发表机构
University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究精确简化库仑摩擦问题，利用其结构设计求解器，采用外层迭代更新非关联耦合、内层求解锥约束二次规划的方法，在刚体基准测试中能再现精确库仑互补性且无需处理摩擦定律。
AI 中文摘要
现有的摩擦接触动力学方法通常要么修改库仑定律以提高数值稳健性，要么以完全耦合的整体形式求解精确定律。然而，精确的库仑摩擦在简化形式下可写为具有增强速度的锥互补问题，这揭示了锥约束线性响应与切向速度引起的标量非关联耦合之间的自然分裂。我们在求解器设计中利用了这种结构。我们的方法使用外层迭代显式更新非关联耦合，并对强凸锥约束二次规划进行内层求解。这种分离还使内层求解器模块化，因此可以使用不同的数值方案而不改变外层迭代。我们在具有粘滑转变和摩擦堆叠的刚体基准上评估了该方法，结果表明它无需平滑或松弛摩擦定律就能再现精确的库仑互补性。
英文摘要
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.
Comments14 pages. Accepted to SCA 2026 (ACM SIGGRAPH / Eurographics Symposium on Computer Animation); published open access in Computer Graphics Forum. DOI: 10.1111/cgf.70576. Project page: https://www.cs.ubc.ca/research/fbf-friction
Journal refComputer Graphics Forum 45(8), 2026
