An Efficient Odor Source Localization Method for Wheeled Mobile Robots in Indoor Ventilated Environments

Abstract

Odor source localization (OSL) using mobile robots in indoor ventilated environments remains challenging due to turbulent dispersion, uneven concentration distribution, and weak robustness in conventional algorithms. This paper proposes an efficient OSL strategy for wheeled mobile robots by integrating time-varying smoke plume modeling, particle filtering (PF), and information entropy. A multi-sensor fusion perception system is developed, including an LDS-02 LiDAR, ultrasonic anemometer, and PMS5003 particle sensor. The proposed method employs a plume model to characterize odor particle propagation, uses particle filtering to estimate the posterior distribution of the source location, and introduces information entropy to quantify perceptual uncertainty and optimize robot path planning. Comparative simulations and real-world experiments are conducted in a 5 m × 3 m indoor ventilated environment against the traditional gradient–bionic hybrid algorithm. Results demonstrate that the proposed algorithm significantly reduces the average search time and improves the localization success rate. The long-distance localization success rate exceeds 90%, and the positioning error is controlled within 0.5 m. The proposed strategy provides a reliable and practical solution for OSL in indoor ventilation environments.

1. Introduction

The expansion of hazardous industries in modern society has increased the risk of chemical leakage in storage facilities, making rapid OSL critical for mitigating potential hazards. Traditional detection methods suffer from low efficiency, limited coverage, and poor adaptability to hazardous environments. Therefore, olfactory tracking and localization technology based on wheeled mobile robots has been developed to address complex hazardous scenarios. In the field of single-robot OSL, Russell proposed a passive detection method [1], while Z-shaped and spiral traversal algorithms have also been widely adopted. Previous scholars have developed various OSL strategies based on mobile robot platforms and verified their effectiveness [2,3].

These methods can be generally categorized into four types: chemotaxis, anemotaxis, probabilistic inference, and machine learning, all of which rely on sensor information for robot localization. However, such algorithms commonly exhibit drawbacks, including high computational complexity, low positioning accuracy, and poor environmental adaptability in complex scenarios. This study focuses on smoke particle source localization algorithms and explores novel techniques and strategies based on existing methods. It aims to address the difficulties of OSL in indoor ventilated environments, which are mainly caused by turbulent gas diffusion and uneven concentration distribution. A prototype of an OSL robot equipped with a laser-based smoke particle sensor is developed. Comparative simulations and experiments are conducted to compare the gradient–bionic hybrid algorithm with the proposed plume model-based particle filter search algorithm. The integrated method exhibits remarkable advantages in enhancing the robot’s global search capability, improving target detection efficiency, and facilitating optimal solution acquisition, thus demonstrating high novelty and application potential [4,5].

2. Materials and Methods

2.1. Z-Shaped Algorithm

In the Z-shaped algorithm, the robot moves along a straight line at a certain angle to the downwind or upwind direction and changes its direction upon encountering an obstacle. Considering the limited spatial constraints of the experimental environment, this study employs the Z-shaped algorithm for the odor search task, ensuring that the robot’s movement direction always maintains a specific angle to the wind direction. The specific movement pattern is illustrated in Figure 1. The Z-shaped search is the most fundamental search behavior: when no scent information is detected, the robot moves freely within the working area according to the rules of the Z-shaped algorithm, covering as large an area as possible to search for smoke plumes.

2.2. Particle Filter Search Algorithm Based on a Smoke Plume Model

This paper presents a comprehensive review of robotic OSL algorithms, with particular emphasis on the fusion of particle filtering and information entropy-based methods within gas plume models [6,7,8]. To better characterize realistic plume dynamics, a time-varying smoke plume propagation model is established to predict particle positions and update particle weights [9,10,11]. Under the influence of time-varying airflow fields, the diffusion behavior of particles within smoke plumes complies with the following physical principle:

$$\dot{X}(t)=U(X,t)+N(t)+E_s$$

(1)

where X(t) denotes the position of a smoke particle at time t; U(X, t) represents the mean airflow velocity; and N(t) refers to the Gaussian random process characterizing the stochastic motion of particles, with a zero mean and variances denoted by $({{\sigma }_x}^2,{{ \sigma }_y}^2, {{\sigma }_z}^2)$, where x, y, and z denote the longitudinal, horizontal, and vertical components of the airflow, respectively. $E_s$ represents the gravitational settling effect along the gravity direction, whose value depends on the flow Reynolds number, smoke particle density, and air density. Accordingly, the position of this smoke particle at time t + ∆t can be derived as follows:

$$X(t+∆t){\int }_t^{t+∆t}U(X(\tau ))\mathrm{d}\tau +{\int }_t^{t+∆t}N(\tau )\mathrm{d}\tau +{\int }_t^{t +∆t}{E}_s+X(t)$$

(2)

Let $P(x,y,z)$ denote the probability of detecting a particle. Under normal conditions, Z = 0 (no particle detected) can be expressed as follows [4]:

$$P(x,y)={\displaystyle \frac{Q}{2\pi {\sigma }_y{\sigma }_z}}{\mathrm{e}}^{- {\displaystyle \frac{y^2}{2{\sigma }_y^2}}}$$

(3)

Leveraging the established plume trajectory model, a fusion framework integrating particle filtering (PF) and information entropy is proposed for OSL and robotic path planning. Particle filtering (PF) estimates the source location by approximating the posterior probability distribution of the odor source position using a set of weighted virtual particles [12]. Information entropy quantifies the perceptual uncertainty and guides robot motion [13]. When the robot detects an odor concentration exceeding the predefined threshold, the particle set is initialized using real-time sensor measurements. Particle weights are updated in real time by fusing concentration information, with high-weight particles retained and low-weight particles discarded to enhance localization accuracy. The posterior probability and information entropy are calculated based on the particle distribution, with the low-entropy region serving as the robot’s movement direction for the next time step. At each iteration, the algorithm first performs a source localization estimation and verifies the termination criteria. If the criteria are met, the iteration terminates; otherwise, particle weights are updated and resampling is performed to continue the particle filtering process. Based on these fundamental principles, the specific implementation steps of the particle filtering algorithm are elaborated as follows. The overall workflow of the proposed algorithm is shown in Figure 2.

(1) Particle Initialization: The particle set is first initialized via Equation (7) to approximate the probability distribution of the smoke plume trajectory at time t. When the robot first detects a concentration exceeding the predefined threshold, the plausible propagation path of the smoke plume is estimated in reverse using the recorded wind direction and velocity data. Based on this, the positions of the generated particles are adjusted, thereby completing initialization of the particle set $\left\{L_K^i, i = 1, 2, \cdots ,{ N}_s\}\right.$, which characterizes the posterior probability distribution of the odor source location. Here, $L_K^i$ denotes the position of each particle, and the particle number is set to $N_s=1000$.

(2) Weight Update: The weight of a particle quantifies the likelihood that its corresponding position represents the true odor source. At each time step, the weight $W_K^i$ is recursively updated as follows:

$$W_K^i\propto W_{K-1}^{i}p(Z_k|L_K^i)$$

(4)

where $p(Z_k|L_K^i)$ is the likelihood provided by the measurement model. All particles are initialized with a weight of $1/N_s$ and normalized to ensure the sum of particle weights equals 1, satisfying:

$${\sum }_{i=1}^{N_s}{W}_K^i=1$$

(5)

Assuming each time step is 1 (1 < K), odor packets are continuously released from the odor source at $L_K^i$. Let $p_{ir}(1,k)$ denote the probability density that an odor patch released at point $L_K^i$ reaches the robot’s position $L_K^i$ after K time steps. When no odor packet is detected at $L_K^R$, the probability is $(1-\mu {\int }_{S_p}{p}_{iR}(\mathrm{l},k)dA)$, where $S_p$ denotes the area covered by the odor source, and μ represents the odor detection probability of the gas sensor, which is empirically set to 0.9. Given that the odor source is approximated as a point source, the probability can be further simplified to $1-\mu S_p{p}_{iR}(1,k)$. The motion model of the odor plume is formulated as follows:

$$L_{2 }=L_1+{\int }_{t_1}^{t_2}U(L(t))dt+{\int }_{t_1}^{t_2}N(t)dt$$

(6)

where U(L(t)) denotes the average velocity vector of the odor packet at position L(t) at time t, expressed as ${[U_x(L(t)),U_y(L(t))]}^T$; ${\int }_{t_1}^{t_2}N(t)d{t}_2$. Its stochastic motion component is modeled as a zero-mean Gaussian noise process with covariance ${[(t_2-t_1){{\sigma }_x}^2,(t_2-t_1){{\sigma }_y}^2]}^T$, where ${[{{\sigma }_x}^2,{{\sigma }_y}^2]}^T$ represents the velocity variance of the airflow components. This variance is determined by recording wind speed values over 10 s. Accordingly, the displacement of the odor packet within a 10-s period is given by:

$${\int }_{t_l}^{t_j}U(L(t))dt \approx {\sum }_{i =\mathrm{l}}^{j}U(L_R(t_i))T ={[s_x(t_l,t_j),s_y(t_l,t_j)]}^T$$

(7)

where T denotes the control cycle of the robot, which is set to 0.5 s. The shaded region within the elliptical area $O_{L,k}$ at $L_K^i$ corresponds to the value of $p_{iR}(1,k)$. $O_{L,k}$ corresponds to the odor packet released at time step 1, which arrives at ($L_k^R$) at time step K, and accounts for the probability density exceeding a predefined threshold at any point within this region. ${\delta }_{ix}(1,k)$ and ${\delta }_{iy}(1,k)$ represent the distances between the centroids of $L_K^i$ and $O_{L,k}$ along the x- and y-axes, respectively. $s_x(1,k)$ and $s_y(1,k)$ denote the estimated advection distances of the airflow along the x- and y-directions from time step 1 to time step K, respectively (as shown in Figure 3).

Considering the continuous release of odor packets from time step f to k − 1, the probability of not detecting an odor patch at time step k at location $L_k^R$ can be expressed as ${\prod }_{l -f}^{k-1}[1-\mu S_p{p}_{iR}(1,k)]$, where f denotes the first recorded time step in the wind sequence. Accordingly, the likelihood function $p(z_k|L_K^i)$ is formulated as follows:

$$p(z_k|L_K^i)=\left\{\begin{array}{ll}{\prod }_{\mathrm{l}=f}^{k -1}[1-\mu S_p{p}_{iR}(1,k)]& z_k = 0,\\ 1-{\prod }_{l=f}^{k-1}[1-\mu S_p{p}_{iR}(1,k)]& z_k = 1.\end{array}\right.$$

(8)

The probability density $p_{iR}(1,k)$ is solved using the following equation:

$$p_{iR}(\mathrm{l},k)={\displaystyle \frac{1}{2\prod {\sigma }_x{\sigma }_y(k -\mathrm{l})\Delta t}}{\mathrm{e}}^{-{\displaystyle \frac{{({\delta }_{ix}(\mathrm{l},k))}^2}{2{{\sigma }_x}^2(k -\mathrm{l})\Delta t}}}{\mathrm{e}}^{-{\displaystyle \frac{{({\delta }_{iy}(\mathrm{l},k))}^2}{2{{\sigma }_y}^2(k -\mathrm{l})\Delta t}}}$$

(9)

The sampling period of the robotic system is $∆t$ = 0.5 s, where ${[{{\sigma }_x}^2,{{\sigma }_y}^2]}^T$ denotes the velocity variance of the airflow components, which is estimated according to ${\{U(L_j^R)\}}_j^k=f$. ${\delta }_{ix}(\mathrm{l},k)=l_{Rx}- l_{ix}-S_x(\mathrm{l},k)$, and ${\delta }_{iy}(\mathrm{l},k)= l_{Ry}-l_{iy}-S_y(\mathrm{l},k)$, where $(l_{Rx}, l_{Ry})$ and $(l_{ix},l_{iy})$ represent the coordinates of $L_k^R$ and $L_k^i$, respectively. $s_x(\mathrm{l},k)$ and $s_y(l,k)$ denote the displacement of the airflow in the x- and y-directions from time step 1 to k, respectively, which can be approximated by ${{[s}_x(l,k),s_y(l,k)]}^T\approx {\sum }_{j =1}^{k}U(L_j^R)\Delta t$.

(3) Resampling: Particle filtering is susceptible to the particle degeneracy problem. For this reason, it is necessary to first assess whether the particle filter is in a degenerate state using the following equation:

$$N_{eff}<N_{thr}$$

(10)

where $N_{thr}$ is a constant set to 0.5 $N_s$ and $N_{eff}$ is the effective particle number, which can be estimated from relevant literature as follows:

$${\widehat{N}}_{eff }=1/{\sum }_{i =1}^{N_s}{(W_k^i)}^2$$

(11)

The resampling instants are determined by detecting particle degeneracy, with the objective of redistributing particle weights and positions. This study adopts the simplest Russian roulette method to reduce computational load: For each particle $L_k^i$ whose weight satisfies $W_k^i<$ 1/$N_s$, its survival probability is given by the maximum value between ${N_{s}W}_k^i$ and 0.5. For particles $L_k^j$ satisfying $W_k^j\ge 1/N_s$, new particles are generated in their vicinity according to a normal distribution, and the original particles $L_k^j$ are removed. The mean of the normal distribution for the new particles is $L_k^j$, with variances of $0.25 {\mathrm{m}}^2$ in both x- and y-directions. The number of particles spawned from $L_k^j$ is min$\left\{\mathrm{i}\mathrm{n}\mathrm{t}(N_s{W}_k^j),5\right\}$, where int(*) denotes the floor function. After resampling, the particle number $N_s$ may change, and all particle weights are reset to 1/$N_s$.

(4) Source Position Estimation: The weight of the i-th particle in the algorithm satisfies $W_k^i\propto p(L_K^i|z_{0:k})$, where $p(L_K^i|z_{0:k})$ denotes the posterior probability density of the source position at ${\mathrm{L}}_{\mathrm{K}}^{\mathrm{i}}$ during time step k. For OSL, all generated particles are iterated to compute their weighted average position—summing the position of each particle multiplied by its corresponding weight. The estimated positions are stored in a list that retains only the most recent 20 locations. The estimated position of the odor source at time step k is given by:

$$P_k={\sum }_{i =1}^{N_s}{W}_k^i{L}_K^i$$

(12)

In the proposed algorithm, particles are initialized only after the robot first detects an odor signal. Prior to detection, no prior assumption regarding the source location is required. During the PF-based odor source search, the particle weights are dynamically updated according to the sensor measurements, while the particle positions remain unchanged. The Russian roulette strategy is adopted to discard particles with weights below the average value and generate new particles around those with weights above the average, thereby optimizing the overall particle distribution.

Termination Conditions: Accurate localization of the odor source constitutes the core objective of the target search task. The proposed algorithm adopts dual convergence criteria integrated with two necessary confirmation conditions as the termination rule. First, the number of estimated odor source positions is checked. If the count of historical position estimates is below the predefined upper limit of 20, the target is considered not yet located. Meanwhile, a maximum allowable search duration of 600 s is set. The time difference from the start of the search to the current moment is calculated; if it exceeds the maximum allowable search time, the OSL is deemed unsuccessful. The algorithm terminates only when two prerequisites are satisfied simultaneously: particle convergence and convergence of the estimated odor source position. Particle convergence is assessed by calculating the weighted variance, defined as the sum of the squares of the weighted distances between each particle and the weighted average position. When this variance falls below a predefined convergence radius, the particle positions are deemed to have converged stably. The particles approximate a quasi-Gaussian distribution, with convergence determined by the formula:

$${{\sigma }_k}^2\le R_{conv}$$

(13)

where ${\sigma }_k^2={\sum }_{i =1}^{N_s}{{[|L}_k^i-P_k|}^2{w}_k^i]$ denotes the weighted variance of particles and $R_{conv}$ (0.5 m) is the convergence circle radius, respectively. To assess positional convergence, the sequence of the last 20 estimated positions is selected: $\left\{P_j|z_j=1\right\}$. The mean of this sequence is calculated as $\overline{P}$. If the distance between all elements in the sequence and the mean is less than the radius of the tolerance circle, the estimated position at the current time step is considered converged. The determination formula is expressed as follows:

$$|P_j-\overline{P}|\le R_{err}$$

(14)

where $R_{err}$ is the radius of the permissible error circle (set to 0.5 m). If the distance between any estimated position and the average position exceeds this threshold, the estimated position is deemed non-convergent. Conversely, the current estimated position $P_k$ is considered a potential odor source location. In addition to satisfying particle convergence and estimated position convergence, two additional necessary conditions must be met to confirm the successful localization of the odor source: First, the Euclidean distance between the estimated position and the actual source position must fall within the permissible error margin (0.5 m). Second, the estimated position must not be located within any obstacle region, which can be verified by querying the environmental map to avoid potential collisions between the robot and obstacles.

To improve the accuracy of OSL and tracking, this paper incorporates information entropy theory into the particle filter framework. Information uncertainty is quantified to model and analyze the propagation characteristics of odor plumes [14]. Higher information entropy implies greater uncertainty in the estimated odor source position, whereas lower entropy indicates higher localization confidence. Directing the robot toward the direction of minimum information entropy enables efficient acquisition of critical plume information and optimizes the source-seeking process [15,16,17]. Let the motion control set in the robot coordinate system be defined as $M_k\left\{\uparrow ,\downarrow ,\leftarrow ,\to \right\}$, which corresponds to the four basic motion commands: forward, backward, left, and right relative to the robot’s current pose. This study employs Shannon information entropy, calculating the corresponding entropy value based on the probability distribution of the odor source location:

$$H(X)=E(-\log p(z_k|L_k^i))=-{\sum }_{i=1}^{n}p(z_k|L_k^i)\log p(z_k|L_k^i)$$

(15)

The robot first calculates the expected entropy values for each potential movement target, and then it selects the target direction with the minimum expected entropy to maximize the information gain regarding the odor plume path. The movement direction selection formula is expressed as follows:

$$m_k^{*}=\mathrm{a}\mathrm{r}\mathrm{g}\underset{m_k\in M_k}{\min }\left\{H(m_k)\right\}$$

(16)

Based on the above process, this study employs a particle filter algorithm to converge the particle state vector while continuously sampling odors and updating the posterior probability distribution of the odor source. Subsequently, the information entropy algorithm calculates the information gain and predicts the robot’s movement trend, driving the robot to move along the direction with the fastest decrease in information entropy. Through iterative updates, the robot approaches the odor source.

3. Results

3.1. Simulation and Results Analysis

To verify the effectiveness of the proposed algorithm, a two-dimensional simulation environment was established based on LiDAR, in which a two-dimensional smoke plume model was adopted to characterize the odor propagation characteristics. Simulation experiments were conducted in the RVIZ environment of the Robot Operating System (ROS) framework, within a 5 m × 3 m area. The odor source was set at position (0, 0 m), continuously releasing smoke particles at a speed of 0.1 m/s to simulate a persistent odor emission scenario; the source was represented by a cube in the simulation. In the experiments, the robot was initialized at multiple starting positions to perform odor source tracking tasks. The performance of the algorithm was evaluated using multiple metrics, including particle evolution, robot trajectories, and the variation of information entropy. A gradient-bionic hybrid algorithm was adopted as the benchmark method for comparative analysis to ensure comprehensive and reliable validation.

Simulation Results Analysis: Under indoor ventilation conditions, the odor source search process using the particle filter algorithm based on the smoke plume model is depicted in Figure 4. The execution logic of the algorithm is as follows: During tracking, the robot continuously detects the odor concentration. When the concentration exceeds a preset threshold, particle initialization is triggered immediately. After initialization, particle weights are dynamically adjusted based on the smoke plume trajectory model. Meanwhile, real-time measurements of wind direction and wind speed are incorporated to refine the weight update mechanism, thereby ensuring the accuracy of the tracking direction. If the effective particle number falls below a predefined threshold during tracking, resampling is performed immediately. This maintains tracking robustness by redistributing weights and adjusting spatial positions. Through such a dynamic optimization strategy, real-time consistency between the robot state and the particle state is achieved, which significantly improves the tracking accuracy under complex environmental conditions. In the simulation map, the green line represents the robot’s trajectory, while other points indicate particles generated during tracking. Particles are colored according to their updated weights, with orange denoting the maximum weight and cyan indicating the minimum weight. The particle filter algorithm employed 1000 particles in the experiment.

As shown in Figure 4a, the robot initiates the search from its initial position (2.15, 3.60 m) at t = 0 s. At t = 8 s, the robot first detects the odor at the point (1.89, 3.29 m), as depicted in Figure 4b. As the robot moves, the system continuously generates estimated points for the potential odor source location, which are shown as blue dots in the figure. When the number of estimated points exceeds 20, the localization result is optimized by averaging all estimated positions. The average estimated position is shown as green dots in Figure 4c. After iterative updates via the particle filter algorithm, the robot performs resampling operations at positions (1.39, 2.72 m), (0.89, 1.70 m), and (0.03, 0.35 m). The particle positions continued to evolve, ultimately converging at (0.20, 0.41 m) at t = 110 s—a position with high accuracy relative to the actual odor source.

The confirmation phase for OSL requires dual convergence conditions. First, particle convergence is determined by comparing the weighted variance of particles against a convergence radius of 0.5 m. If the variance is smaller than this threshold, the particle positions are deemed to have converged stably, as illustrated in Figure 4g, where all weighted variances lie below the convergence radius. Second, positional convergence is verified by calculating the weighted variance of the odor source estimates derived from particles and comparing it with the convergence radius of 0.5 m. As shown in Figure 4h, convergence is successfully achieved. In addition, two supplementary necessary conditions must be satisfied to confirm successful localization: first, the Euclidean distance between the mean estimated position and the actual source position must fall within the permissible error range; and second, the estimated position must not lie within any obstacle region. As observed in Figure 4i, the mean estimated position falls within the target region of the odor source, satisfying all convergence and validation criteria, thereby confirming successful OSL. Figure 5 depicts the variation in information entropy during the search process. As the robot gradually approaches the odor source, the information entropy exhibits a continuous decreasing trend, which indicates that the robot is moving along a correct search direction and that the localization process is steadily converging toward the true odor source location.

To further validate the feasibility and robustness of the proposed algorithm, a second simulation experiment was conducted with the robot’s initial position adjusted to (2.40, 4.55 m). The search process is illustrated in Figure 6. Figure 6a shows the robot initiating the search from this initial position at t = 0 s. At t = 18 s, the robot first detects the odor at the point (1.54, 3.64 m), as depicted in Figure 6b. When the number of estimated position points exceeds 20, the mean value is calculated by iterating through all estimated positions, which is represented by the green points in Figure 6c. Through iterative updates of the particle filter algorithm, the robot performs resampling at positions (1.62, 2.01 m), (0.84, 1.28 m), and (0.02, 0.32 m), continuously optimizing the particle positions. The particles ultimately converge to (0.10, 0.01 m) at t = 120 s. During the odor source confirmation phase, Figure 6g indicates that the particles converge near the odor source, while Figure 6h shows that the estimated positions converge around the source. In Figure 6i, the green point represents the mean estimated position, confirming that the odor source is successfully identified within the source region. The results of this experimental group are consistent with those of the first group, further verifying that the proposed particle filter algorithm possesses stable and reliable odor source tracking and localization capabilities under different initial position conditions.

Figure 7 illustrates the information entropy curve during the search process. As the robot approaches the odor source, the information entropy decreases monotonically, which further validates the rationality of the search direction adopted in this study.

To investigate the impact of the initial position on algorithm performance, two sets of comparative simulation experiments were conducted, with the robot’s initial positions set to (2.15, 3.60 m) and (2.40, 4.55 m), respectively. Each experimental set was independently repeated 50 times, and the statistical analysis of the results is presented in

Table 1. Simulation results of particle filter algorithm.

Starting Point	Terminal	Estimated Average Position	Average Time (s)	Success Count	Success Rate
(2.15, 3.60 m)	(0.40, 0.35)	(0.31, 0.21)	110 s	47	94%
(2.40, 4.55 m)	(0.02, 0.32)	(0.10, 0.01)	120 s	45	90%

. When starting from (2.15, 3.60 m), the robot achieved an average search time of 110 s, with 47 successful localization trials, corresponding to a success rate of 94%. When starting from (2.40, 4.55 m), the average search time was 120 s, with 45 successful localization trials and a success rate of 90%. The simulation results indicate that the closer the initial starting point is to the odor source, the shorter the average search time and the higher the localization success rate, demonstrating that the localization efficiency of the proposed algorithm is dependent on the robot’s initial position.

To validate the robot’s tracking performance at varying distances and positions, the particle filter search algorithm based on the plume model proposed in this paper was compared with the traditional gradient–bionic hybrid search algorithm. Five distinct initial positions were selected: (1.90, 2.50 m), (2.00, 3.00 m), (2.15, 3.60 m), (2.40, 4.00 m), and (2.40, 4.55 m), with the odor source fixed at (0, 0 m). The corresponding distances from the source were 3.14 m, 3.60 m, 4.19 m, 4.66 m, and 5.14 m, respectively. Simulation results demonstrated that the robot successfully detected and tracked the odor source from all five initial positions. Figure 8a shows the relationship curves between tracking time and the initial distance from the source for both algorithms, while Figure 8b presents the relationship curves between localization success rate and initial distance. When the initial position is close to the odor source (less than 4 m), both algorithms achieve high localization success rates and short processing times. However, when the initial position is far from the odor source (greater than 4 m), the proposed algorithm exhibits superior performance, with a localization success rate above 90% and significantly shorter processing times.

Overall, the particle filter algorithm based on the plume model fully exploits wind speed and direction information to achieve efficient and directional tracking, thereby enhancing tracking performance, especially in long-distance tracking scenarios. By comparison, the concentration gradient algorithm features low computational complexity and stable performance under limited hardware conditions, making it more suitable for resource-constrained robotic platforms.

3.2. Experimental Platform Setup and Validation Analysis

Based on the proposed algorithms and simulations, as well as comparisons with the gradient–bionic hybrid algorithm, an experimental platform was constructed using the TurtleBot3 robot, as shown in Figure 9. The system employs OpenCR as the motion control core and a Raspberry Pi as the main processing unit. The perception layer integrates an LDS-02 LiDAR, an ultrasonic anemometer for wind direction and speed measurements, and a PMS5003 smoke sensor [18,19,20,21,22,23]. A “PC + embedded” architecture is adopted to accomplish data acquisition, algorithm computation, and motion control. High-performance Dynamixel XL430-W250 servo motors are utilized to drive the robot platform, ensuring stable and reliable motion. The overall algorithm framework comprises two core modules: basic functions and localization search. The former implements robot localization, navigation, and environmental perception, while the latter integrates the proposed plume model-based particle filter algorithm and the comparative gradient–bionic hybrid algorithm. SLAM technology is applied to achieve robot self-localization and environmental mapping. The LDS-02 LiDAR acquires environmental point cloud data, which are fused with the robot’s kinematic information via the GMapping algorithm to simultaneously estimate the robot’s pose and construct a 2D indoor grid map. This algorithm performs periodic resampling to retain high-probability particles, iteratively refining the map based on the real-time robot pose and LiDAR observations, thereby establishing the spatial foundation for autonomous navigation and odor source detection [24].

The experiment utilized a 5 m × 3 m indoor test area with stable airflow as the testing environment, as shown in Figure 10 and Figure 11. Sandalwood was used as the odor source, and a small fan was employed to simulate a gas leakage scenario under ventilated conditions. During the experiment, control variables were established and multiple initial positions were set to conduct a comparative evaluation of the two algorithms. In this study, a static odor source experimental platform with a size of 5 m × 3 m was constructed, and small fans were adopted to generate quasi-stable airflow for controlled variable conditions. It should be noted that such an experimental environment cannot reproduce the multi-scale vortex structure and concentration fluctuation characteristics of turbulence in real scenarios. Turbulent diffusion is the dominant form of odor propagation in both indoor and outdoor environments. Restricted by experimental conditions, this paper primarily verifies the localization performance of the proposed algorithm in a stable ventilation environment. In future work, a turbulence generation device equipped with grids or a multi-fan array will be developed to simulate realistic complex airflow environments, so as to further validate the robustness of the algorithm under turbulent conditions [25,26].

3.2.1. Particle Filter Algorithm Experiment

To evaluate the practicality of the algorithm, the odor source was placed at (0, 0 m). The robot performed comparative experiments starting from two initial positions: (2.15, 3.60 m) and (2.40, 4.55 m). A concentration binarization strategy was adopted with a threshold of 200 ppm: values below the threshold were set to 0 (gas not detected), and values above the threshold were set to 1 (gas detected) [27,28,29]. The total number of particles was set to N = 1000, with a particle convergence radius of 0.5 m.

In the initial search phase, the robot adopts a zigzag algorithm for global exploration and continues the zigzag traversal when no valid odor signal is detected, so as to increase the probability of encountering the odor plume. When the smoke concentration measured by the sensor exceeds the preset threshold of 200 ppm, the robot is deemed to have entered the odor plume area. The global zigzag search is immediately terminated, particle initialization is triggered, and the robot switches to a particle filter tracking mode based on the plume model and information entropy. As shown in Figure 12a, at t = 8 s, it reaches point a (2.05, 3.6 m) and enters the odor tracking phase. The particle distributions at the corresponding time instants are illustrated in Figure 13a and Figure 14a. The system determines the movement direction by analyzing the particle distribution and information entropy, guiding the robot to approach the odor source along the direction of decreasing information entropy. When the robot detects the odor again at points b and c in Figure 12a and points B and C in Figure 12b, particle resampling is triggered. The distribution update processes are shown in Figure 13b,c and Figure 14b,c. Eventually, the particles gradually converge near the odor source, as depicted in Figure 13d and Figure 14d. The robot completes OSL at point d (0.09, 0.36 m) in Figure 12a at t = 169 s and at point D (0.07, 0.19 m) in Figure 12b at t = 183 s.

Figure 12a shows that the algorithm estimates the source coordinates as (0.09, 0.12 m), with deviations of 0.09 m and 0.12 m in the x- and y-directions, respectively, and a Euclidean distance error of 0.15 m. Figure 12b presents the estimated source coordinates as (0.02, 0.42 m), with deviations of 0.02 m and 0.42 m in the x- and y-directions, respectively, and a Euclidean distance error of 0.42 m, demonstrating the high positioning accuracy of the proposed algorithm.

Figure 13 and Figure 14 illustrate the dynamic evolution of particles when the robot starts from (2.15, 3.60 m) and (2.40, 4.55 m), respectively. Figure 13a displays the particle distribution initialized at t = 8 s after the robot detects an odor concentration exceeding the threshold. Subsequently, Figure 13b,c and Figure 14b,c depict the resampling and position updating of particles during tracking based on variations in odor concentration. Finally, in Figure 13d and Figure 14d (t = 183 s), the particles converge near the odor source and form a concentrated distribution region, indicating that the approximate location of the odor source has been successfully locked. Figure 15 and Figure 16 illustrate the variation trends of information entropy under different initial positions. A rising entropy value indicates an increase in data volume and higher uncertainty. During the robot’s tracking phase, the entropy gradually decreases until accurate OSL is realized, which validates the core logic of the algorithm: reducing system uncertainty to achieve precise positioning.

Figure 17 and Figure 18 present the recorded environmental data, including wind direction, wind speed, and odor concentration. These figures show that the wind speed gradually increases over time. The robot dynamically adjusts its search strategy based on changes in the wind field and odor concentration, successfully completing OSL. This validates the adaptability and effectiveness of the proposed algorithm in real-world environments.

The experimental results from starting points (2.15, 3.60 m) and (2.40, 4.55 m) are shown in

Table 2. Experimental results from starting point (2.15, 3.60 m).

Starting Point	Number of Trials	Time	Endpoint	Estimated Position	Euclidean Distance	Successful
(2.15, 3.60)	1	172 s	(0.24, 0.42)	(0.24, 0.12)	0.26	√
	2	182 s	(0.01, 0.35)	(0.35, 0.14)	0.37	√
	3	176 s	(0.26, 0.24)	(0.17, 0.28)	0.32	√
	4	169 s	(0.09, 0.36)	(0.09, 0.12)	0.15	√
	5	165 s	(0.12, 0.24)	(0.34, 0.15)	0.37	√

and

Table 3. Experimental results from starting point (2.40, 4.55 m).

Starting Point	Number of Trials	Time	Endpoint	Estimated Position	Euclidean Distance	Successful
(2.40, 4.55)	1	179 s	(0.34, 0.16)	(0.24, 0.34)	0.41	√
	2	186 s	(0.24, 0.14)	(0.12, 0.28)	0.09	√
	3	183 s	(0.16, −0.05)	(0.02, 0.42)	0.42	√
	4	192 s	(0.27, 0.17)	(0.24, 0.37)	0.44	√
	5	187 s	(0.11, 0.31)	(0.41, 0.15)	0.43	√

, respectively. It can be seen that both experimental groups achieved a 100% localization success rate. Compared with the experiments starting from the initial position (2.40, 4.55 m), the average search time was shorter when the robot started from (2.15, 3.60 m). This demonstrates the practicality of the proposed algorithm, and its localization efficiency increases as the initial position approaches the odor source.

3.2.2. Analysis of Experimental Results

The experiments compared the performance of the proposed particle filter algorithm and the traditional concentration gradient algorithm in OSL tasks. The specific experimental results are presented in

Table 4. Results of different algorithms starting from point (2.15, 3.60 m).

Algorithm	Starting Point	Average Time Spent	Success Rate
Concentration gradient algorithm	(2.15, 3.60 m)	255.6	100%
Particle filtering algorithm		172.8	100%

and

Table 5. Results of different algorithms starting from point (2.40, 4.55 m).

Algorithm	Starting Point	Average Time Spent	Success Rate
Concentration gradient algorithm	(2.40, 4.55 m)	266.0	100%
Particle filtering algorithm		185.4	100%

:

The experimental results demonstrated that the proposed particle filter algorithm significantly outperformed the gradient–bionic hybrid algorithm in task completion efficiency, enabling faster identification of odor source location. Although the gradient–bionic hybrid algorithm exhibited advantages such as lower computational burden and stable operation under resource-constrained conditions, it required longer execution times in actual search processes.

According to the comprehensive comparison, the OSL algorithm based on particle filter and information entropy proposed in this paper exhibits more robust and efficient localization performance in both simulation experiments and real-scenario tests, which can meet the requirements of OSL tasks in indoor ventilated environments. The performance discrepancies between simulation and field measurement mainly stem from the low-turbulence and quasi-stable airflow characteristics of the experimental environment. Such differences are not caused by the failure of the algorithm itself, but result from the mismatch of environmental boundary conditions. The robustness of the algorithm under different search distances is demonstrated in Figure 8, proving that the proposed method still has theoretical applicability under more complex airflow conditions. In follow-up work, the experimental platform will be upgraded to introduce a turbulent environment for further verification.

Limited by objective conditions such as the endurance capacity of the mobile robot platform, the long-term working stability of sensors, and the difficulty of completely reproducing the indoor airflow environment, this study does not further increase the repetition times of physical experiments. However, the existing repeated tests at multiple different initial positions, localization error statistics, and convergence verification fully support the reliability of the experimental results, demonstrating that the algorithm has favorable robustness.

4. Discussion

This paper addresses the technical challenges of OSL in indoor ventilation environments by proposing a positioning method that integrates smoke plume modeling, particle filtering, and information entropy. A multi-sensor fusion mobile robot platform is developed based on TurtleBot3, and the effectiveness of the proposed algorithm is verified through theoretical modeling, numerical simulations, and real-world experiments. The proposed method employs smoke plume modeling to characterize the dynamic motion pattern of odor particles, uses particle filtering to achieve dynamic estimation of the posterior probability distribution of the odor source, and introduces information entropy to quantify perceptual uncertainty and optimize the robot’s path planning. Combined with an improved resampling mechanism and dual convergence criteria, the proposed method effectively overcomes the drawbacks of traditional algorithms, such as long localization time and weak robustness. Simulation and experimental results show that the proposed algorithm can achieve accurate OSL from different initial positions, with a long-distance localization success rate exceeding 90% and the localization error controlled to within 0.5 m. Compared with the traditional gradient–bionic hybrid algorithm, the proposed method significantly reduces the average search time, and the localization efficiency improves as the initial position approaches the odor source. This study provides a feasible technical solution for indoor OSL. In future research, the proposed method can be extended to indoor scenarios with complex obstacles and outdoor turbulent environments. Furthermore, multi-robot cooperative localization strategies can be explored to improve the practical application value of the algorithm. Restricted by objective factors, including the limited endurance of the mobile robot platform, insufficient long-term operational stability of sensors, and the difficulty in accurately reproducing indoor airflow conditions, the number of physical experiment repetitions in this work is limited. Subsequent studies will conduct repeated validations in more diversified scenarios to further optimize the algorithm’s performance and enhance its generalization capability.