Persistent Monitoring of Stochastic Spatio-temporal Phenomena with a Small Team of Robots

This paper presents a solution for persistent monitoring of real-world stochastic phenomena, where the underlying covariance structure changes sharply across time, using a small number of mobile robot sensors. We propose an adaptive solution for the problem where stochastic real-world dynamics are modeled as a Gaussian Process (GP). The belief on the underlying covariance structure is learned from recently observed dynamics as a Gaussian Mixture (GM) in the low-dimensional hyper-parameters space of the GP and adapted across time using Sequential Monte Carlo methods. Each robot samples a belief point from the GM and locally optimizes a set of informative regions by greedy maximization of the submodular entropy function. The key contributions of this paper are threefold: adapting the belief on the covariance using Markov Chain Monte Carlo (MCMC) sampling such that particles survive even under sharp covariance changes across time; exploiting the belief to transform the problem of entropy maximization into a decentralized one; and developing an approximation algorithm to maximize entropy on a set of informative regions in the continuous space. We illustrate the application of the proposed solution through extensive simulations using an artificial dataset and multiple real datasets from fixed sensor deployments, and compare it to three competing state-of-the-art approaches.