Robotics
Friction cone
Definition
A friction cone is the set of contact forces permitted by a Coulomb friction model at a contact that pushes but does not pull. The allowable tangential force magnitude is bounded by the normal force multiplied by a friction coefficient.
Also known as: Coulomb friction cone, Friction cones
Updated
Normal force limits tangential force
For a stationary point contact, write the model as norm(f_t) <= mu * f_n, with nonnegative normal force f_n. Here f_t is the force parallel to the surface and mu is the friction coefficient. Modern Robotics explains why the set forms a cone around the contact normal.
A robot foot pushing harder into the floor can, within this model, transmit more sideways force before sliding. The same idea applies to fingers squeezing an object during manipulation.
Using the cone in planning
Walking and grasp planners can require contact forces to remain inside the cone. For computation, a circular cone is often approximated by a pyramid with a finite number of edges. An inner approximation sacrifices some available forces; a coarse or incorrectly oriented approximation can change the predicted contact capability.
The contact model is approximate
Modern Robotics calls Coulomb friction an empirical approximation. Real friction can depend on material, surface condition, and whether contact is sticking or sliding. When sliding occurs, the friction direction opposes slip and does not remain an arbitrary force inside the cone. Adhesion, soft contact patches, and torsional friction need additional modeling beyond the basic point-contact cone.
Sources
Related terms
Force closure
Force closure is a contact condition in which the admissible contact wrenches can collectively oppose any external wrench direction on an object. The condition depends on contact locations, normals, and the assumed friction model.
Support polygon
The support polygon is the convex hull of a robot’s active contact points or contact patches projected onto a common support plane. It describes the available support region in planar contact models.
Force control
Force control regulates the force or wrench a robot applies to its environment. It may use a robot model, measured interaction forces, or both to produce joint commands that achieve a desired contact load.
Contact-implicit optimization
Contact-implicit optimization plans motion while allowing contact events and forces to emerge from contact constraints in the optimization. It avoids requiring every contact transition to be fixed in a predefined mode sequence.