Intelligent Systems for Machine Olfaction: Tools and Methodologies

The method presented in this chapter computes an estimate of the location of a single gas source from a set of localized gas sensor measurements. The estimation process consists of three steps. First, a statistical model of the time-averaged gas distribution is estimated in the form of a two-dimensional grid map. In order to compute the gas distribution grid map the Kernel DM algorithm is applied, which carries out spatial integration by convolving localized sensor readings and modeling the information content of the point measurements with a Gaussian kernel. The statistical gas distribution grid map averages out the transitory effects of turbulence and converges to a representation of the time-averaged spatial distribution of a target gas. The second step is to learn the parameters of an analytical model of average gas distribution. Learning is achieved by nonlinear least squares fitting of the 250 Improved Gas Source Localization with a Mobile Robot Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. INTRODUCTION A major problem for gas source localization in a natural environment is the strong influence of turbulence on the dispersal of gas. Typically, turbulent transport is considerably faster compared to molecular diffusion (Nakamoto et al., 1999; Roberts and Webster, 2002). Apart from very small distances where turbulence is not effective, molecular diffusion can thus be neglected concerning the spread of gas. A second important transport mechanism for gases is advective transport due to prevailing fluid flow. Relatively constant air currents are typically found even in an indoor environment without ventilation (Wandel et al., 2003) as a result of pressure (draught) and temperature inhomogeneities (convection flow). Turbulent flow comprises at any instant a high degree of vortical motion, which creates packets of gas that follow chaotic trajectories (Shraiman and Siggia, 2000). This results in a concentration field, which consists of fluctuating, intermittent patches of high concentration. The instantaneous concentration field does not exhibit smooth concentration gradients that indicate the direction toward the centre of a gas source (Lilienthal and Duckett, 2004b; Russell, 1999). Figure 1 illustrates actual gas concentration measurements recorded with a mobile robot along a corridor containing a single gas source. It is important to note that the noise is dominated by the large fluctuations of the instantaneous gas distribution and not by the electronic noise of the gas sensors. Turbulence is chaotic in the sense that the instantaneous flow velocity at some instant of time is insufficient to predict the velocity a short time later. Consequently, a snapshot of the distribution of a target gas at a given instant contains little information about the distribution at another time. However, under certain assumptions (e.g. that the air flow is uniform and steady) the time-averaged concentration field varies smoothly in space with moderate concentration gradients (Roberts and Webster, 2002). analytical model to the statistical gas distribution map using Evolution Strategies (ES), which are a special type of Evolutionary Algorithm (EA). This step provides an analysis of the statistical gas distribution map regarding the airflow conditions and an alternative estimate of the gas source location, i.e. the location predicted by the analytical model in addition to the location of the maximum in the statistical gas distribution map. In the third step, an improved estimate of the gas source position can then be derived by considering the maximum in the statistical gas distribution map, the best fit, as well as the corresponding fitness value. Different methods to select the most truthful estimate are introduced, and a comparison regarding their accuracy is presented, based on a total of 34 hours of gas distribution mapping experiments with a mobile robot. This chapter is an extended version of the conference paper (Lilienthal et al., 2005). Improved Gas Source Localization with a Mobile Robot 251 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. It is often desirable to know the spatial structure of the time-averaged gas distribution. The Kernel Distribution Mapping (Kernel DM) algorithm was introduced by Lilienthal and Duckett (Lilienthal and Duckett, 2003b) to compute a grid map representation of the structure of the time-averaged gas distribution. The input to the Kernel DM algorithm is a set of localized gas sensor readings. In this chapter we consider the case that the readings were collected by a mobile robot. The algorithm is summarized in Section ”The Kernel DM Algorithm”. In itself, gas distribution mapping is useful for any application that requires estimating the average distribution of a certain gas in a particular area of the environment. For example, mobile robots that are able to build such a map can be used for pollution monitoring (DustBot Consortium, 2006), they could indicate contaminated areas in a rescue mission, or could be used in Precision Farming (Blackmore & Griepentrog, 2002) to provide a non-intrusive way of assessing certain soil parameters or the status of plant growth to enable a more efficient usage of fertilizer. In this chapter, which is an extended version of a paper by the authors (Lilienthal et al., 2005), we describe a method to use statistical gas distribution grid maps in order to locate a gas source. An obvious clue for the gas source position is the maximum in the map. Experiments in an indoor environment indeed demonstrated that the concentration maximum estimate (CME)1 provides a satisfying approximation of the source location in many cases (Lilienthal & Duckett, 2004a). Under certain assumptions discussed in Sec. “Analytic Gas Distribution Model”, the spread of a gas that evaporates from a stationary source can be approximated as a Fickian diffusion process. Instead of the small diffusion constant that describes molecular diffusion the turbulent diffusion is ruled by a substantially larger turbulent diffusion constant K (eddy diffusivity). In the event of negligible advective transport due to a weak air current, the resulting average gas distribution takes a circular shape. In such cases, it was observed that the distance between the CME and the true source Figure 1. Normalized raw response readings from an example trial 252 Improved Gas Source Localization with a Mobile Robot Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. location was small. By contrast, the localization capability of the CME was found to be considerably degraded when the concentration map showed a stretched out distribution due to a dominant wind direction. According to the equations, which describe the time-averaged stationary gas distribution analytically (see Sec. “Analytic Gas Distribution Model”), the concentration decreases slowly along the direction of a constant air current. Thus, even small distortions due to rudiments of turbulent concentration peaks can cause a large displacement of the point of maximum concentration. Also the localization error introduced by the fact that gas sensor measurements are acquired not exactly level with the gas source is more pronounced in the case of stronger air current. A method that formalizes this qualitative argument is presented in Sec. “Step 3 – Selection of Source Location Estimate”. The method allows distinguishing situations, where the CME is a reliable approximation of the source location from situations where the CME is unlikely to indicate the gas source position accurately. This is accomplished by comparing how well the statistical gas distribution map can be approximated by the analytical model (detailed in Sec. “Analytic Gas Distribution Model”), which describes the time-averaged gas distribution under certain idealized assumptions. Apart from providing a measure of the reliability of the CME, the introduced method allows to derive an alternative estimate of the gas source position, which can be used in situations where the CME fails. To determine the analytical model, which approximates the given statistical gas distribution map most closely, the parameter set is optimized by means of nonlinear least squares fitting. Since the model parameters include the position of the gas source, the best fit naturally corresponds to an estimate of the source position. In contrast to the CME, the best fit estimate (BFE) is derived from the whole distribution represented in the statistical gas distribution grid map. The rest of this chapter is structured as follows. First, the Kernel DM algorithm to compute statistical gas distribution grid maps is described in Sec. “Step 1 Computation of a Statistical Gas Distribution Model”. Second, the adapted physical model that was used to approximate the time-averaged gas concentration is introduced in Sec. “Analytic Gas Distribution Model”. Then, the evolutionary strategy method to learn the optimal model parameters is detailed in Sec. “Step 2 – Learning Parameters of the Analytical Model”. Next, reasons that cause deviations between the physical model and the statistical gas distribution grid map are discussed in Sec. “Sources of Inaccuracy” and two strategies to select the best estimate of the gas source location are presented in Sec. “Step 3 – Selection of Source Location Estimate”. Finally details of the experimental setup are given in Sec. “Experimental Setup” and results are presented in Sec. “Results”, followed by conclusions and suggestions for future work in the final Section “Conclusions and Outlook”. Improved Gas Source Localization with a Mobile Robot 253 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. STEP 1: COMPUTATION OF A STATISTICAL GAS DISTRIBUTION MODEL Creating Gas Distribution Grid Maps By contrast to metric grid maps extracted from sonar or laser range scans, a single measurement from a gas sensor represents the measured quantity (in the case of metal oxide sensors: the rate of redox reactions) only at the comparatively small area of the sensor’s surface, typically around 1 cm2. Nevertheless, the gas sensor readings contain information about the time-averaged gas distribution of a larger area. First, this is due to the smoothness of the time-averaged gas distribution, which allows extrapolating on the averaged gas sensor measurements because the average concentration field does not change drastically in the vicinity of the point of measurement. Second, the metal-oxide gas sensors perform temporal integration of successive readings implicitly due to their slow response and long recovery time. Modeled as a first-order sensor, the time constants of rise and decay for the complete gas sensitive system used here were estimated as τr ≈ 1.8s and τd ≈ 11.1s, respectively (Lilienthal & Duckett, 2003a). Thus the measurements contain information that is spatially integrated along the path driven by the robot. The Kernel DM Algorithm Based on the observations mentioned in Sec. “Creating Gas Distribution Grid Maps”, the Kernel DM algorithm introduced in (Lilienthal & Duckett, 2004a) uses a Gaussian kernel function to model the decreasing likelihood that a particular reading represents the true quantity (here: the time-averaged relative concentration) with respect to the distance from the point of measurement. For each measurement, two quantities are calculated for grid cells k: an importance weight and a weighted reading. In practice, only those cells in the vicinity of the point of measurement need to be considered, i.e. the cells for which the corresponding centre x(k) lies within a certain radius around the point xt where the measurement was taken at time t. Cells that are further away from the measurement can be ignored since the effect of the update is negligible. The importance weight is calculated by evaluating the twodimensional, uni-variate Gaussian function