Environmental monitoring robots often need to reconstruct spatial fields (e.g., salinity, temperature, bathymetry) under tight distance and energy constraints. Classical boustrophedon lawnmower surveys provide geometric coverage guarantees but can waste effort by oversampling predictable regions. In contrast, informative path planning (IPP) methods leverage spatial correlations to reduce oversampling, yet typically offer no guarantees on reconstruction quality. This paper bridges these approaches by addressing informative path planning with guaranteed estimation uncertainty: computing the shortest path whose measurements ensure that the Gaussian-process (GP) posterior variance -- an intrinsic uncertainty measure that lower-bounds the mean-squared prediction error under the GP model -- falls below a user-specified threshold over the monitoring region. We propose a three-stage approach: (i) learn a GP model from available prior information; (ii) transform the learned GP kernel into binary coverage maps for each candidate sensing location, indicating which locations' uncertainty can be reduced below a specified target; and (iii) plan a near-shortest route whose combined coverage satisfies the global uncertainty constraint. To address heterogeneous phenomena, we incorporate a nonstationary kernel that captures spatially varying correlation structure, and we accommodate non-convex environments with obstacles. Algorithmically, we present methods with provable approximation guarantees for sensing-location selection and for the joint selection-and-routing problem under a travel budget. Experiments on real-world topographic data show that our planners meet the uncertainty target using fewer sensing locations and shorter travel distances than a recent baseline, and field experiments with bathymetry-mapping autonomous surface and underwater vehicles demonstrate real-world feasibility.

翻译：环境监测机器人通常需要在严格的航程与能量约束下重建空间场（如盐度、温度、水深地形）。经典的往复式割草机式扫描可提供几何覆盖保证，但可能因对可预测区域过度采样而浪费资源。相比之下，信息路径规划方法利用空间相关性来减少过采样，但通常无法保证重建质量。本文通过研究具有保证估计不确定性的信息路径规划来弥合这两种方法：计算最短路径，使得其测量值能确保高斯过程后验方差——一种在高斯过程模型下均方预测误差下界的内在不确定性度量——在整个监测区域内低于用户指定的阈值。我们提出一种三阶段方法：（i）从可用先验信息中学习高斯过程模型；（ii）将学习到的高斯过程核函数转换为每个候选传感位置的二值覆盖图，标示哪些位置的不确定性可降低至指定目标以下；（iii）规划一条近似最短路径，其综合覆盖满足全局不确定性约束。为处理非均匀现象，我们引入了能捕捉空间变化相关结构的非平稳核函数，并适应带障碍物的非凸环境。在算法层面，我们提出了在传感位置选择问题以及旅行预算下的联合选择与路径规划问题上具有可证明近似保证的方法。在真实地形数据上的实验表明，相较于近期基线方法，我们的规划器能以更少的传感位置和更短的行驶距离达到不确定性目标；通过用于水深测绘的自主水面和水下机器人进行的实地实验验证了其实用可行性。