From Impact to Insight: Dynamics-Aware Proprioceptive Terrain Sensing on Granular Media

TL;DR

This paper presents a physics-based framework for dynamic terrain characterization using proprioceptive sensing, emphasizing the importance of acceleration-dependent effects during high-speed hopping on granular media.

Contribution

It introduces an acceleration-aware force decomposition and estimator that improve terrain property estimation during dynamic locomotion.

Findings

Quasi-static assumptions lead to large estimation errors at high speeds.

Acceleration-dependent added-mass effects dominate transient force responses.

The proposed methods enable accurate granular stiffness estimation during dynamic hopping.

Abstract

Robots that traverse natural terrain must interpret contact forces generated under highly dynamic conditions. However, most terrain characterization approaches rely on quasi-static assumptions that neglect velocity- and acceleration-dependent effects arising during impact and rapid stance transitions. In this work, we investigate granular terrain interaction during high-speed hopping and develop a physics-based framework for dynamic terrain characterization using proprioceptive sensing alone. Through controlled hopping experiments with systematically varied impact speed and leg compliance, our measurements reveal that quasi-static based assumptions lead to large discrepancies in granular terrain property estimation during high-speed hopping, particularly upon touchdown and controller-induced stiffness transitions. Velocity-dependent drag alone cannot explain these discrepancies. Instead, acceleration-dependent added-mass effects-associated with grain entrainment beneath the foot-dominate transient force responses. We integrate this force decomposition with a momentum-observer-based estimator that compensates for rigid-body inertia and gravity, and introduce an acceleration-aware weighted regression to account for increased force variance during high-acceleration events. Together, these methods enable consistent recovery of granular stiffness parameters across locomotion conditions, closely matching linear-actuator ground truth. Our results demonstrate that accurate terrain inference during high-speed locomotion requires explicit treatment of acceleration-dependent granular effects, and provide a foundation for robots to characterize complex deformable terrain during dynamic exploration of terrestrial and planetary environments.