Abstract
Foot-ground interaction signals recorded by quadruped robots may enable spatially distributed, in situ characterization of soil strength. As a first step, we test whether the internal friction angle $φ$ of cohesionless soil can be identified from the force history of a simplified rotating leg. A two-dimensional continuum model implemented with the material point method, benchmarked against measured rotating-leg force histories, generates the training data, and two Gaussian-process surrogates support Bayesian inversion of the full histories. In matched-model experiments, the framework recovers 14 off-grid friction angles with a median absolute error of approximately $0.1^\circ$ (maximum $\sim 0.7^\circ$); the reported credible intervals contain the true value in every case. These results establish that $φ$ is identifiable when the forward model is correctly specified, and support further development of proprioceptive soil sensing for spatially variable terrain, with applications from physics-grounded world models for robot training to post-wildfire slope assessment.
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Cite this article
APA 7
Xu, D., & Wang, Z. (2026). Inferring Soil Friction Angle from Robot Foot-Ground Force Histories: A Bayesian Inverse Approach to Proprioceptive Soil Sensing. https://omanscience.com/en/articles/inferring-soil-friction-angle-from-robot-foot-ground-force-histories-a-bayesian-inverse-approach-to-proprioceptive-soil-sensing
MLA 9
Xu, Dawei, and Zhijie Wang. "Inferring Soil Friction Angle from Robot Foot-Ground Force Histories: A Bayesian Inverse Approach to Proprioceptive Soil Sensing." https://omanscience.com/en/articles/inferring-soil-friction-angle-from-robot-foot-ground-force-histories-a-bayesian-inverse-approach-to-proprioceptive-soil-sensing.
Chicago (author–date)
Xu, Dawei, and Zhijie Wang. 2026. "Inferring Soil Friction Angle from Robot Foot-Ground Force Histories: A Bayesian Inverse Approach to Proprioceptive Soil Sensing." https://omanscience.com/en/articles/inferring-soil-friction-angle-from-robot-foot-ground-force-histories-a-bayesian-inverse-approach-to-proprioceptive-soil-sensing.
Harvard
Xu, D. and Wang, Z. (2026) 'Inferring Soil Friction Angle from Robot Foot-Ground Force Histories: A Bayesian Inverse Approach to Proprioceptive Soil Sensing', Available at: https://omanscience.com/en/articles/inferring-soil-friction-angle-from-robot-foot-ground-force-histories-a-bayesian-inverse-approach-to-proprioceptive-soil-sensing.
Vancouver
Xu D, Wang Z. Inferring Soil Friction Angle from Robot Foot-Ground Force Histories: A Bayesian Inverse Approach to Proprioceptive Soil Sensing. https://omanscience.com/en/articles/inferring-soil-friction-angle-from-robot-foot-ground-force-histories-a-bayesian-inverse-approach-to-proprioceptive-soil-sensing
IEEE
D. Xu, and Z. Wang, "Inferring Soil Friction Angle from Robot Foot-Ground Force Histories: A Bayesian Inverse Approach to Proprioceptive Soil Sensing," https://omanscience.com/en/articles/inferring-soil-friction-angle-from-robot-foot-ground-force-histories-a-bayesian-inverse-approach-to-proprioceptive-soil-sensing.