Coulomb friction is the classic model where sliding resistance is proportional to the pressing force — the simple rule (and its 'friction cone') that underpins how robots reason about grasping, walking, and contact.
Coulomb friction is the basic rule that the harder you press two surfaces together, the more they grip before sliding. The 'friction cone' is the range of push directions the surface can resist without slipping — key to whether a robot's grip holds.
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The most-used friction rule in robotics is also the oldest and simplest: press harder, grip more. That's Coulomb friction, and its "friction cone" is the geometric idea behind whether a robot's grasp holds or its foot slips.
The law
Coulomb (dry) friction says the friction force resisting sliding is at most proportional to the normal (pressing) force:
F_friction ≤ μ · N
where N is how hard the surfaces are pressed together and μ is the friction coefficient. Two consequences a robot relies on: friction is (approximately) independent of contact area and of sliding speed, and there's a threshold — the contact holds without sliding until the tangential force exceeds μN, then it slips.
Press harder, resist more — up to a limit
Friction can resist tangential force up to μ·N. Stay inside that budget and the contact holds; exceed it and it slips — the basic contact rule for grasping and walking.
The friction cone
Coulomb's law has a beautiful geometric form: the friction cone. At a contact point, the total contact force must stay within a cone (half-angle arctan μ) around the surface normal — otherwise the surface would have to supply more sideways force than friction allows, and it slips. This cone is the workhorse of grasp analysis: a grasp achieves force closure when the contacts' friction cones together can resist any disturbance. Bigger μ = wider cone = easier grip; slippery surface = narrow cone = precarious.
Where robots use it
Grasping. Every grasp-stability calculation checks whether forces stay inside the friction cones.
Locomotion. A foot doesn't slip as long as the ground reaction force stays inside its friction cone — the constraint behind stable stepping and traction.
Manipulation and pushing. Predicting whether a pushed object slides or sticks.
The limits
Coulomb friction is an idealization. Real friction has distinct static vs kinetic values (stick-slip), depends on speed at low velocities, and varies with surface condition — captured only by richer friction models. But Coulomb's simplicity and its friction-cone geometry make it the default for reasoning about contact, with margins added for reality.
Why it matters
Coulomb friction — and especially the friction cone — is the fundamental way robots reason about contact stability. It's the mathematical bedrock of grasp planning and legged locomotion, turning "will it slip?" into a clean geometric condition. Understanding it is essential to all of contact-rich robotics.
