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

2025-08-17

AI Summary

Joint reconstruction of deformable object shape and mechanical properties remains challenging. Method: This paper proposes a novel approach integrating tactile interaction with elastic statics-based signed distance field (SDF) modeling. Unlike conventional geometry- or vision-only methods, it employs force-controlled surface probing to acquire sparse pose and force measurements, then solves a controlled Poisson equation to jointly estimate the undeformed-state SDF and material stiffness under quasi-static elastic assumptions. Contribution/Results: It is the first framework unifying tactile feedback with elastic statics SDF modeling, with provable theoretical convergence and robustness against non-ideal contact conditions—including pose uncertainty, non-normal contact forces, and surface curvature mismatch. Experiments in simulated soft-body interactions demonstrate high-precision shape reconstruction (mean error < 1.2 mm) and accurate Young’s modulus estimation (relative error < 8.5%).

Technology Category

• Intelligent Robots: State Estimation
• Humans and AI: Interaction Techniques and Devices
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Reconstruct shape and mechanical properties of deformable objects
• Estimate static and dynamic response of soft materials
• Recover undeformed SDF from deformed observations

Innovation

• Uses elastostatic SDFs for deformable object reconstruction
• Integrates palpative interaction with force-controlled probing
• Estimates material stiffness from displacement responses