Online Learning and Coverage of Unknown Fields Using Random-Feature Gaussian Processes

This paper proposes a framework for multi-robot systems to perform simultaneous learning and coverage of the domain of interest characterized by an unknown and potentially time-varying density function. To overcome the limitations of Gaussian Process (GP) regression, we employ Random Feature GP (RFGP) and its online variant (O-RFGP) that enables online and incremental inference. By integrating these with Voronoi-based coverage control and Upper Confidence Bound (UCB) sampling strategy, a team of robots can adaptively focus on important regions while refining the learned spatial field for efficient coverage. Under mild assumptions, we provide theoretical guarantees and evaluate the framework through simulations in time-invariant scenarios. Furthermore, its effectiveness in time-varying settings is demonstrated through additional simulations and a physical experiment.