Probabilistic Air Flow Modelling Using Turbulent and Laminar Characteristics for Ground and Aerial Robots

For mobile robots that operate in complex, uncontrolled environments, estimating air flow models can be of great importance. Aerial robots use air flow models to plan optimal navigation paths and to avoid turbulence-ridden areas. Search and rescue platforms use air flow models to infer the location of gas leaks. Environmental monitoring robots enrich pollution distribution maps by integrating the information conveyed by an air flow model. In this paper, we present an air flow modelling algorithm that uses wind data collected at a sparse number of locations to estimate joint probability distributions over wind speed and direction at given query locations. The algorithm uses a novel extrapolation approach that models the air flow as a linear combination of laminar and turbulent components. We evaluated the prediction capabilities of our algorithm with data collected with an aerial robot during several exploration runs. The results show that our algorithm has a high degree of stability with respect to parameter selection while outperforming conventional extrapolation approaches. In addition, we applied our proposed approach in an industrial application, where the characterization of a ventilation system is supported by a ground mobile robot. We compared multiple air flow maps recorded over several months by estimating stability maps using the Kullback-Leibler divergence between the distributions. The results show that, despite local differences, similar air flow patterns prevail over time. Moreover, we corroborated the validity of our results with knowledge from human experts.