Inverse Resistive Force Theory (I-RFT): Learning granular properties through robot-terrain physical interactions

2026-03-08

AI Summary

This work addresses the challenge of real-time terrain property estimation for legged robots operating on soft granular media, where existing approaches often rely on prescribed foot trajectories and struggle to accommodate natural gaits. The authors propose a novel inverse modeling framework that integrates Granular Resistive Force Theory with Gaussian process regression, embedding physical principles directly into the learning process. By leveraging only proprioceptive contact forces collected under arbitrary gait patterns, the method enables accurate inference of granular medium properties while preserving physical consistency and data efficiency. Demonstrated across diverse gaits and foot geometries, the approach also quantifies predictive uncertainty, which informs both foot design and information-efficient gait optimization. This capability highlights its potential for autonomous terrain exploration in unstructured environments.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

For robots to navigate safely and efficiently on soft, granular terrains, it is crucial to gather information about the terrain's mechanical properties, which directly affect locomotion performance. Recent research has developed robotic legs that can accurately sense ground reaction forces during locomotion. However, existing tests of granular property estimation often rely on specific foot trajectories, such as vertical penetration or horizontal shear, limiting their applicability during natural locomotion. To address this limitation, we introduce a physics-informed machine learning framework, Inverse Resistive Force Theory (I-RFT), which integrates the Granular Resistive Force Theory model with Gaussian Processes to infer terrain properties from proprioceptively measured contact forces under arbitrary gait trajectories. By embedding the granular force model within the learning process, I-RFT preserves physical consistency while enabling generalization across diverse motion primitives. Experimental results demonstrate that I-RFT accurately estimates terrain properties across multiple gait trajectories and toe shapes. Moreover, we show that the quantified uncertainty over the terrain resistance stress map could enable robots to optimize foot design and gait trajectories for efficient information gathering. This approach establishes a new foundation for data-efficient characterization of complex granular environments and opens new avenues for locomotion strategies that actively adapt gait for autonomous terrain exploration.

Problem

• granular terrain
• terrain property estimation
• robot-terrain interaction
• locomotion
• contact forces

Innovation

• Inverse Resistive Force Theory
• physics-informed machine learning
• granular terrain characterization
• Gaussian Processes
• proprioceptive force sensing