The Contact Shortcut

Contact simulation in robotics requires solving complementarity problems — finding contact forces that are non-negative, only active when surfaces touch, and satisfy Newton’s laws simultaneously. This is a constrained optimization at every timestep. In dense contact scenes — a multi-fingered hand grasping an object — the number of constraints explodes with the number of contact points.

ComFree-Sim removes the complementarity formulation entirely. Instead of solving a constrained optimization, it computes contact forces analytically from penetration depth and surface geometry, with a smooth penalty model that has no switching between contact states. No complementarity constraints, no linear complementarity solvers, no pivoting algorithms.

The result: 2-3x higher throughput than MuJoCo Warp in dense contact scenes, with near-linear runtime scaling in the number of contacts. Fast enough for real-time model-predictive control on a physical multi-fingered hand performing in-hand manipulation.

The through-claim: the complementarity formulation was faithful physics, not necessary computation. Real contacts don’t solve complementarity problems — they apply forces proportional to deformation. The complementarity formulation was an idealization that made the physics elegant at the cost of making computation hard. Replacing it with a smooth penalty model sacrifices the mathematical exactness of perfectly rigid contact (which no real surface is) for computational tractability that enables real-time control. The shortcut isn’t an approximation to the truth — it’s closer to the truth than the formulation it replaces.