[Paper Review] Informative Path Planning to Estimate Quantiles for Environmental Analysis

Isabel M. Rayas Fernández, Christopher E. Denniston+2 more|arXiv (Cornell University)|Jan 25, 2022

Species Distribution and Climate Change4 citations

TL;DR

This paper proposes an adaptive robotic path planning framework that uses novel objective functions—quantile change and quantile standard error—to improve estimation of environmental quantiles (e.g., deciles of chlorophyll or plant health). It then employs a cross-entropy loss function to select optimal physical specimen collection locations. The method reduces median error by 10.2% compared to entropy-based baselines and 15.7% compared to best-visited point baselines in real-world trials.

ABSTRACT

Scientists interested in studying natural phenomena often take physical specimens from locations in the environment for later analysis. These analysis locations are typically specified by expert heuristics. Instead, we propose to choose locations for scientific analysis by using a robot to perform an informative path planning survey. The survey results in a list of locations that correspond to the quantile values of the phenomenon of interest. We develop a robot planner using novel objective functions to improve the estimates of the quantile values over time and an approach to find locations which correspond to the quantile values. We test our approach in four different environments using previously collected aquatic data and validate it in a field trial. Our proposed approach to estimate quantiles has a 10.2% mean reduction in median error when compared to a baseline approach which attempts to maximize spatial coverage. Additionally, when localizing these values in the environment, we see a 15.7% mean reduction in median error when using cross-entropy with our loss function compared to a baseline.

Motivation & Objective

• To address the limitation of heuristic-based specimen collection in environmental science, where expert rules often lead to suboptimal spatial sampling.
• To improve the accuracy of quantile estimation (e.g., deciles, upper quantiles) in environmental phenomena such as chlorophyll concentration or plant health.
• To develop a robot-planning pipeline that adaptively selects measurement locations to refine quantile estimates over time.
• To identify physically realizable specimen collection locations that correspond to estimated quantile values in the environment.
• To validate the method in simulated and real-world settings, including drone and AUV deployments.

Proposed method

• The method uses a Gaussian Process (GP) to model spatial distributions of environmental variables from robot-sensed data.
• It introduces two novel objective functions—quantile change and quantile standard error—for informative path planning to iteratively improve quantile estimates.
• The quantile standard error objective function minimizes uncertainty in the estimated quantile values across the spatial field.
• A separate differentiable loss function is proposed to map estimated quantile values to physical locations, enabling optimization over candidate sites.
• The loss function is used with black-box optimizers like cross-entropy to select specimen collection points that best match the estimated quantile values.
• The system is evaluated using point sensors (chlorophyll) and camera sensors (crop health), with real-world field trials on drones and AUVs.

Experimental results

Research questions

• RQ1 Can informative path planning with quantile-specific objective functions improve the accuracy of environmental quantile estimation compared to traditional spatial coverage or entropy-based methods?
• RQ2 How well can a robot-planned survey estimate quantiles such as deciles or upper tail values (e.g., 0.90, 0.95, 0.99) in real environmental fields?
• RQ3 Can a differentiable loss function effectively map estimated quantile values to physically realizable specimen collection locations in complex environments?
• RQ4 Does the use of cross-entropy optimization with the proposed loss function outperform baselines like selecting the best-visited measurement points?
• RQ5 How does the method scale across different sensor modalities (point sensors vs. imaging) and real-world deployment constraints?

Key findings

• The proposed quantile standard error objective function reduced median error by 10.2% compared to the entropy-based baseline in quantile estimation across all test environments.
• The cross-entropy optimizer using the proposed loss function achieved a 15.7% mean reduction in median error when selecting specimen collection locations compared to the baseline of selecting the best-visited measurement points.
• In field trials with a drone over a grassy field, the system successfully identified diverse specimen collection locations corresponding to deciles of greenness, even when the robot did not visit the most visually distinct areas.
• The method demonstrated robustness across different sensor types, including point sensors (chlorophyll) and imaging sensors (crop health), with consistent performance gains.
• The system outperformed Bayesian optimization and information-theoretic baselines in both estimation accuracy and location selection fidelity.
• The approach enables scalable, adaptive, and scientifically meaningful specimen collection planning in real-world environmental monitoring tasks.