Distributed Gaussian Process Mapping for Robot Teams with Time-varying Communication

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.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 employ truncated signed-distance field (TSDF) as the map representation, and propose an Incremental Sparse Gaussian Process (GP) methodology to regress over TSDF for multi-robot mapping. Doing so permits each robot in the network to track a local estimate of an approximated GP posterior and perform weighted averaging of its parameters with its (possibly time-varying) set of neighbors. We focus on probabilistic variants of mapping due to its potential utility in down-stream tasks such as uncertainty-aware path-planning. We establish conditions on the GP representation, as well as communications 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.