Multi-robots Gaussian estimation and coverage control: From client-server to peer-to-peer architectures

In this work we study the problem of multi-robot coverage of a planar region when the sensory field used to approximate the density of event appearance is not known in advance. We address the problem by considering two different communication architectures: client-server and peer-to-peer. In the first architecture the robots are allowed to communicate with a central server/base station. In the second the robots communicate among neighboring peers by means of a gossip protocol in a distributed fashion. For both the architectures, we resort to nonparametric Gaussian regression approach to estimate the unknown sensory field of interest from a collection of noisy samples. We propose a probabilistic control strategy based on the posterior of the estimation error variance, which lets the robots to estimate the true sensory field with any arbitrary accuracy while simultaneously computing and exploiting the corresponding centroidal Voronoi partitions. We also present a numerically efficient approximation based on a spatial discretization to trade-off the accuracy of the estimated map against the required computational complexity. This trade-off can be tuned based on explicit estimation error bounds which depend on the spatial resolution and the Gaussian kernel parameters. Finally, we test the proposed solutions via extensive numerical simulations.