Title: Persistent Monitoring of Stochastic Spatio-temporal Phenomena with a Small Team of Robots,
Abstract: 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.