  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.
