Hardware & control
Centre of pressure
The centre of pressure is the point on a support surface at which the resultant of a distributed contact pressure or ground-reaction force can be represented as acting. In legged robotics it summarises how load is applied through one foot or across coplanar contacts and is commonly estimated from a measured contact wrench.
Also known as: center of pressure, CoP
Updated
Distributed contact becomes one equivalent point
A foot does not press on the floor at only one physical spot. Pressure and shear are distributed across the contact patch. The centre of pressure replaces that distribution with an equivalent resultant contact force at a point on the support surface, together with any remaining moment about the surface normal.
Force plates, instrumented feet and force–torque sensors can provide the force and moment needed to calculate the point. The calculation becomes ill-conditioned when the normal force is close to zero, so a centre of pressure during swing or uncertain contact should not be treated as a reliable measurement.
CoP and ZMP are related but not interchangeable definitions
Sardain and Bessonnet define the centre of pressure from ground–foot contact forces and the zero moment point from gravity and inertia forces. Under a dynamically balanced motion on a common support plane, the two coincide through the equations of motion.
That equivalence does not erase their different interpretations. A measured CoP describes the contact wrench that actually exists. A planned ZMP can describe the contact wrench a trajectory would require. If that requested point lies outside the feasible support region, it is not an achievable physical CoP for the assumed contact.
Multiple contacts require a declared surface
For one flat foot, the centre of pressure lies within the convex hull of the pressure-bearing contact region under the usual unilateral-contact assumptions. If the loaded patches are separated, the equivalent point can lie between them rather than on a directly loaded patch. With two coplanar feet, a combined value can be expressed on the shared plane. Hands, knees, stairs or feet on differently oriented surfaces do not provide one natural planar centre of pressure without an additional modelling convention.
Data should therefore identify the supporting contacts, reference plane and coordinate frame, sensor origin, sign convention, normal-force threshold and filtering. Per-contact and combined values should remain distinguishable.
Sources
Related terms
Hardware & control
Zero moment point
The zero moment point is a support-surface point used in legged-robot dynamics at which the tipping moment vanishes. ISO defines it from the resultant support forces, while classical biped literature uses the corresponding gravity-and-inertia formulation; for dynamically balanced planar contact, these formulations coincide with the centre of pressure.
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
Centre of mass
The centre of mass is the mass-weighted average position of a body or multibody system. For a humanoid, the whole-robot centre of mass changes as its joints move or its payload changes, and its position and acceleration are central variables in balance, locomotion and whole-body control.
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
Locomotion
Robot locomotion is the process by which a robot transports its body from one place to another through physical interaction with its environment. Robots may walk, roll, crawl, hop, fly, or swim. For a humanoid, locomotion usually means coordinated legged movement such as walking, turning, stepping, climbing, or recovering balance.