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Multi-agent exploration of spatial dynamical processes under sparsity constraints

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Abstract

This paper addresses the development of an efficient information gathering and exploration strategy for robotic missions when a high level of autonomy is expected. A multi-agent system is considered, which consists of several mobile sensing platforms with the goal to identify the parameters of a spatio-temporal process modeled by a partial differential equation. Specifically, an exploration of a diffusion process driven by an unknown number of sparsely located sources is considered. A probabilistic approach toward partial differential equations and sparsity constraints modeling with factor graphs is developed and realized by a customized message passing algorithm. The algorithm permits efficient identification of source parameters: the number of sources, their locations and amplitudes. In addition, an exploration strategy to guide the agents to more informative sampling locations is proposed; this accelerates identification of the source parameters. The message passing implementation facilitates efficient distributed implementation, which is of significant advantage with respect to scalability, computational complexity and an implementation in a multi-agent system. The effectiveness of the algorithm is demonstrated using synthetic data in simulations.

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Notes

  1. Note that this is true provided that \( \varvec{M} [n]\) is a selection matrix, i.e., when \(y_c[n]\) is a noisy version of \(f_c[n]\).

  2. Note that \(\tau _c>0\)

  3. Recall that the message \(m_{G_c \rightarrow u_c[n]}\) is responsible for this prior.

  4. Rectangular domains can be considered just as easily.

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Authors and Affiliations

  1. Institute of Communications and Navigation of the German Aerospace Center (DLR), 82234, Oberpfaffenhofen, Wessling, Germany

    Thomas Wiedemann, Christoph Manss & Dmitriy Shutin

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  1. Thomas Wiedemann
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  2. Christoph Manss
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Correspondence to Thomas Wiedemann.

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Wiedemann, T., Manss, C. & Shutin, D. Multi-agent exploration of spatial dynamical processes under sparsity constraints. Auton Agent Multi-Agent Syst 32, 134–162 (2018). https://doi.org/10.1007/s10458-017-9375-7

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