PROD：通过弹性静力学符号距离函数对可变形物体进行触诊式重建
PROD: Palpative Reconstruction of Deformable Objects through Elastostatic Signed Distance Functions
AI总结：
本文提出PROD方法，通过力控触诊交互和弹性静力学符号距离函数，从稀疏位姿与力测量中重建可变形物体的形状和材料刚度，并证明其在多种误差条件下具有鲁棒性。
摘要：
我们提出PROD（Palpative Reconstruction of Deformables，可变形物体的触诊式重建），这是一种利用弹性静力学符号距离函数（SDF）重建可变形物体形状和力学特性的新方法。与依赖纯几何或视觉数据的传统方法不同，PROD整合了触诊式交互——通过力控表面探测进行测量——来估计软材料的静态和动态响应。我们将物体的变形建模为弹性静力学过程，并推导出一个控制泊松方程，用于从稀疏的位姿和力测量集合中估计其SDF。通过引入稳态弹性动力学假设，我们证明未变形的SDF可以从变形观测中恢复，且具有可证明的收敛性。我们的方法还通过分析对不同力输入的位移响应来实现材料刚度的估计。我们展示了PROD在模拟软体交互中处理位姿误差、非正向力施加和曲率误差方面的鲁棒性。这些能力使PROD成为在从机器人操作到医学成像和触觉反馈系统等应用中重建可变形物体的强大工具。
英文摘要：
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.
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