PROD: Palpative Reconstruction of Deformable Objects through Elastostatic Signed Distance Functions
This work addresses the challenge of accurately modeling deformable objects for applications in robotic manipulation, medical imaging, and haptic feedback systems, representing a novel integration of palpative data but with incremental advancements in elastostatic modeling.
The paper tackles the problem of reconstructing the shape and mechanical properties of deformable objects by introducing PROD, a method that uses elastostatic signed distance functions and palpative interaction to estimate static and dynamic responses, with demonstrated robustness in handling pose errors and non-normal forces in simulations.
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.