Robot-Motion-Uncertainty-Aware Informative Path Planning with Guaranteed Estimation Uncertainty

Environmental monitoring robots often need to estimate data fields (e.g., salinity, temperature, bathymetry) under tight resource constraints and operational uncertainty from localization error, actuation noise, and disturbances. Classical lawnmower surveys provide geometric coverage guarantees but can oversample predictable regions. Informative path planning (IPP) leverages spatial correlations to reduce such redundancy, but typically offers no estimation-quality guarantees, especially when robot motion is stochastic. This paper addresses motion-uncertainty-aware IPP with guaranteed estimation uncertainty in complex environments$:$ computing a shortest path whose measurements ensure that the Gaussian process (GP) posterior variance—an intrinsic uncertainty measure that lower-bounds the mean-squared prediction error \ka{under the GP model}—remains below a user-specified threshold over the monitoring region, even under execution noise.

We propose a three-stage approach$:$ (i) learning a GP model from prior information; (ii) transforming the GP kernel into binary coverage maps that identify where uncertainty can be reduced below the target threshold while accounting for deviations between planned and realized sensing locations; and (iii) planning a near-shortest route satisfying the global uncertainty constraint. Our approach supports non-stationary kernels for spatially varying correlations and non-convex environments with obstacles. We provide near-optimal approximation guarantees for selecting sensing locations and for the joint selection-and-routing problem, including guarantees that remain valid under stochastic robot motion. Experiments on real-world topographic data show that our planners meet uncertainty targets with fewer sensing locations and shorter travel distances than representative baselines. Field experiments with autonomous surface and underwater vehicles validate the practical feasibility of the approach.