Building gas concentration gridmaps with a mobile robot

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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 comparatively 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 suitability 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.

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. 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 mapping 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.

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 convection 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 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 distribution 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 provides 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 τr ≈ 1.8 s and τd ≈ 11.1 s respectively [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 integrates many gas measurements over an extended period of time. Spatial integration 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].

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 are then discussed in Section 4 and an experimental comparison of the different exploration strategies is given in Section 5, followed by conclusions and suggestions for future work (Section 6).

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 available 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 suggestions 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 min at 33 grid points distributed over an area of 2 m × 1 m was used in Ref. [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. Furthermore, 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].

Gas measurements acquired with a mobile robot were used by Hayes et al. to create a representation of the gas distribution by means of a two-dimensional histogram [7]. The histogram bins contained the number of “odour hits” received in the corresponding area while a random walk behaviour was performed. “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. It would also take a very long time to obtain statistically reliable results, and there is no extrapolation on the measurements apart from the quantisation into the histogram bins. So it is doubtful whether this approach would scale well to larger environments. A further disadvantage of this method is that it requires perfectly even coverage of the inspected area by the mobile robot.

Section snippets

Robot and gas sensors

The experiments were performed with a Koala mobile robot equipped with the Mark III mobile nose [15], comprising six tin oxide sensors manufactured by Figaro (see Fig. 2). This type of chemical sensor shows a decreasing resistance in the presence of reducing volatile chemicals in the surrounding air. 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

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. Gas sensor readings represent only the concentration at the very small area of the sensor’s surface (≈1 cm2). Nevertheless these readings contain information about a larger area, for two reasons. First, despite the jagged, fluctuating nature of gas distribution [18],

Data acquisition strategy

This section describes the different exploration strategies used by the mobile robot to collect the sensor data for concentration mapping in our experiments.

The actual trajectory along which the sensor readings were recorded is expected to have a minor influence on the resulting concentration map. While uniform exploration is not necessary, it is required that the trajectory roughly covers the available space. In order to obtain better accuracy, it is further advantageous to pass particular

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 h of experiments and more than 5 km of travel.

Due to the local character of single gas sensor measurements, it takes some time to build concentration gridmaps. In addition to spatial coverage, a certain amount of temporal averaging is also necessary in order to represent the time-constant structure of the gas distribution. Some examples showing the

Conclusions and future work

This paper presents a new technique for modelling gas distributions by constructing concentration gridmaps with a mobile robot. The method is discussed in terms of its suitability regarding the slow response and recovery of the sensors. Results of almost 70 h of mapping experiments with three different exploration strategies are presented and analysed with respect to the time needed to represent the time-invariant structures of the gas distribution. This was achieved more quickly with reactive

Achim Lilienthal is a Ph.D. student at the WSI Computer Science Department, Tübingen University, Germany. He received his diploma in cluster physics from the University of Konstanz where he worked on the investigation of the structure of (C60)n+ clusters using gas phase ion chromatography. Recently he submitted his Ph.D. thesis in computer science, which is concerned with gas distribution mapping and gas source localisation with a mobile robot. His research interests include gas sensing, mobile

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    Achim Lilienthal is a Ph.D. student at the WSI Computer Science Department, Tübingen University, Germany. He received his diploma in cluster physics from the University of Konstanz where he worked on the investigation of the structure of (C60)n+ clusters using gas phase ion chromatography. Recently he submitted his Ph.D. thesis in computer science, which is concerned with gas distribution mapping and gas source localisation with a mobile robot. His research interests include gas sensing, mobile robots, ethological models, machine learning, biologically inspired control strategies, and human–robot communication.

    Tom Duckett is a docent (associate professor) at the Department of Technology, Örebro University, Sweden. He is leader of the Learning Systems Laboratory, one of four research laboratories within the Centre for Applied Autonomous Sensor Systems, Department of Technology, Örebro University. He obtained his Ph.D. from Manchester University, M.Sc. from Heriot-Watt University and B.Sc. (Hons.) from Warwick University, and has also studied at Karlsruhe and Bremen Universities. His research interests include autonomous robots, machine learning and neural networks, artificial intelligence, navigation systems, and biologically inspired sensor systems.

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