Inferring Soil Friction Angle from Robot Foot-Ground Force Histories: A Bayesian Inverse Approach to Proprioceptive Soil Sensing

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 $\phi$ 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 $\phi$ 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.