Creating gas concentration gridmaps with a mobile robot

TL;DR: In this article, the authors address the problem of mapping the features of a gas distribution by creating concentration gridmaps from the data collected by a mobile robot equipped with an electronic nose.

Abstract: This paper addresses the problem of mapping the features of a gas distribution by creating concentration gridmaps from the data collected by a mobile robot equipped with an electronic nose. By contrast to metric gridmaps extracted from sonar or laser range scans, a single measurement of the electronic nose provides information about a comparatively small area. To overcome this problem, a mapping technique is introduced that uses a Gaussian density function to model the decreasing likelihood that a particular reading represents the true concentration with respect to the distance from the point of measurement. This method is evaluated in terms of its suitability regarding the slow response and recovery of the gas sensors. The stability of the mapped features and the capability to use concentration gridmaps to locate a gas source are also discussed.

Summary

1 Introduction

• This paper addresses the problem of representing gas distribution in indoor environments by a mobile robot equipped with a gas sensitive system, comprising an on-board array of gas sensors.
• Gridmaps were originally introduced to mobile robotics in the 1980s as a means of creating maps using wide-angle measurements from ultrasonic range-finder sensors [4].
• Thus, considerable integration of successive measurements is carried out by the sensors themselves.
• To overcome these problems, a mapping technique is introduced that integrates many gas measurements over an extended period of time.
• After a brief review of related work (Section 1.1), the experimental setup is described in Section 2.

1.1 Related Work

• Most work on chemical sensing for mobile robots assumes an experimental setup that reduces the influence of turbulent transport by either minimising the source-to-sensor distance in trail following [26, 28, 27, 21] or assuming a strong airstream in the environment [9, 25, 23, 7].
• The effect of turbulent air movement can be described in this case with a diffusion-like behaviour.
• “Odour hits” were counted whenever the sensed concentration exceeded a fixed threshold.
• In addition to the dependency of the gas distribution map on the selected threshold, the problem with using only binary information from the gas sensors is that much useful information about fine gradations in the average concentration is discarded.
• A further disadvantage of this method is that it requires perfectly even coverage of the inspected area by the mobile robot.

2.1 Robot and Gas Sensors

• The experiments were performed with a Koala mobile robot equipped with the Mark III mobile nose [15], comprising 6 tin oxide sensors manufactured by Figaro (see Fig. 2).
• In consequence of the measurement principle, metal oxide sensors exhibit some drawbacks, including low selectivity, comparatively high power consumption (caused by the heating device) and weak durability.
• The sensors were placed in sets of three (of type TGS 2600, TGS 2610 and TGS 2620) inside two separate tubes containing a suction fan each.
• Multiple, redundant sensor types were used only to increase the robustness of the system (there was no attempt to discriminate different odours).
• The distance between the two sets of sensors was 40 cm.

2.2 Environment, Gas Source and Absolute Positioning System

• All experiments were performed in a rectangular laboratory room at Örebro University (size 10.6 × 4.5 m2).
• The air conditioning system in the room was deactivated in order to eliminate the possibility of a dominant constant airflow.
• Ethanol was used because it is non-toxic and easily detectable by the tin oxide sensors.
• To record the position of the robot, the vision-based absolute positioning system W-CAPS [16] was applied, which tracks a distinctly coloured object mounted on top of the robot (the cardboard “hat” shown in Fig. 2).
• The figure shows a floor plan of the laboratory room, and the fields of view for each of the four cameras that were used to track the robot’s position, shaded according to the number of cameras that can sense a particular region.

3 Gas Concentration Gridmaps

• This section presents the method for creating gas concentration gridmaps from a sequence of sensor measurements collected by a mobile robot.
• In order to create gas concentration gridmaps, the cells have to be updated multiple times.
• Nevertheless these readings contain information about a larger area, for two reasons.
• Second, the metal-oxide gas sensors perform temporal integration of successive readings implicitly due to their slow response and recovery time.
• By applying this model, the algorithm is able to determine the spatial structure of the average gas distribution with limited distortion (discussed in Section 3.3) from a series of readings, which do not represent the gas concentration directly due to the response characteristics of the sensors.

3.1 The Algorithm

• The sensor readings are convolved using the radially symmetric two dimensional Gaussian function f( x) = 1 2πσ2 e− x2 2σ2 .
• In detail the following steps are performed: .
• In the first step the normalised readings rt are determined from the raw sensor readings.
• Then, for each grid cell (i, j) within a cutoff radius Rco, around the point xt where the measurement was taken at time t, the displacement δ (i,j) t from the grid cell’s centre x (i,j) is calculated as δ (i,j) t = x (i,j) − xt. (3) 4. Discretisation of the Gaussian weighting function onto the grid.
• First, thirteen cells are found to have a distance of less than the cutoff radius from the point of measurement (Fig. 4, left).
• The weights are represented by shadings of grey.

3.2 Parameter Selection

• The concentration mapping algorithm requires three parameters: the width σ of the Gaussian function, the cutoff radius Rco and the threshold Wmin.
• A value of σ has to be chosen that is high enough to satisfy the requirement for sufficient extrapolation on the gas concentration measurements, but low enough to preserve the fine details of the mapped structures.
• Fig. 5 shows the sum of the Gaussian weighting functions for a sequence of steps along a straight line (with a step width of 2σ).
• The figure shows the last four steps plus the current one indicated by an arrow.
• Due to the memory effect of the metal oxide sensors, the sensor readings represent a low-pass filtered concentration value integrated along the path driven.

3.3 Impact of Sensor Dynamics

• As a consequence of the memory effect of the gas sensors, the mapped values show asymmetrically blurred edges and a slightly shifted centre of the area of maximum concentration compared to the real distribution.
• Comparing the real distribution with the mapped values in Fig. 6(d), the asymmetrical shift as well as the blurring effect can be seen.
• The figure shows (a) a simulated step stimulus varying between the minimum and maximum concentration levels, (b) the sensor response as calculated for the Örebro Mark III mobile nose, (c) the Gaussian weighting functions multiplied by the corresponding sensor readings, and (d) the resulting curve of the mapped values.
• In addition, the directional component of both effects would be averaged out if the robot passed a given point from different directions.

4 Data Acquisition Strategy

• This section describes the different exploration strategies used by the mobile robot to collect the sensor data for concentration mapping in their experiments.
• In order to obtain better accuracy, it is further advantageous to pass particular points from multiple directions (see Section 3.3).
• Two different predefined trajectories, a rectangular spiral and a sweeping movement (see Sections 4.1 and 4.2) were tested here.
• And rescue operations) if gas sensors could easily be added to existing mobile robots without the need to severely modify the behaviour.
• The concentration mapping algorithm was also tested with data obtained using reactive gas source tracing strategies (see Section 4.3).

4.1 Predefined Path – Rectangular Spiral

• The robot followed a sequence of rectangular spirals around the location of the gas source.
• Thus, points are passed equally often from opposite directions.
• A constant speed was also found to enhance the gas source localisation capability [19, 5].
• At the corners, the robot was rotated slowly (10◦/s) in order to minimise additional disturbance.
• These cycles were repeated with a randomly chosen starting corner and direction at the start of each trial.

4.2 Predefined Path – Sweeping Movement

• In the second strategy, the robot performs a sweeping movement that encloses nine squares (80 cm × 80 cm), as shown in Fig. 7 (a), providing nine possible locations in which to place the gas source .
• The sweeping movement was implemented as a trajectory consisting of the four segments shown in Fig. 7, which were executed repeatedly in the given sequence.
• In contrast to the previous strategy, points on the path are not traversed equally often from opposite directions.
• Opposite edges of the nine squares, however, are passed from opposite directions in the course of each cycle.
• In contrast to the spiral movement, however, the location of the source is not especially distinguished by the symmetry of the path.

4.3 Reactive Gas Source Tracing

• As a sub-task of the general gas source localisation problem, gas source tracing is supposed to guide a gas-sensitive mobile system towards a source using its own measurements of the gas distribution.
• Two Braitenberg-type strategies were implemented, corresponding to uncrossed and crossed sensor-motor connections (see [17] for full details).
• In contrast to the previous strategies, the trajectory is of course not known in Fig. advance in the case of Braitenberg-type strategies.
• It is thus not guaranteed that the path complies with the mentioned conditions for concentration mapping.
• In reaction to a certain gas distribution, the resulting trajectory might not cover all regions and the robot might always approach some points from the same direction.

5.1 Stability of the Mapped Structures

• The concentration mapping algorithm was tested extensively using sensor data acquired with the Mark III mobile nose over a total of almost 70 hours of experiments and more than 5 kilometres of travel.
• Some examples showing the evolution of the gridmaps during these experiments can be seen in Figs. 8 and 9.
• In the experiments where the robot followed a predefined path, it was found that the mapped distribution stabilised when the robot had passed each point in the vicinity of the gas source at least two times from opposite directions.
• Thus, it took approximately 25 minutes in the trials where a rectangular spiral was driven, while stabilisation was observed after approximately 10 minutes in the sweeping trials.
• The results show that the gridmaps obtained are qualitatively very similar, and that the distance from the source to the concentration maximum reached the same level in all cases after roughly 25 minutes.

5.2 Suitability for Gas Source Localisation

• In the case of a gas distribution controlled purely by diffusion, the location of a static, constantly evaporating gas source would correspond to the concentration maximum in the gridmap.
• Each part corresponds to two completed cycles as defined in Section 4.2. tion maximum fell below some selected thresholds.
• The lower performance of the sweeping strategy could be explained by the fact that points are not traversed equally often from opposite directions with this strategy, as discussed in Section 4.
• Poorer localisation performance was obtained when the area of high concentration formed a plume-like structure, as can be seen in Fig.
• The maximum average concentration is also expected not to be suitable for gas source localisation if the airflow situation changes drastically during an experiment.

Figures

Fig. 1. Example of gas sensor readings recorded while the robot passed a gas source (ethanol) along a straight line at a low speed of 0.25 cm/s. The curve displays relative conductance values of two metal oxide sensors mounted on the left and right side of the robot with a separation of 40 cm.

Table 1 Percentage of time steps for which the distance between the maximum concentration grid cell and the centre of the gas source was below the specified thresholds. The values were calculated from 6 spiralling trials with a total length of 754 minutes, 8 sweeping trials (976 minutes), and 11 Braitenberg trials (1720 minutes). The covered experimental area was 2.4 × 2.4 m2 (Spiral), 2.8 × 2.8 m2 (Sweeping), and 3.4 × 4.1 m2 (Braitenberg).

Full text

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Preprint
This is the submitted version of a paper published in Robotics and Autonomous Systems.
Citation for the original published paper (version of record):
Lilienthal, A J., Duckett, T. (2004)
Building gas concentration gridmaps with a mobile robot
Robotics and Autonomous Systems, 48(1): 3-16
https://doi.org/10.1016/j.robot.2004.05.002
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Building Gas Concentration Gridmaps
with a Mobile Robot
Achim Lilienthal
a
Tom Duckett
b
a
University of T¨ubingen, WSI, D-72076 T¨ubingen, Germany.
lilien@informatik.uni-tuebingen.de
b
Center for Applied Autonomous Sensor Systems, Dept. of Technology, University
of
¨
Orebro, S-70182
¨
Orebro, Sweden. Tom.Duckett@tech.oru.se
Abstract
This paper addresses the problem of mapping the structure of a gas distribution by
creating concentration gridmaps from the data collected by a mobile robot equipped
with gas sensors. By contrast to metric gridmaps extracted from sonar or laser range
scans, a single measurement from a gas sensor provides information about a com-
paratively small area. To overcome this problem, a mapping technique is introduced
that uses a Gaussian weighting function to model the decreasing likelihood that a
particular reading represents the true concentration with respect to the distance
from the point of measurement. This method is evaluated in terms of its suitabil-
ity regarding the slow response and recovery of the gas sensors, and experimental
comparisons of different exploration strategies are presented. The stability of the
mapped structures and the capability to use concentration gridmaps to locate a gas
source are also discussed.
Key words: mobile nose, gas distribution mapping, gas source localisation.
Preprint submitted to Elsevier Science 23 April 2004

1 Introduction
This paper addresses the problem of representing gas distribution in indoor
environments by a mobile robot equipped with a gas sensitive system, compris-
ing an on-board array of gas sensors. A new algorithm is presented for creating
concentration gridmaps by combining the recorded gas sensor readings of the
robot with location estimates. Intended applications include chemical map-
ping of hazardous waste sites and localisation of a gas source, especially in
environments where it is impractical or uneconomical to install a fixed array
of gas sensors. The proposed method does not require artificial ventilation
of the environment, e.g., by imposing a strong, unidirectional airflow as in
previous approaches for gas source localisation [12, 25, 7].
Gridmaps were originally introduced to mobile robotics in the 1980s as a means
of creating maps using wide-angle measurements from ultrasonic range-finder
sensors [4]. The basic idea is to represent the robot’s environment by a grid
of small cells. In a conventional gridmap, each cell contains a certainty value
representing the belief that the corresponding area is occupied by an object.
In a gas concentration gridmap, each cell contains an estimate of the relative
concentration of a detected gas in that particular area of the environment.
There are several problems in creating such a representation that are specific
to mobile robots equipped with gas sensors.
Fig. 1. Example of gas sensor readings recorded while the robot passed a gas source
(ethanol) along a straight line at a low speed of 0.25 cm/s. The curve displays
relative conductance values of two metal oxide sensors mounted on the left and
right side of the robot with a separation of 40 cm.
A major problem is that the distribution of gas molecules in an environment
that is not strongly ventilated tends to be dominated by turbulence and con-
vection flow rather than diffusion, which is known to be a considerably slower
transport mechanism for gases in general [20]. This typically results in a jagged
2

pattern of temporally fluctuating eddies [18, 22]. These effects are illustrated
in Fig. 1, which shows typical sensor readings in the vicinity of a gas source
(evaporating liquid ethanol). In this experiment, the robot passed the source
along a straight line at low speed in order to measure the distribution of
the analyte accurately. The curve in Fig. 1 indicates that the turbulent gas
distribution creates many local concentration maxima, and that the absolute
maximum is often located some distance from the actual location of the gas
source if this source has been active for some time. In addition, the gas distri-
bution varies over time.
Other problems relate to the gas sensors. In contrast to range-finder sensors
such as sonar or laser, a single measurement from an electronic gas sensor pro-
vides information about a very small area. This problem is further complicated
by the fact that the metal-oxide sensors typically used for this purpose do not
provide an instantaneous measurement of the gas concentration. Rather, these
sensors are affected by a long response time and an even longer recovery time.
The time constants of rise and decay for the complete gas sensitive system
(mobile nose) used here were estimated as τ
r
≈ 1.8sandτ
d
≈ 11.1sre-
spectively [15]. Thus, considerable integration of successive measurements is
carried out by the sensors themselves. The impact of this memory effect on
concentration mapping is discussed in Section 3.3.
To overcome these problems, a mapping technique is introduced that inte-
grates many gas measurements over an extended period of time. Spatial inte-
gration of the point measurements is carried out by using a Gaussian weighting
function to extrapolate on the measurements, assuming a decreasing likelihood
that a given measurement represents the true concentration with respect to the
distance from the point of measurement. By integrating many measurements
along the path of the robot, the underlying structure of the gas distribution
can be separated from the transient variations due to turbulence. We show
also that it is possible under certain limited conditions to use the grid cell
with the maximum concentration value as an approximation to the location
of the gas source, particularly when the shape of the distribution is roughly
circular with a strong central peak.
In order to build complete concentration gridmaps, the path of the robot
should roughly cover the entire space, although perfectly uniform exploration
is not necessary. To increase spatial accuracy it is also advantageous to pass
particular points from multiple directions. The method assumes that the pose
of the mobile robot is known with high accuracy. In this paper, the location
estimates required for map building were obtained from the external, vision-
based absolute positioning system W-CAPS [16], which is briefly described
in Section 2. However, the results are expected to apply to any mobile robot
equipped with a suitably accurate positioning system, e.g., by carrying out
simultaneous localisation and mapping with other sensor systems [3].
3

The rest of this paper is structured as follows. After a brief review of related
work (Section 1.1), the experimental setup is described in Section 2. Next, the
algorithm for creating gas concentration gridmaps is introduced (Section 3)
and discussed in terms of parameter selection (Section 3.2) and its suitability
regarding the slow response and recovery of the gas sensors (Section 3.3).
Different data acquisition strategies arethendiscussedinSection4andan
experimental comparison of the different exploration strategies is given in
Section 5, followed by conclusions and suggestions for future work (Section 6).
1.1 Related Work
Most work on chemical sensing for mobile robots assumes an experimental
setup that reduces the influence of turbulent transport by either minimising
the source-to-sensor distance in trail following [26, 28, 27, 21] or assuming a
strong airstream in the environment [9, 25, 23, 7]. A strong airstream means
that additional information about the local wind speed and direction can be
obtained from an anemometer. Thus strategies become feasible that utilise the
instantaneous direction of flow as an estimate of the source direction [2] by
combining gas searching behaviours with periods of upwind movement. Under
the assumption of isotropic and homogeneous turbulence, and a unidirectional
wind field with a constant average wind speed, it is further possible to model
the time-averaged spread of gas [8]. The effect of turbulent air movement
can be described in this case with a diffusion-like behaviour. Under these
assumptions, the effect of turbulent air movement can be described with a
diffusion-like behaviour ruled by an additional diffusion coefficient. The avail-
able wind measuring devices, however, are limited in their applicable range.
With state-of-the-art anemometers based on the cooling of a heated wire [12],
the bending of an artificial whisker [24] or the influence on the speed of a small
rotating paddle [23], reliable readings can be obtained only for wind speeds in
the order of at least 10 cm/s.
To the best knowledge of the authors, there have been only a few sugges-
tions for creating spatial representations of gas distribution. A straightforward
method to create a representation of the time-averaged concentration field is
to measure the response over a prolonged time with a grid of gas sensors. This
technique has been used on various occasions by Ishida and co-workers. The
time-averaged gas sensor response over 5 minutes at 33 grid points distributed
over an area of 2 × 1m
2
was used in [11], for example, to characterise the
experimental environment. With an increasing area, however, establishing a
dense grid of gas sensors would involve an arbitrarily high number of fixed gas
sensors, which poses problems such as cost and a lack of flexibility. Further-
more, an array of metal oxide sensors would cause a severe disturbance to the
gas distribution due to the convective flow created by the heaters built into
these sensors [13].
4

Frequently asked questions

Q1. How can a gas source be traced?

Under the assumption of a concentration field that exhibits smooth gradients, thus neglecting the effects of turbulence, gas source tracing can be accomplished by reactive gradientfollowing. 

Q2. What have the authors contributed in "Building gas concentration gridmaps with a mobile robot" ?

This paper addresses the problem of mapping the structure of a gas distribution by creating concentration gridmaps from the data collected by a mobile robot equipped with gas sensors. To overcome this problem, a mapping technique is introduced that uses a Gaussian weighting function to model the decreasing likelihood that a particular reading represents the true concentration with respect to the distance from the point of measurement. 

Q3. What future works have the authors mentioned in the paper "Building gas concentration gridmaps with a mobile robot" ?

Future work could also include development of an actual source finding strategy based on the information about the peaks and plume-like structures extracted from these maps. 

Q4. What is the problem with using only binary information from the gas sensors?

In addition to the dependency of the gas distribution map on the selected threshold, the problem with using only binary information from the gas sensors is that much useful information about fine gradations in the average concentration is discarded. 

Q5. How many times did the robot pass each point in the vicinity of the gas source?

In the experiments where the robot followed a predefined path, it was found that the mapped distribution stabilised when the robot had passed each point in the vicinity of the gas source at least two times from opposite directions. 

Q6. When was the first use of gridmaps introduced to mobile robotics?

Gridmaps were originally introduced to mobile robotics in the 1980s as a means of creating maps using wide-angle measurements from ultrasonic range-finder sensors [4]. 

Q7. What are the drawbacks of metal oxide sensors?

Inconsequence of the measurement principle, metal oxide sensors exhibit some drawbacks, including low selectivity, comparatively high power consumption (caused by the heating device) and weak durability. 

Q8. How long did the time constants of rise and decay for the complete gas sensitive system (mobile?

The time constants of rise and decay for the complete gas sensitive system (mobile nose) used here were estimated as τr ≈ 1.8 s and τd ≈ 11.1 s respectively [15]. 

Q9. What is the way to model changing gas distributions?

It would also be possible to model changing gas distributions by aging the measurements instead of averaging, so that older measurements gradually lose their weight. 

Q10. What are the disadvantages of a dense grid of gas sensors?

With an increasing area, however, establishing a dense grid of gas sensors would involve an arbitrarily high number of fixed gas sensors, which poses problems such as cost and a lack of flexibility. 

Q11. How does the robot measure the distribution of gas in an environment?

In this experiment, the robot passed the source along a straight line at low speed in order to measure the distribution of the analyte accurately. 

Q12. How was the robot rotated at the corners?

a constant speed of 5 cm/s was applied along the straight lines and the robot was rotated with a speed of 10◦/s at the corners. 

Q13. How did the researchers measure the distance of the grid cell from the centre of the gas source?

In order to evaluate the stability of the mapped distribution, the authors measured the distance of the grid cell with the maximum concentration value from the centre of the gas source. 

Q14. What is the common type of gas sensor used on mobile robots?

this type of gas sensor is most often used on mobile robots because it is inexpensive, highly sensitive and relatively unaffected by changing environmental conditions such as room temperature and humidity. 

Q15. How can the results be applied to a mobile robot?

the results are expected to apply to any mobile robot equipped with a suitably accurate positioning system, e.g., by carrying out simultaneous localisation and mapping with other sensor systems [3]. 

Q16. What is the way to estimate the position of a gas source?

By comparing the location of the maximum concentration in the gridmap with the centre of the gas source, it was demonstrated that the location of the average maximum concentration can often be used to estimate the position of a source.