Learning a Spatial Field in Minimum Time with a Team of Robots

We study an informative path-planning problem where the goal is to minimize the time required to learn a spatially varying entity. We use Gaussian Process (GP) regression for learning the underlying field. Our goal is to ensure that the GP posterior variance, which is also the mean square error between the learned and actual fields, is below a predefined value. We study three versions of the problem. In the placement version, the objective is to minimize the number of measurement locations while ensuring that the posterior variance is below a predefined threshold. In the mobile robot version, we seek to minimize the total time required to visit and collect measurements from the measurement locations using a single robot. We also study a multi-robot version where the objective is to minimize the time required by the last robot to return to a common starting location called depot. By exploiting the properties of GP regression, we present constant-factor approximation algorithms. In addition to the theoretical results, we also compare the empirical performance using a real-world dataset, with other baseline strategies.