提出可凸优化的细长体与刚体接触模拟方法，实现高精度摩擦力计算。
A Convex Formulation of Compliant Contact between Filaments and Rigid Bodies
- 采用弹性杆模型结合压力场接触建模，构建凸优化接触框架
- 每步求解全局最优，确保接触速度与冲量满足互补关系
- 可用于软体机器人抓取和鞋带系结等复杂交互场景
我们提出一种用于模拟细长纤维与刚体之间接触的计算框架。由于纤维是嵌入三维空间的一维结构，其模拟极具挑战性。现有方法常假设纤维与刚体永久连接。本框架融合离散弹性杆（DER）建模、压力场接触模型与凸接触公式，首次实现了细长纤维与刚体间摩擦相互作用的精确模拟。得益于接触的凸优化形式，每个时间步均可求解至全局最优，保证接触速度与冲量间的互补性。通过评估摩擦力精度并对比基线方法的物理保真度验证了该框架的有效性。最后，我们在软体机器人（如随机纤维抓手）和可变形物体操作（如鞋带系结）中展示了其适用性，为涉及复杂纤维-纤维及纤维-刚体相互作用的系统提供了通用仿真工具。
原文摘要 · Abstract (English)
We present a computational framework for simulating filaments interacting with rigid bodies through contact. Filaments are challenging to simulate due to their codimensionality, i.e., they are one-dimensional structures embedded in three-dimensional space. Existing methods often assume that filaments remain permanently attached to rigid bodies. Our framework unifies discrete elastic rod (DER) modeling, a pressure field patch contact model, and a convex contact formulation to accurately simulate frictional interactions between slender filaments and rigid bodies - capabilities not previously achievable. Owing to the convex formulation of contact, each time step can be solved to global optimality, guaranteeing complementarity between contact velocity and impulse. We validate the framework by assessing the accuracy of frictional forces and comparing its physical fidelity against baseline methods. Finally, we demonstrate its applicability in both soft robotics, such as a stochastic filament-based gripper, and deformable object manipulation, such as shoelace tying, providing a versatile simulator for systems involving complex filament-filament and filament-rigid body interactions.
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