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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper addresses the collective odor source localization (OSL) problem in a time-varying airflow environment using mobile robots. A novel OSL methodology which combines odor-source probability estimation and multiple robots’ search is proposed. The estimation phase consists of two steps: firstly, the separate probability-distribution map of odor source is estimated via Bayesian rules and fuzzy inference based on a single robot’s detection events; secondly, the separate maps estimated by different robots at different times are fused into a combined map by way of distance based superposition. The multi-robot search behaviors are coordinated via a particle swarm optimization algorithm, where the estimated odor-source probability distribution is used to express the fitness functions. In the process of OSL, the estimation phase provides the prior knowledge for the searching while the searching verifies the estimation results, and both phases are implemented iteratively. The results of simulations for large-scale advection–diffusion plume environments and experiments using real robots in an indoor airflow environment validate the feasibility and robustness of the proposed OSL method.

The olfactory sense is crucial to the survival for many creatures, and has long played a fundamental role in human development and biosocial interaction. Electronic noses (e-noses), which are instruments designed to mimic the mammalian olfaction system, focus on identifying, classifying and quantifying the odor mixture—the fundamental function of animals’ smell sense. They are very useful for numerous applications in the food and pharmaceutical industry, in gaseous contamination monitoring, clinical diagnostics, contrabands inspection [

Research into the use of one or more mobile robots equipped with odor/gas sensors and/or a wind sensor to search for odor/gas sources is called odor source localization (OSL) research [

The task of behavior-based OSL can be decomposed into three sub-procedures (namely, plume finding, plume traversal, and source declaration) according to Hayes

Analytical-model based methods have also been proposed by several OSL researchers. The analytical-model based odor-source estimation could make up for the disadvantage of commonly used gas sensors with small detection range as well as the discrete distribution of plumes caused by turbulence. Ishida

Up to now, most OSL research work was implemented using a single robot. Compared with the single-robot search, multiple robots might have at least two advantages: the expected search time could be decreased; and multi-robot systems could provide a greater robustness against hardware failures. Hayes [

Multi-robot based OSL has not been well studied and has mostly been restricted to simulated robots and simulation environments. To our knowledge, only a few publications [

A novel collective OSL strategy which combines multi-robot search with gas source probability estimation is proposed in this paper. The source probability estimation consists of two steps. Firstly, separate gas source probability map is estimated via Bayesian rules and fuzzy inference by using a single robot’s detection information; secondly, the distance and superposition methods are used to fuse separate source probability maps into one combined map. Multi-robot search is realized by a PSO algorithm, in which the local and global fitness functions are replaced by the estimated separate and combined gas source probability, respectively. The gas source probability estimation and multi-robot searching are implemented iteratively. The estimation phase exploits the detected information to guide multi-robot search, and multiple robots’ search can further verify the estimation result by updating their locations continuously. The proposed collective OSL strategy has been verified in both the simulated and real time-varying plume environments.

One of the main contributions of this manuscript is that a new OSL methodology which combines the estimation and searching is proposed. The previously published OSL work either only used behavior based searching methods or only used analytical based estimation methods, however, few research works related to OSL combining both the estimation and searching methods have been published. The behavior-based OSL searching without estimation has blindness, while the feedback of estimation based OSL is difficult to be obtained without robot searching. In the P-PSO algorithm proposed in our research, the estimation process exploits the detected information to guide the multi-robot search, while the multi-robot search coordinated via PSO method updates the estimation result by exploring more areas, thus a better OSL performance could be achieved.

The remainder of this paper is organized as follows. The characteristics of an advection-diffusion plume are analyzed in Section 2. Section 3 presents the framework of the collective OSL strategy. The realization of separate and combined gas-source probability estimation is explained in Section 4. Section 5 introduces PSO-based collective gas-source search strategy using the estimated source probability as the fitness function. The simulation and multiple real-robot experiments for collective OSL and search are given in Sections 6 and 7, respectively. Finally, conclusions are summarized.

The transport of a gas in the air is influenced by advection, turbulent diffusion and molecular diffusion. The effect of advection is that the gas is transferred by the time-averaged flow movement; the effect of turbulent diffusion is that the gas diffuses by turbulent kinetics; the molecular diffusion is caused by molecular motion. The speed of turbulent diffusion is much faster than that of molecular diffusion. For example, in the air the difference is about 10^{5}–10^{6} times, therefore the molecular diffusion in turbulence could be neglected [_{x}_{y}_{x}_{y}

Without loss of generality, suppose the wind direction is along the x axis,

Since _{y}_{L}_{1} and _{2} at time _{1} and _{2}, respectively, so
_{1} and _{2}, respectively. In _{2} > _{1},
_{1} = _{2}, _{1},_{1}) > _{2},_{2}). The characteristic of advection-diffusion is fundamental to the collective gas-source probability estimation presented in Section 4.

In the proposed collective OSL process, the gas-source probability estimation and multi-robot search are implemented iteratively. The estimation is used for guiding robots’ search, and multiple robots’ search can further verify the estimation result by updating their locations continuously. The proposed methodology includes the following four phases. The flowchart is illustrated in

The algorithm proposed by Li

The gas source probability estimation consists of two steps, the first is separate estimation based on single robot’s detection events by using Bayesian rules and fuzzy inference (see Section 4.1), the second is fusing the separate estimation to form a combined probability map by using the distance based superposition method (see Section 4.2).

Because the accurate turbulent model is hard to set up, the posterior probability of gas source could not be obtained from it. The separate gas source probability estimated using Bayesian rule is expressed as follows:

∵

The estimation process of the probabilities

_{max} and 2_{max}, respectively. _{max} and _{max} are the maximal gas concentration and fluctuation intensity detected until now, respectively.

According to the dynamic characteristics of gas plume described in Section 2, the square area Δ centered on the gas and wind sensors is determined as follows:
_{t}_{0} is set to 10 m in simulations and 2 m in experiments; _{t}_{t}_{t}_{t}

Suppose _{ref}_{ref}_{t}_{t}_{t}_{t,In}_{t}_{ref}_{t}_{ref}_{t,In}_{plume}_{plume}_{t,In}

As _{x′y′} with the central coordinate (_{xy}_{x′y′}) = _{xy}

It is supposed that each detected filament travels directly from the gas source to the sensor in the estimated area. The separate posterior probability _{x′y′}|_{t}_{x′y′} being gas source in the area Δ by the detection event _{t}_{M}_{M}_{x′} denotes the wind magnitude. When the event _{t,In}_{x′y′}|_{t}_{x′y′}|_{t}_{x′y′}) denotes the separate prior probability that the gas source is in the grid _{x′y′}. Considering the volume of robot, the initial abscissa in the estimation area should be more than half of the robot side length _{robot}_{t,In}|_{x′y′}) is represented as follows [_{x′y′}; _{x′y′} and the square’s centerline being parallel with the wind direction (see _{x′y′} to the position of the sensor. Here the prior probability _{x′y′}) in Δ is set to be equal in separate gas source probability estimation, so it can be deleted. Substituting

Let _{y′}_{x}_{′} denotes the moving time of the puffs from the grid _{x′y′} to the position of the sensor. Therefore

The separate probability map in square area Δ with the supposed moving time of the detected puff from 0 to _{M}

When the robot does not detect the gas, the posterior probability distribution is represented as follows:

When the detection event _{t,In}_{x′y′}|_{t,In}

When the detection events
_{1} and ξ_{2} are two constants with the range of (0, 1). For the detection events
_{1} · _{t−1,In}) is used to approximate the value of
_{1} was set to 0.8). In _{2} (in our experiments, ξ_{2} was set to 0.2). The value of _{x′y′}|_{t}_{xy}_{t}) in the world coordinate system X−Y by the transform equation _{x′y′}) = _{xy}

The purpose of estimating combined gas source probability map is to guide the subsequent search of robots. To make the estimation results more reliable, all the separate probability maps from different spaces and different time are merged into one combined gas source probability map.

When _{x,y} denotes the central coordinates of the grid _{xy}_{i}_{i,t} (

Finally the combined gas source probability map is calculated by superposing the maps at different sampling times:

A particle swarm optimization (PSO) algorithm is used to coordinate multiple robots search for the gas source. The PSO uses the estimated separate and combined gas source probabilities instead of real values (gas concentration, for example) as the local and global fitness functions, respectively. Here we call it the Probability-fitness-function based Particle Swarm Optimization (P-PSO) algorithm.

If all the searchers have not detected the gas after many attempts, robots move toward different directions to re-find the plume; otherwise, the robots move according to the searching algorithm based on the result of estimation. The basic formula of standard PSO [_{1} and _{2} are two constants; _{1} and _{2} denote two random numbers; _{i}_{i}_{i}_{g}

In the P-PSO, _{i}_{g}_{xy}_{i,t}_{xy}

In the proposed P-PSO, _{i}_{g}

The necessity of coordinating multi-robot to search gas source by P-PSO includes two aspects. First, the proposed P-PSO uses the estimation probability distribution as a clue for re-finding the plume, thus it could reduce the probability of losing the plume. Second, the real gas concentration fluctuates violently, but the probability distribution changes slowly, so the probability distribution instead of real concentration is adopted as the fitness function.

The size of the robot is negligible compared with the large scale of the search space (100 m × 100 m). It is assumed that each robot is equipped with one gas sensor and one wind sensor. The gas sensor has relatively quick response and recovery (further details are presented in Section 6.3). The wind sensor measures wind speeds from 0 to 10 m/s and wind directions from 0° to 359°. Zero-mean Gaussian noise is added to the output of the wind sensor, and the variances of the wind speed and direction are set to 0.05 m/s and 1°, respectively. The sampling frequency of the gas concentration and wind sensors is 10 Hz. In view of the influence of the recovery and response time of metal oxide semiconductor (MOS) sensors, the motion mode of “run-stop-run-stop” is adopted here. Each robot stops at one location for 5 s to collect the gas and wind information, and then the robot runs for 1 s again according to the velocity and direction calculated by the algorithm. Each robot knows its current location and moves in a speed ranging from 0.2 m/s to 0.8 m/s. The initial and largest side length of Δ is set to be 10 m. The smallest side length of Δ is 2 m. Gas concentration and wind information data recorded by the robots are sent to a workstation via wireless communication. The motion mode of each robot is planned by the algorithm running in the workstation.

In Farrell’s model [

The advection–diffusion model is composed of a large number of advected and dispersed filaments. Given the large number of filaments, the overall instantaneous concentration at _{i}_{i}

MOS sensors are widely used for chemical plume tracing because of their low cost and small size. To simulate the real response and recovery characteristics of MOS sensors, a second-order sensor model is built here, with the response and recovery phases of the sensors both regarded as second-order inertia links. The two phases have different time constants, and therefore their design parameters are different. The left block in _{res}_{rec}

In our simulations, the discrete sensor models [_{res}_{rec}_{res}_{rec}

The size of the simulation environment is 100 m × 100 m. Each square grid of the environment is 0.5 m × 0.5 m. The rate of puff released by the source is 5 puffs/s. The plume-model update period is 0.01 s. The wind speed range is between 0.5 and 2.5 m/s. The gas source is located at (20, 0) and the robots start at (90, −30), where the coordinate units are meters. The gas-source localization algorithm is demonstrated for two different plume environments, which we refer to as slightly wandering and medium-wandering. The extents of the two plumes in the vertical direction are 20, 60 (measured at

The CPSO (see Reference [

The simulation results are illustrated in _{1} (_{1} = 0.5 m) and the center being actual gas source. To reduce the chance of random arrival, a more rigorous metric, _{2} (_{2} = 5 m) and the center being actual gas source.

It takes more time to localize the gas source via the P-PSO algorithm in medium-wandering plume environments than that in the slightly wandering environments. The trails adopting CPSO method in slightly meandering plume environments consume longer time than both the conditions employing P-PSO algorithms. That is, the P-PSO algorithm gains an advantage over the CPSO in respect of the searching efficiency. Furthermore, the searching time gets reduced for both algorithms as the number of robots increases. In contrast with the searching time, as

The collective odor source estimation and search experiments were carried out in a centralized way. The sensed gas concentrations and airflow information were sent from each robot to a central workstation, and the control commands were sent from the workstation to each robot, both via wireless communication. If all the robots approach the real source and converge in a specified area, the algorithm is stopped manually.

Four small olfaction robots, named MrCollie (Mobile Robots for Cooperative Odor-source LocaLization in Indoor Environments), were used in the experiments. The robots were designed and assembled by the Institute of Robotics and Autonomous Systems of Tianjin University in 2006. One of the MrCollie robots and its onboard sensors is illustrated in

High sensitivity, long life-span and low cost make MOS sensors the most widely used gas sensors in mobile robots. TGS2620, a kind of MOS sensor produced by Figaro Engineering Inc., was used in our real-robot OSL experiments. TGS2620 consists of a silicon semiconductor layer formed on an alumina substrate of a sensing chip together with an integrated heater. In the presence of a detectable gas, the voltage across the heater causes an oxygen exchange between the volatile gas molecules and the metal coating material. Electrons are attracted to the loaded oxygen and result in decreases in sensor conductivity. A simple electrical circuit can convert the change in conductivity to an output signal which corresponds to the gas concentration [

The relationship between the gas concentration and the sensor resistance is expressed as follows [_{s}_{0} represent the sensor resistances in gas and air, respectively; _{out}_{0}

The calibration process is described as follows: a certain amount of liquid ethanol was injected into a flask, and a fan was employed to speed up the evaporation. The amount of ethanol liquid was calculated according to the desired concentration of the ethanol vapor and the volume of the flask. The vapor was sucked by an air pump into a chamber and contacted with the gas sensor therein. The sensor outputs were recorded after the readings got steady. The calibration device is given in

An overhead charge coupled device (CCD) camera sent the image of each robot’s location identifier to the workstation, and the position and orientation of each robot were extracted by the workstation via a simple pattern recognition algorithm.

The location identifier is shown in

The experimental scene is captured by the overhead CCD camera and sent to the workstation. Then the workstation can recognize the location identifier by a series of binarization, filtering and pattern recognition process. Finally, the position, orientation and serial numbers of the robots are obtained. Sometimes the CCD camera failed to localize the robots, so dead reckoning was also used for correction.

A traffic-rule based method was adopted to avoid robot collisions. The multiple robots are coordinated by seven simple rules. To apply these rules, the surrounding area of each robot is divided into five zones, see _{i} and _{j}, respectively.

The traffic rules applied by robot

If the nearest robot

If robot

If robot _{i}×_{j}| > 0, then robot

If robot _{i}×_{j}| < 0, then robot

If robot _{i}×_{j}| > 0, then robot

If robot _{i}×_{j}| < 0, then robot

If robot

The multi-robot system can realize basic collision avoiding functions by applying the above traffic rules, but the radii and angles of the five zones need to be adjusted in advance.

Multi-robot CPT experiments were conducted in the laboratory of the Institute of Robotics and Autonomous System at Tianjin University. The laboratory had two doors and two windows. The area of the lab was 5.3 m × 5.0 m (the detailed dimensions can be seen in

The robots moved in two different airflow fields,

As

In the experiments, the robots moved in a run-stop-run-stop mode (running for 5 s and stopping for 5 s). The motion speed of each robot was set to 2.5 cm/s–∼4 cm/s. Both the airflow and gas concentration were sampled five times during the 5-second-stop.

The robots searched in two different indoor environments, one is artificial airflow, and the other is natural airflow. For each airflow environment, the robots started from the right side and the lower right corner of the search area. Thus, there are four different experimental situations. The gas source localization experiments were run 40 times in total, 10 trials for each situation. Before each new experiment was run, the doors and windows were opened till the detected gas concentration was less than 5 ppm. If the three robots did not approach the gas source (

The experimental results are presented in _{av}_{a}_{av}_{a}

From the experimental results it can be found that the average search time for the artificial wind fields is shorter than that for the natural wind fields. By analyzing the experiment processes and results, we think this is due to at least two reasons. First, the variation in the direction of the natural wind was greater than that of the artificial wind. Second, in the natural wind field, sometimes there existed long-duration weak airflows (less than 5 cm/s, which the anemometer could not detect reliably). The reasons that the search time from the right side was shorter than that from the lower right corner might be explained from two aspects. First, the distance between the robots and the real gas source is shorter for the right-side starting location. Second, the robots starting from the lower right corner were apt to fall into the big eddy field, which resulted in useless search for a period of time, so the total time increased.

As mentioned above, the big eddy area (see the red circle in

Although one run failed owing to the big eddy, the other nineteen experiment runs for the artificial airflow field succeeded. For the natural airflow case, two failures (one for RS-NW and one for LR-NW) were because of long-duration weak airflow (less than 5 cm/s, which the anemometer could not detect reliably), one failure (for LR-NW) was due to the big eddy.

Simulation results using time-varying and large-scale advection–diffusion plume models demonstrate the feasibility and robustness of the proposed odor source localization method via multi-robot search and estimation. Compared with the CPSO based method, the plume-tracking strategy based on the estimation-searching frame proposed in this paper can find the single odor source in less time with a higher success rate. For slow-changing airflow environments (slightly wandering large-scale advection–diffusion plumes, for example), relatively few robots using the proposed plume-tracking strategy can successfully approach the odor source, and the use of more robots does not noticeably decrease the search time. It takes longer to search in the medium-wandering plume environment using the P-PSO-based method. Therefore, the P-PSO-based plume-tracking method has good robustness regarding different plume environments when the number of robots is sufficient. The proposed multiple-robot based collective gas-source localization method is also demonstrated with real robots experiments in indoor time-variant airflow environments. Except the extreme airflow conditions such as the long-period weak airflow and big eddy areas, the proposed method works well in both the natural and artificial airflow fields. Limited by our experimental infrastructure, the proposed OSL strategy was only evaluated in a small-scale indoor environment. If the infrastructure is improved, the strategy might be extended to large-scale scenarios, even outdoor airflow environments.

The feasibility and robustness of the proposed multi-robot gas source localization method comes from two aspects. First, the tradeoff between exploration and exploitation is achieved in the proposed gas source localization strategy. The estimation process exploits the detected information to guide multi-robot search, while the multi-robot search updates the estimation result by exploring more areas. Second, the gas source probability estimated using both the gas and airflow information, instead of simple gas concentration and wind direction, is utilized.

The proposed P-PSO method might fail in the region where obstacles or boundaries (e.g., wall) exist because the hypotheses of homogeneity and isotropy are false. How to estimate gas source probability in such situations will be our next research.

The detection of wind and gas event

_{t}

The detection event z happening in the time period [

_{t}

Undetected event happening in the time period [

_{t,In}

Detected event, the robot is in the plume

Undetected event, the robot is on the edge of the plume

Undetected event, the robot is outside of the plume

_{i,t}

Detection event by the robot i in the time period [

_{t}

_{1,t},

_{2,t}, …,

_{N,t}}

Detection vector by N robots in the time period [

_{1}

_{t}

_{1},

_{2}, …,

_{t}}

Detection vector by N robots from time 1 to t

A small connected domain

The smallest space unit of gas source probability estimation

_{xy}

The grid with the central coordinate (

_{x′,y′}

The grid with the central coordinate (

Probability that the gas source is in Δ

Posterior probability that the gas source is in

Posterior probability that the gas source is in

Posterior probability that the gas source is in Δ when

Posterior probability that the gas source is in

_{l}

_{x′y′})

(Prior probability that the gas source is in the grid _{x′y′} in local coordinate system

_{l}

_{t,In}|

_{x′y′})

Conditional probability that _{t,In}_{x′y′} in local coordinate system

_{l}

_{t}|

_{x′y′})

Conditional probability that _{t}_{x′y′} in local coordinate system

_{l}

_{x′y′}|

_{t},Δ)

Posterior probability of any grid _{x′y′} being gas source when the source is in the area Δ and _{t}

_{l}

_{x′y′}|

_{t,In},Δ)

Posterior probability of any grid _{x′y′} being gas source when the source is in the area Δ and _{t,In}

_{l}

_{x′y′}|

_{t},Δ)

Posterior probability of any grid _{x′y′} being gas source when the source is in the area Δ and _{t}

_{l}

_{x′y′}|

_{t,In})

Posterior probability of any grid _{x′y′} being gas source when _{t,In}

Posterior probability of any grid _{x′y′} being gas source when

Posterior probability of any grid _{x′y′} being gas source when

_{l}

_{t})

Posterior probability of the gas source being in the area Δ when _{t}

_{l}

_{t,In})

Posterior probability of the gas source being in the area Δ when _{t,In}

Posterior probability of the gas source being in the area Δ when

Posterior probability of the gas source being in the area Δ when

_{xy}|

_{i,t})

Separate probability of the gas source being in _{xy}

_{xy}|

_{t})

Combined probability of the gas source being in _{xy}

_{xy}|

_{1t})

Combined probability of the gas source being in _{xy}

This work was supported by the China “863” High-Tech Program (No. 2007AA04Z219), the National Natural Science Foundation of China (No. 60875053, 60802051), Tianjin Natural Science Foundation (09JCYBJC02100) and the Program for New Century Excellent Talents in University (NCET).

The schematic diagram of probability density distribution of puffs.

The flowchart of the proposed gas source localization strategy.

The flowchart of the separate gas source probability estimation.

The MOS sensor model.

The combined gas source probability maps estimated at six different times.

The small mobile MrCollie robot and onboard sensors.

The device for gas sensor calibration. A TGS2620 gas sensor was mounted inside the air chamber.

The location identifier labeled at the top of the robot.

The surrounding area division for collision avoidance.

Real-robot experiment arena as seen from the overhead camera.

The average wind speed and direction of each anemometer over 300 s.

Two of recorded collective OSL and search processes, the robots started from the lower right corner.

The times of robots successfully approaching the source out of 20 trails.

P-PSO-S | 15 | 17 | 19 | 20 | 20 | 20 | 20 | 20 |

CPSO-S | — | 2 | 5 | 12 | 13 | 17 | 17 | 19 |

P-PSO-M | 12 | 16 | 18 | 18 | 19 | 20 | 20 | 20 |

CPSO-M | — | 0 | 0 | 1 | 1 | 2 | 2 | 4 |

Experimental results for plume finding/tracking experiments.

_{av} |
309 | 493 | 521 | 709 |

_{a} |
10 | 9 | 9 | 8 |