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This paper introduces a novel splitting architecture for solving exact reduced Coulomb friction, addressing the limitations of existing methods that either modify the Coulomb law or rely on monolithic solutions. By reformulating the problem as a cone complementarity problem with an augmented velocity, the authors create a clear separation between linear responses constrained by cones and the non-associated coupling from tangential velocities. The proposed solver demonstrates superior numerical robustness and accuracy, successfully reproducing exact Coulomb complementarity in rigid-body benchmarks without the need for smoothing or relaxing the friction law.
Exact Coulomb friction can be solved with unprecedented accuracy and robustness by separating linear responses from non-associated couplings, revolutionizing frictional contact dynamics.
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.
