Friction

When a foot pushes sideways on the floor, friction pushes back. It can resist up to a limit set by how hard the foot presses down, the normal force $N$, and the materials’ coefficient of friction $\mu$ (Coulomb’s law):

$$|F_{\text{tangential}}| \le \mu\, N$$

Below the limit the foot sticks. Push harder sideways and it slides.

The friction cone

Together, the allowed contact forces form a cone around the surface normal: the total force must point within an angle $\arctan \mu$ of straight up. Pushing at a shallower angle makes the foot slip. A foot that carries little weight can push very little sideways, which is why a fighter must load a foot before driving off it.

In simulation

Simulators model friction at every contact, usually with a sliding coefficient and sometimes also rolling and twisting (torsional) friction. Get it wrong and feet skate: they slide across the floor in a way that looks plainly fake, even if the body stays up.

In this project

The muscular body’s hands use a grippier material than the rest of the body. The recovery reward includes a penalty for skating, feet sliding while they carry weight, so the policy can’t recover by gliding its feet across the mat.