Robot control
Center of pressure
Definition
The center of pressure is the point on a contact surface where the resultant normal contact force can be treated as acting to reproduce the surface pressure distribution's moment. Legged robots use it to describe how ground load is distributed under one or more supporting feet.
Also known as: Centre of pressure, CoP
Updated
A resultant location for distributed pressure
A flat foot produces pressure over an area rather than at one mathematical point. The center of pressure summarises that distribution as a location for the resultant normal force. With several coplanar contacts, it can be computed as the normal-force-weighted average of the contact positions, as derived in the MIT Underactuated Robotics notes.
If every contact can only push on the surface, the center of pressure lies inside the convex hull of the active contact points. For a humanoid standing on flat ground, this connects the measured ground reaction forces to the current support polygon.
Relationship to the zero-moment point
The center of pressure and zero-moment point coincide under common flat, rigid-contact assumptions, but the names emphasise different constructions. Center of pressure starts from the distributed contact force. Zero-moment point starts from a moment-balance condition for the robot dynamics. Sardain and Bessonnet analyse the relationship and the conditions under which the points should be distinguished.
Controllers can command a desired center of pressure to influence center-of-mass acceleration. Foot-mounted force sensors or a force plate can estimate it from contact loads, provided the normal force is large enough and the measurements are expressed in a consistent frame.
The point does not describe every stability limit
A center of pressure inside the foot is useful evidence that the measured resultant can be supported without tipping under the assumed contact model. It does not by itself show that tangential force stays inside the friction cone, that the foot will not deform or roll, or that a dynamic disturbance can be recovered.
The estimate becomes sensitive to noise when the normal load approaches zero. On uneven or non-coplanar contacts, a single point on one plane can also hide important three-dimensional force and moment information. A full contact wrench or separate per-contact measurements may then be more informative.
Sources
Related terms
Zero-moment point
The zero-moment point is a point on a chosen support plane where the net moment associated with the ground reaction wrench has zero components parallel to that plane. In flat-ground walking with the usual contact assumptions, it coincides with the center of pressure.
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.
Center of mass
The center of mass is the mass-weighted average position of a body or a collection of bodies. For an articulated robot, its position changes as the links move.
Force-torque sensor
A force-torque sensor is a transducer that measures forces and moments applied through a robot interface. A common six-axis sensor reports three force components and three torque components as a wrench in the sensor's coordinate frame.