Robotic Gas Source Localization with Probabilistic Mapping and Online Dispersion Simulation

TL;DR

Results from both simulated and real experiments show the capabilities of the current proposal to deal with source localization in complex indoor environments, and the concept of probabilistic gas-hit maps, which provide a higher level of abstraction to model the time-dependent nature of gas dispersion.

Abstract

Gas source localization (GSL) with an autonomous robot is a problem with many prospective applications, from finding pipe leaks to emergency-response scenarios. In this work, we present a new method to perform GSL in realistic indoor environments, featuring obstacles and turbulent flow. Given the highly complex relationship between the source position and the measurements available to the robot (the single-point gas concentration, and the wind vector) we propose an observation model that derives from contrasting the online, real-time simulation of the gas dispersion from any candidate source localization against a gas concentration map built from sensor readings. To account for a convenient and grounded integration of both into a probabilistic estimation framework, we introduce the concept of probabilistic gas-hit maps, which provide a higher level of abstraction to model the time-dependent nature of gas dispersion. Results from both simulated and real experiments show the capabilities of our current proposal to deal with source localization in complex indoor environments.

Figures (13)

• Figure 1: Pipeline of the proposed GSL method. We propose an observation model based on the comparison of the hit-map derived from sensor measurements and those predicted by a dispersion model.
• Figure 2: (A) Gas-hit probability map built from e-nose measurements. The color scale goes from blue (lowest) to red (highest). (B) Gas-hit maps predicted by the dispersion model for two candidate source positions (marked in the images with a black dot). (C) Probability distribution of the source location, estimated by comparing A and B.
• Figure 3: (A) The influence of a measurement ($\lambda_i$) over the probability of $H_i$ is calculated by sampling a 2D gaussian kernel of initial $\sigma = \sigma_0$, centered on the measurement location, that is stretched and rotated by the wind vector. The values of $a$ and $b$ are calculated using the method outlined in kerneldm. (B) One-dimensional simplification of the relation between $\lambda_{ik}$ and $P(H_i | z_k)$, as described by Equation \ref{['eq:conditional_h']}.
• Figure 4: The vector $\hat{v}_n$ used in Eq. \ref{['eq:lamda_obs']} is the direction from the considered cell $i$ to the cell $n \in N$ that is part to the shortest path between $i$ and $k$. $\delta_{ik}$ is the total length of said path.
• Figure 5: Effect of modifying the fraction of cells that are subdivided on each coarse-to-fine step ($\rho$). (A) Computation time for updating the source probability distribution. (B) Kullback-Leibler divergence of the resulting source location probability distribution with respect to the distribution predicted by considering all the cells.