厳密な低次元クーロン摩擦のための分割アーキテクチャ
A Splitting Architecture for Exact Reduced Coulomb Friction
摩擦接触問題を、円錐制約付き線形応答と接線速度による非結合スカラー項に分割し、外側反復と内側の凸二次計画で解く手法を提案。摩擦則を緩めずに厳密な解を実現する。
著者: Hongcheng Song, Ye Fan, Uri M. Ascher, Dinesh K. Pai
分類: cs.GR, cs.NA, cs.RO, math.NA
原文アブストラクト
Existing approaches to frictional contact dynamics typically either modify the Coulomb law to improve numerical robustness or solve the exact law in a fully coupled monolithic form. However, in its reduced form, exact Coulomb friction can be written as a cone complementarity problem with an augmented velocity, which reveals a natural split between a cone-constrained linear response and a scalar non-associated coupling induced by tangential velocity. We exploit this structure in the solver design. Our method uses an outer iteration to update the non-associated coupling explicitly, and an inner solve for a strongly convex cone-constrained quadratic program. This separation also makes the inner solver modular, so different numerical schemes can be used without changing the outer iteration. We evaluate the method on rigid-body benchmarks with stick-slip transitions and frictional stacking, and show that it reproduces exact Coulomb complementarity without smoothing or relaxing the friction law.