# A Convex Formulation of Compliant Contact between Filaments and Rigid Bodies

arXiv: https://arxiv.org/abs/2509.13434 · HTML: https://mlsanity.com/paper/2509.13434/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2025.

## Built on by (most cited first, 1 of 1)

- [Robustness without Wrinkles: Parallel Simulation and Robust MPC for Certified Deformable Manipulation](https://mlsanity.com/paper/2606.14188/) (2026)

## Abstract (arXiv)

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.