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In terrestrial robot locomotion, the center of pressure is the ground point summarizing the normal load shared by the active contacts. With contact positions $(x_i,y_i)$ and nonnegative normal reactions $N_i$, its coordinates are the weighted averages $x_P={\sum }_i{N}_i{x}_i/{\sum }_i{N}_i$ and $y_P={\sum }_i{N}_i{y}_i/{\sum }_i{N}_i$, provided the total normal force is positive. It lies in the current support polygon, but is a contact-force quantity rather than the robot's center of mass position.^[ref]

Force-sensor coordinates matter when reconstructing this point. Suppose a sensor origin lies height $h$ above a horizontal contact plane, with parallel coordinate axes. If it reports force $(F_x,F_y,F_z)$ and moment $(M_x,M_y,M_z)$, the plane point is located at $(x_P,y_P,-h)$ relative to that origin. Moment translation givesThe ground-plane transformation of a measured contact wrench must therefore precede interpreting moment/force ratios as a contact location.

For an original sensor example, take $h=0.05\mathrm{m}$, force $(30,-20,600)\mathrm{N}$, and measured roll/pitch moments $(17,-49.5)\mathrm{N}\mathrm{m}$. The reconstructed point is $(0.080,0.030)\mathrm{m}$. Ignoring the origin height would instead give $(0.0825,0.02833)\mathrm{m}$. Those millimetre differences are coordinate effects, not a change in the physical pressure distribution.

During motion, the contact point need not equal the horizontal projection of the center of mass. The source's constant-height, negligible-angular-momentum-rate model relates their difference to horizontal acceleration; those assumptions must be established before using that simplified relation.^[ref] A robot-foot experiment can compare known applied loads with the sensor's translated force/moment measurements. When $F_z$ approaches zero, reconstruction becomes sensitive to moment error; at zero normal load the normal-pressure point is undefined. A residual yaw couple may remain, as explained in residual contact torque at the center of pressure.

A force platform, or force plate, measures the resultant forces transmitted through its surface; multicomponent platforms also measure moments about defined axes. It is used in gait and balance experiments to observe external loading during contact. A manufacturer's six-output description specifies three force and three moment components from which a center of pressure can be calculated.^[ref]

A platform combines a load-bearing surface, force-sensitive transducers, signal acquisition and a calibration relating sensor outputs to mechanical quantities. Applying known loads at known locations tests both force response and moment sensitivity. Off-diagonal calibration terms can matter when a nominal load produces responses in several channels; the instrument indication must be interpreted in its specified coordinate frame.

An original calculation chooses the origin on the top surface, with $z$ normal to it and a positive normal resultant $F_z$. For a resultant represented at $(x,y,0)$ plus a residual moment normal to the plate,These signs follow from $\mathbf{M}=\mathbf{r}\times \mathbf{F}$ in the stipulated right-handed frame. A manufacturer origin below the surface or a different force-sign convention requires the corresponding transformation; the formulas are not coordinate-free instructions.

For chosen readings $F_z=500\mathrm{N}$, $M_x=-25\mathrm{N}\mathrm{m}$ and $M_y=-50\mathrm{N}\mathrm{m}$, the calculated point is $(0.10,-0.05)\mathrm{m}$. If the same moment uncertainty is divided by a much smaller $F_z$, position uncertainty increases. At zero normal load this ratio does not define a meaningful contact location.

The center of pressure is a summary of the measured loading, not the body's center of mass. Motion observations can supply additional evidence for an inverse-dynamics analysis, but the force platform alone does not directly measure every joint force or muscle action. If several contacts share one plate, its resultant can also conceal their separate contributions. Recording which contacts occurred and synchronizing the platform with motion measurements makes the mechanical interpretation testable.

A ground-plane transformation of a measured contact wrench combines a change of coordinate axes with a change of the point about which moments are reported. A six-component wrench is incomplete without both pieces of metadata. Drake's primary SpatialForce reference explicitly tracks the application point and expressed-in frame separately from the stored force and torque values.^[ref]

Let $R$ rotate sensor-frame components into ground-frame components, and let $p$ be the ground-frame vector from ground origin $O$ to sensor origin $S$. For measured force $f_S$ and moment $M_S$ about $S$, the equivalent result about $O$ isThe plus sign uses the stated vector from the new origin to the old one. A shift expressed with the opposite vector uses the opposite sign. The offset and force must be expressed in the same axes before taking the cross product.

For a planar normal-pressure reconstruction with $f_{G,z}>0$, computeThe special parallel-axis height correction in center of pressure is recovered with $p=(0,0,h)$ and $R=I$.

For an original rotated-sensor example, use a 90-degree rotation about $z$, sensor readings $f_S=(10,0,100)\mathrm{N}$ and $M_S=(1,2,3)\mathrm{N}\mathrm{m}$, and $p=(0.05,-0.02,0.10)\mathrm{m}$. Rotation gives $f_G=(0,10,100)\mathrm{N}$ and $R{M}_S=(-2,1,3)\mathrm{N}\mathrm{m}$. The translated moment is $M_O=(-5,-4,3.5)\mathrm{N}\mathrm{m}$, yielding $(x_P,y_P)=(0.040,-0.050)\mathrm{m}$. The yaw moment remaining at that point is $3.1\mathrm{N}\mathrm{m}$, so translating to the centroid does not erase the entire wrench.

A bench check applies known loads at known ground locations and repeats after changing sensor orientation. Geometry, tare loads, units and axis signs must all be included. A correct rotation with the wrong moment origin can still give an incorrect pressure location; a small normal load also amplifies reconstruction uncertainty.