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 spatial field. Specifically, our goal is to ensure that 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. In the mobile robot version, we seek to minimize the total time required to visit and collect measurements from the measurement locations. A multi-robot version is studied as well where the objective is to minimize the time required by the last robot to return back to a common starting location called depot. By exploiting the properties of Gaussian Process regression, we present constant-factor approximation algorithms that ensure the required guarantees. In addition to the theoretical results, we also compare the empirical performance using a real-world dataset with other baseline strategies.