Hardware & control
Friction cone
A friction cone is the set of contact-force vectors allowed by a Coulomb friction model: the normal force is nonnegative and the tangential force magnitude cannot exceed the friction coefficient times that normal force. It represents a force constraint at a contact, not a physical cone or a guarantee that the robot will not slip.
Also known as: Coulomb friction cone, Contact friction cone, Friction cones
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Normal force sets the tangential limit
At a non-adhesive contact, the surfaces can push against each other but cannot sustain a tensile normal force. In the basic Coulomb model, a stationary contact can transmit tangential force up to mu * f_n, where mu is the friction coefficient and f_n is the compressive normal force. Modern Robotics' friction chapter derives the cone from this inequality.
A larger friction coefficient widens the admissible set. In the basic sliding model, friction lies on its boundary and opposes the sliding direction. The model is an approximation: the same source distinguishes a single-coefficient law from models with separate static and kinetic friction coefficients.
For a humanoid foot, a desired sideways contact force must be compatible with the available normal load and assumed surface friction. A foot location inside a support polygon alone does not check that force constraint.
A friction pyramid is an approximation
The spatial Coulomb cone has a curved boundary. Optimisation methods may replace it with a polyhedral cone, often called a friction pyramid. Modern Robotics demonstrates an inscribed approximation built from a finite set of edge forces; more edges approximate the curved cone more closely.
An inscribed approximation excludes some forces that the original cone allows. When comparing controllers or datasets, specify the actual approximation rather than assuming every “friction cone constraint” implements the same feasible set.
Contact forces and whole-body feasibility differ
A point-contact friction cone constrains force at that point. Expressing its effect about another origin also introduces the moment generated by the contact's lever arm. Combining several contacts produces a wrench set, which matters for force closure and whole-body contact planning.
Store contact position, surface normal, force frame, friction coefficient and contact model with any feasibility label. Distinguish measured force from an optimiser's proposed force, and record whether the coefficient was measured, estimated or simply assumed. Satisfying a modelled cone does not verify the real surface or the robot's actuation limits.
Sources
Related terms
Hardware & control
Force closure
Force closure is a property of a set of contacts whose admissible forces can collectively generate a wrench opposing any external disturbance wrench under the chosen contact model. It describes directional force and moment capability without, by itself, accounting for finite actuator strength, object damage or uncertainty in the contacts.
Hardware & control
Force–torque sensing
Force–torque sensing is the measurement of forces and rotational moments transmitted through a robot interface, commonly with a six-axis sensor reporting three force components and three torque components. The combined quantity is a wrench expressed at a specified origin and in a specified coordinate frame. It measures the resultant load at the sensor, not a spatial pressure map across every contact.
Hardware & control
Support polygon
The support polygon is the convex hull of a robot’s contact areas on a declared support surface. For a biped on level ground it is formed by the loaded parts of one or both feet; it changes when contacts are added, removed or reduced to an edge or toe.
Hardware & control
Whole-body control
Whole-body control coordinates a humanoid’s full multibody state, actuated joints and environmental contacts to pursue several motion or force objectives while respecting constraints such as balance, joint limits and friction. It is a family of hierarchical or optimisation-based methods, not one algorithm; implementations may output joint positions, accelerations or torques.
Hardware & control
Tactile sensing
Tactile sensing is the detection and measurement of physical contact properties at a robot's surface or contact interface. Depending on the sensor, it can report pressure or force distribution, contact location, shear, vibration, slip, texture, temperature, or deformation. Tactile data complements vision by measuring interactions that may be hidden at the point of contact.