A Splitting Architecture for Exact Reduced Coulomb Friction

Abstract: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.

14 pages. Accepted to SCA 2026 (ACM SIGGRAPH / Eurographics Symposium on Computer Animation); published open access in Computer Graphics Forum. DOI: https://doi.org/10.1111/cgf.70576. Project page: this https URL

Graphics (cs.GR); Robotics (cs.RO); Numerical Analysis (math.NA)

I.6.8; I.3.5; G.1.6

arXiv:2607.19599 [cs.GR]

(or arXiv:2607.19599v1 [cs.GR] for this version)

https://doi.org/10.48550/arXiv.2607.19599 arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1111/cgf.70576 DOI(s) linking to related resources