提出一种精确求解库仑摩擦的新架构，分离核心机制提升稳定性与可扩展性。
A Splitting Architecture for Exact Reduced Coulomb Friction
- 将摩擦问题分解为锥约束响应与切向速度耦合两部分，分层求解
- 在刚体基准测试中精确复现粘滑过渡和摩擦堆叠行为，无需平滑或松弛摩擦律
- 内层求解器模块化，支持灵活替换数值方法，外层迭代保持不变
现有摩擦接触动力学方法通常通过修改库仑定律来提升数值鲁棒性，或以全耦合单体形式求解精确定律。然而，在其约化形式下，精确库仑摩擦可表述为带增广速度的锥互补问题，天然揭示了锥约束线性响应与由切向速度引发的标量非关联耦合之间的分离结构。本文利用该结构设计求解器：采用外层迭代显式更新非关联耦合，内层求解强凸锥约束二次规划。这种分离使内层求解器具备模块化特性，不同数值方案可独立替换而不影响外层迭代。在包含粘滑转换与摩擦堆叠的刚体基准测试中，方法成功复现了精确库仑互补关系，未使用任何摩擦律的平滑或松弛处理。
原文摘要 · Abstract (English)
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.
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