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In this paper we consider a probabilistic method for mapping a spatial process over a distributed multi-agent system and a coordinated level curve tracking algorithm for adaptive sampling. As opposed to assuming the independence of spatial features (e.g. an occupancy grid model), we adopt a novel model of spatial dependence based on the grid-structured Markov random field that exploits spatial structure to enhance mapping. The multi-agent Markov random field framework is utilized to distribute the model over the system and to decompose the problem of global inference into local belief propagation problems coupled with neighbor-wise inter-agent message passing. A Lyapunov stable control law for tracking level curves in the plane is derived and a method of gradient and Hessian estimation is presented for applying the control in a probabilistic map of the process. Simulation results over a real-world dataset with the goal of mapping a plume-like oceanographic process demonstrate the efficacy of the proposed algorithms. Scalability and complexity results suggest the feasibility of the approach in realistic multi-agent deployments.
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