Probabilistic Modeling of Gas Diffusion with Partial Differential Equations for Multi-Robot Exploration and Gas Source Localization

Employing automated robots for sampling gas distributions and for localizing gas sources is beneficial since it avoids hazards for a human operator. This paper addresses the problem of exploring a gas diffusion process using a multi-agent system consisting of several mobile sensing robots. The diffusion process is modeled using a partial differential equation (PDE). It is assumed that the diffusion process is driven by only a few spatial sources at unknown locations with unknown intensity. The goal of the multi-robot exploration is thus to identify source parameters, in particular, their number, locations and magnitudes. Therefore, this paper develops a probabilistic approach towards PDE identification under sparsity constraint using factor graphs and a message passing algorithm. Moreover, the message passing schemes permits efficient distributed implementation of the algorithm. This brings significant advantages with respect to scalability, computational complexity and robustness of the proposed exploration algorithm. Based on the derived probabilistic model, an exploration strategy to guide the mobile agents in real time to more informative sampling locations is proposed. Hardware-in-the-loop experiments with real mobile robots show that the proposed exploration approach accelerates the identification of the source parameters and outperforms systematic sampling