Multi-Robot Coordination for Estimation and Coverage of Unknown Spatial Fields

We present an algorithm for multi-robot coverage of an initially unknown spatial scalar field characterized by a density function, whereby a team of robots simultaneously estimates and optimizes its coverage of the density function over the domain. The proposed algorithm borrows powerful concepts from Bayesian Optimization with Gaussian Processes that, when combined with control laws to achieve centroidal Voronoi tessellation, give rise to an adaptive sequential sampling method to explore and cover the domain. The crux of the approach is to apply a control law using a surrogate function of the true density function, which is then successively refined as robots gather more samples for estimation. The performance of the algorithm is justified theoretically under slightly idealized assumptions, by demonstrating asymptotic no-regret with respect to the coverage obtained with a known density function. The performance is also evaluated in simulation and on the Robotarium with small teams of robots, confirming the good performance suggested by the theoretical analysis.