In this article, 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 multirobot 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.

中文翻译：

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与机器人团队一起在最短的时间内学习空间领域

在本文中，我们研究了一个信息丰富的路径规划问题，其目标是最小化学习空间变化实体所需的时间。我们使用高斯过程 (GP) 回归来学习基础领域。我们的目标是确保 GP 后验方差（也是学习和实际字段之间的均方误差）低于预定义值。我们研究了这个问题的三个版本。在放置版本中，目标是最小化测量位置的数量，同时确保后验方差低于预定义的阈值。在移动机器人版本中，我们力求使用单个机器人最大限度地减少访问和从测量位置收集测量值所需的总时间。我们还研究了一个多机器人版本，其目标是最小化最后一个机器人返回到称为仓库的公共起始位置所需的时间。通过利用 GP 回归的特性，我们提出了常数因子近似算法。除了理论结果之外，我们还使用真实世界的数据集将经验性能与其他基线策略进行了比较。