通过触觉探查重建软体物体形状与刚度，无需视觉数据
PROD: Palpative Reconstruction of Deformable Objects through Elastostatic Signed Distance Functions
- 用弹性静力学SDF建模物体形变，从稀疏力与位姿数据推断
- 可恢复原始形状，且在力非垂直、姿态误差下仍稳定收敛
- 适合机器人抓取、医疗成像等需感知软体特性的场景
我们提出PROD（触觉驱动的可变形物体重建），一种基于弹性静力学符号距离函数（SDF）的新方法，用于重建可变形物体的形状与力学特性。不同于依赖纯几何或视觉数据的传统方法，PROD结合力控表面探查所获取的触觉信息，估计软材料的静态与动态响应。我们将物体形变建模为弹性静力学过程，推导出由稀疏位姿与力测量数据估计SDF的控制泊松方程。通过引入稳态弹性动力学假设，证明了可从形变观测中恢复原始SDF，并具有可证明的收敛性。该方法还可通过分析不同力输入下的位移响应，估计材料刚度。我们在模拟软体交互中验证了PROD对姿态误差、非法向力施加及曲率误差的鲁棒性。这些能力使其成为机器人操作、医学成像与触觉反馈系统中重建可变形物体的强大工具。
原文摘要 · Abstract (English)
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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