Why does a viscous friction ansatz give accurate multi-contact coulomb friction predictions

The complexity of multi-contact mechanics models limits the applications of multi-legged robots.  We previously presented a geometric connection model for friction-dominated multi-legged locomotion with slipping using a Coulomb-viscous friction ansatz. Our ansatz has a fast-to-compute closed-form solution, unlike the traditional nonlinear and non-smooth Coulomb model, yet gave accurate predictions for body velocity. To check if the ansatz model predicts the correct friction forces, we collected the robot motion tracking data and ground contact forces from the feet of a hexapod. We found the error lies inside a sector bound, once a single friction coefficient is appropriately chosen. We present some mathematical motivation for why this might occur.