Multi-agent mapping is a fundamentally important capability for autonomous robot task coordination and execution in complex environments. While successful algorithms have been proposed for mapping using individual platforms, cooperative online mapping for teams of robots remains largely a challenge. We focus on probabilistic variants of mapping due to its potential utility in downstream tasks such as uncertainty-aware path-planning. A critical question to enabling this capability is how to process and aggregate incrementally observed local information among individual platforms, especially when their ability to communicate is intermittent. We put forth an Incremental Sparse Gaussian Process (GP) methodology for multi-robot mapping, where the regression is over a truncated signed-distance field (TSDF). Doing so permits each robot in the network to track a local estimate of a pseudo-point approximation GP posterior and perform weighted averaging of its parameters with those of its (possibly time-varying) set of neighbors. We establish conditions on the pseudo-point representation, as well as communication protocol, such that robots' local GPs converge to the one with globally aggregated information. We further provide experiments that corroborate our theoretical findings for probabilistic multi-robot mapping.
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