Physics-Based Gas Mapping with Nano Aerial Vehicles: The ADApprox Algorithm

Gas emissions play a crucial role in many environmental and industrial processes, driving a growing effort to understand their dispersion in air. Nonetheless, gas distribution mapping is inherently challenging due to the complex interplay between gas diffusion and wind flows. Mobile robots provide a compelling alternative to static sensor networks for gas sensing, having greater mobility and minimizing the need to permanently deploy assets in the environment. However, robotic platforms typically collect only sparse measurements due to constraints, such as limited battery life, and state-of-the-art methods often fail to accurately interpolate between scattered data. To address this limitation, we introduce ADApprox, a novel gas mapping algorithm. By leveraging the underlying physics which governs gas dispersion, ADAapprox offers superior interpolation capabilities. Our method locally approximates advection-diffusion equation for an entire grid of points and learns the model parameters from gas measurements. The learned parameters are subsequently used to predict gas concentrations across the entire environment. Extensive simulations and physical experiments are conducted using a nano aerial vehicle. The mapping results demonstrate that ADApprox consistently outperforms the stateof-the-art algorithm Kernel DM+V/W while having a comparable computational cost. In addition, we evaluate the effectiveness in localizing a gas source based on the predicted gas maps. Our findings indicate that ADApprox effectively localizes the gas source, achieving a median error of 18 cm on an area of 12 m 2 in physical experiments.