Learning a Spatial Field in Minimum Time with a Team of Robots
This addresses efficient data collection for spatial monitoring tasks, such as environmental sensing, but is incremental as it builds on existing GP and path-planning methods.
The paper tackles the problem of minimizing the time for a team of robots to learn a spatial field using Gaussian Process regression, by developing constant-factor approximation algorithms for placement, single-robot, and multi-robot versions, and shows empirical improvements over baselines on a real-world dataset.
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.