FEM-Based Estimation–Correction with Minimal Indentation Set for Internal Cavity Classification and Geometry Estimation in Deformable Objects

Accurately estimating the internal structure of deformable objects from sparse measurements remains a significant challenge in robotics. This work proposes a three-stage identification framework for this problem. First, a classification strategy determines a minimal informative set of indentation locations using a generalized error computed from pre-simulated FEM force reactions of baseline cavity models and flat-punch indentation estimation. Using this set, the estimation stage detects the cavity type and provides a preliminary estimate of its geometric parameters based solely on measured indentation responses. The correction stage then refines these parameters by replaying measured indentation depths in FEM simulations and deriving geometry corrections from the discrepancy between simulated and homogeneous force responses. Robust loss functions at both stages limit the influence of measurements where local contact conditions deviate from the assumed model, improving reliability across all tested cases. Indentation depth was obtained through gripper proprioception, with an RGB-D camera limited to global pose alignment. Experiments on soft cubes with spherical, cuboid, and pyramidal cavities demonstrate that, within known cavity families and fixed material parameters, the minimal indentation set reliably distinguishes cavity types and the pipeline reconstructs dimensions within error bounds. Extending the framework to non-centered structures and unknown materials remains future work.