Manipulation

Friction Cone

A friction cone is the set of contact forces that a frictional point contact can transmit without slipping, forming a cone around the surface normal whose half-angle is the arctangent of the friction coefficient under the Coulomb model. Grasp and locomotion planners constrain contact forces to lie within their friction cones, often using polyhedral approximations to keep the resulting optimization problems linear or conic.

Why it matters for physical AI

Whether a foot or finger slips is governed by friction cone constraints, so they appear in nearly every contact-aware planner and controller, and violations are a dominant cause of real-world grasp and locomotion failures.