PROD: Palpative Reconstruction of Deformable Objects through Elastostatic Signed Distance Functions

TL;DR

PROD is a new method that reconstructs deformable objects' shape and material properties using elastostatic SDFs and force measurements, improving robustness and accuracy in soft object modeling.

Contribution

It introduces a novel elastostatic SDF-based reconstruction method that integrates palpation data and elastodynamic modeling for deformable objects.

Findings

Robust reconstruction of shape and stiffness from sparse force data.

Effective handling of pose and curvature errors in simulations.

Provable convergence of the undeformed shape estimation.

Abstract

We introduce PROD (Palpative Reconstruction of Deformables), a novel method for reconstructing the shape and mechanical properties of deformable objects using elastostatic signed distance functions (SDFs). Unlike traditional approaches that rely on purely geometric or visual data, PROD integrates palpative interaction -- measured through force-controlled surface probing -- to estimate both the static and dynamic response of soft materials. We model the deformation of an object as an elastostatic process and derive a governing Poisson equation for estimating its SDF from a sparse set of pose and force measurements. By incorporating steady-state elastodynamic assumptions, we show that the undeformed SDF can be recovered from deformed observations with provable convergence. Our approach also enables the estimation of material stiffness by analyzing displacement responses to varying force inputs. We demonstrate the robustness of PROD in handling pose errors, non-normal force application, and curvature errors in simulated soft body interactions. These capabilities make PROD a powerful tool for reconstructing deformable objects in applications ranging from robotic manipulation to medical imaging and haptic feedback systems.