectiveness of the model is evaluated using performance metrics such as the confusion matrix, precision, recall, and the F1 score. The evaluation database used is derived from the NEU Surface Defect Database [51].
<figure><img src="image_10.png" /><figcaption>Figure 9.: Calculating the absolute errors in X and Y coordinates for 10 trials using the Grid search algorithm.</figcaption></figure>

This dataset comprises six common types of surface imperfections observed in hot-rolled steel strips: rolled-in scale, patches, crazing, pitted surface, and inclusion, each containing approximately 300 images. The dataset has been augmented by applying filters, adding noise, and rotating the image. Furthermore, a new defect type, cracks, has been introduced, expanding the original database to 4500 images. Figure 10 provides a visual representation of some of these defects from the database used for training.

Figure 11 illustrates the confusion matrix, which contrasts the actual and predicted labels for various categories of defects. The results reveal that the model achieves 90% precision for inclusion defects, 83% precision for cracks, and 69% for pitted surfaces, with a lower precision score.

Precision is defined as the proportion of accurate positive predictions to the total number of positive predictions, indicating the percentage of predicted positive cases that are actually positive. The precision results can be seen in Figure 12a, indicating that most classes show a high precision level, averaging around 80% across all classes. It is worth noting that the class with the lowest precision score is rolled-in Scale, at 69%. Recall, also known as sensitivity, represents the proportion of correctly predicted true positive labels. Calculated by dividing the number of true positives by the total count of items belonging to the positive class. The recall results can be observed in Figure 12b, where the majority of class scores are approximately 80% for accurately predicted positive instances. The highest performing class is "inclusion" with values exceeding 90%, while the weakest class is "pitted surface." It should be noted that the overall average across all classes reaches 95% with a confidence level of 0.

The F1 score is an evaluation metric that blends precision and recall into a unified value. It is calculated as the harmonic mean of precision and recall. The harmonic mean, a specific form of the average, is obtained by adding the reciprocals of each value in the dataset and then dividing by the total number of values. The F1 score illustrated in Figure 12c displays the F1 scores of various classes within the dataset. Most classes achieve scores around 80%. The mean score in all classes is 68%. This outcome is influenced by the low score of the "pitted-in scale" class, which affects the overall average result.
<figure><img src="image_11.png" /><figcaption>Figure 10.: Examples of images of defects used for training and testing.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 11.: Confusion Matrix of Actual and Predicted Class Labels on a Dataset of Industrial Defects.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 12.: Evaluation of the model’s effectiveness in detecting industrial defects dataset using three metrics: Precision, Recall, and F1-Score.</figcaption></figure>

# 5. Hexapod Prototype

## 5.1. Robot Design

The chosen design features a six-legged hexapod robot, specially designed to perform inspections in confined and difficult-to-access areas. The robot's legs are inspired by spiders and are positioned facing forward. The femurs, or knees, are directed outward and each leg has three degrees of freedom. The physical attributes of the robot are used to develop its kinematic model. The prototype being considered is named ArIA INSPECTOR. Figure 13 provides an overview of the real and simulated versions of the hexapod robot in Gazebo. The hardware design of ArIA Inspector involves capturing the embedded architecture codes through the use of an onboard computer equipped with a GPU (Nvidia Jetson) and multiple sensors like the laser (RPLidar) for odometry and mapping tasks. Visual sensors, such as a stereoscopic camera (RealSense D435i) provide point-cloud information where a depth measurement can be extrapolated. This camera also has an integrated inertial unit (IMU). An Arduino board equipped with a Grove Shield allows measurements on different sensors, here MQ3 gas sensors (MOX). The servomotors are controlled directly by the computer on board (Jetson Nvidia) using U2D2 (Dynamixel Communication Module) for information exchange in the UART protocol. A microcontroller (Groveduino) is used to connect to the gas sensors. Additional sensors such as pressure and hygrometry sensors can also be incorporated. This enables the collection and transmission of data to various ROS nodes via communication topics. The 3D model is constructed using an URDF file to build the various components of the robot and the sensors.
<figure><img src="image_14.png" /><figcaption>a) Hexapod Robot Prototype</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>b) Simulated Hexapod
Robot in Gazebo</figcaption></figure>

<caption>Figure 13.: a) The prototype hexapod robot (ArIA Inspector) developed in the study.
b) The hexapod robot simulated in Gazebo.</caption>

Table 3 provides a comprehensive summary of the key hardware components and characteristics of the robot.

**6. Conclusion**

The research introduces a new method that integrates chemical servoing and visual defect detection in an industrial setting using a hexapod robot. The study highlights the effectiveness of various chemical servoing algorithms and image defect detection methods to identify gas sources through simulations. A prototype of the hexapod robot is created to show its ability to locate and reach a gas source using chemical servoing and to analyze the source with a pretrained convolutional neural network. Combining chemical and visual servoing functions in robots has the potential to enhance the safety and productivity of industrial activities by facilitating the early identification and categorization of gas leaks.

Subsequent investigations may concentrate on enhancing the precision and depend-
ability of gas source identification by refining the chemical servoing algorithms and
image defect detection techniques. There is also potential for exploring the integration
of more sophisticated gas-sensing technologies with the hexapod robot to enhance its
detection abilities. The adaptability and scalability of the suggested approach could be
examined to accommodate various industrial settings and gas-related situations. Real-
world experiments could be carried out to confirm the efficacy of the proposed method
in practical industrial settings. In addition, it may be worthwhile to explore alternative
uses of the hexapod robot, such as performing inspection and maintenance tasks in
diverse industries.
<table><caption>Table 3.: Hexapod robot characteristics.</caption><thead><tr><td>Characteristic</td><td>Details</td></tr></thead><tbody><tr><td>Robot Design</td><td>Hexapod (6 legs), Weight: 4kg, Articulation: Aluminum piece, Structure: Carbon, Coxa: 4.5 cm, Furmur: 11.0 cm, Tibia: 26.6 cm</td></tr><tr><td>ROS Architecture</td><td>Modular architecture with data flow sharing through nodes</td></tr><tr><td>Servomotor Control</td><td>Controlled directly from the onboard computer (Nvidia Jetson) using U2D2 for UART communication.</td></tr><tr><td>Sensors</td><td>Gas sensors, including MQ3(MOX). Sensors for gas measurements are interfaced via a microcontroller (Groveduino). Laser (RPLidar) for odometry and stereoscopic camera (RealSense D435i).</td></tr><tr><td>Communication</td><td>TTL hubs are connected to servomotors and U2D2</td></tr><tr><td>Walking Speed</td><td>Regular Terrain: 0.1 m/s, Rough Terrain: 0.01 m/s</td></tr><tr><td>Gait</td><td>Types: Tripod, Amble, Ripple, and Wave</td></tr><tr><td>Ground Clearance</td><td>Range: 15 to 25 cm</td></tr><tr><td>Carrying Capacity</td><td>Maximum: 0.5 kg</td></tr><tr><td>Obstacle Avoidance</td><td>Maximum Height: 16 cm</td></tr></tbody></table>

## 7. Acknowledgement(s)

The authors express their gratitude to Anne-Marie Haute, CEO of Pilgrim Technology, and Aurélie Guesdon, specializing in 3D/Data Processing at Pilgrim Technology, for providing insightful guidance and unwavering support throughout the project.

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