A Convex Formulation of Compliant Contact between Filaments and Rigid Bodies

2025-09-16

AI Summary

Existing filament–rigid-body contact simulation methods typically assume persistent attachment, failing to capture friction-driven dynamic detachment and recontact. This work proposes a novel framework integrating discrete elastic rods (DER) dynamics, pressure-field patch-based contact modeling, and convex optimization for contact configuration. It is the first to unify these three components within a global optimization paradigm, rigorously enforcing complementarity conditions between contact velocities and impulses—enabling high-fidelity, frictional contact simulation. The method overcomes numerical challenges arising from filament codimensionality, significantly improving physical consistency. Experiments demonstrate superior accuracy and stability in friction force computation compared to state-of-the-art baselines. The framework is validated on complex deformable manipulation tasks—including randomized cable grasping with a multi-fingered gripper and dynamic shoelace knotting—showcasing both efficacy and robustness.

Technology Category

• Intelligent Robots: Manipulation
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

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 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.

Problem

• Simulating frictional interactions between filaments and rigid bodies
• Overcoming codimensionality challenges in filament simulation
• Ensuring global optimality and complementarity in contact dynamics

Innovation

• Convex contact formulation for filament interactions
• Unifies DER modeling with pressure field patches
• Globally optimal per-time-step contact resolution