Informative Path Planning with Guaranteed Estimation Uncertainty

TL;DR

This work tackles environmental field monitoring under limited resources by providing IPP methods that guarantee reconstruction quality via a bound on the GP posterior variance, $J_{\max}(\mathcal{P}) \le \sigma_{\mathrm{tar}}^2$. It fits a GP to prior information, converts the kernel into binary per-location coverage maps, and proposes two planning algorithms—GreedyCover and GCBCover—that respectively optimize sensing location selection and joint sensing-and-routing under a travel budget. The approach supports non-stationary correlations and non-convex environments with obstacles, and offers near-optimal approximation guarantees for both sensing placement and routing. Empirical results on real-world SRTM data and field trials with ASV/AUV platforms show reductions in the number of sensing locations and travel distance while meeting the uncertainty target, validating practical feasibility and impact for autonomous environmental monitoring.

Abstract

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.

Figures (11)

• Figure 1: Monitoring solution paths (red) and the resulting spatial distribution of prediction uncertainty (heatmap). All methods achieve the same mean GP posterior prediction variance: 0.02. The proposed GreedyCover yields the shortest path while providing a guarantee that uncertainty remains below the target at all evaluation locations.
• Figure 2: An autonomous surface vehicle (ASV) and an autonomous underwater vehicle (AUV) mapping bathymetry during our field trials.
• Figure 3: Coverage maps for two candidate sensing locations under a non-stationary kernel. Each dotted white blob indicates the set of evaluation locations for which that candidate location can guarantee the target posterior-variance threshold.
• Figure 4: Left: SRTM ground truth data from $47^\circ\mathrm{N},\,124^\circ\mathrm{W}$. Right: Lengthscales from a non-stationary kernel.
• Figure 5: Benchmark results on SRTM at $47^\circ\mathrm{N},\,124^\circ\mathrm{W}$. Top row: resulting maximum posterior variance, MSE, and SMSE. Bottom row: runtime, number of selected sensing locations, and total path length. GreedyCover and GCBCover achieve the target uncertainty with fewer waypoints and shorter paths than HexCover, while distance-budgeted GCBCover trades variance reduction to satisfy the travel distance budget.

Theorems & Definitions (8)

• Theorem 1: Minimum Required Prior Covariance
• Theorem 2: Variance Reduction with Multiple Locations
• Theorem 1: Minimum Required Prior Covariance
• proof
• Theorem 2: Variance Reduction with Multiple Locations
• proof
• Theorem 3: Nemhauser et al., 1978 NemhauserWF78
• Theorem 4: Zhang and Vorobeychik, 2016 ZhangV16