Centroidal Moment Pivot

The point where a line through the center of mass, parallel to the ground-reaction force, meets the ground.

The centroidal moment pivot was introduced by Herr, Hofmann, and Popovic around 2003–2004 (Goswami and colleagues independently proposed the same point), and a 2005 IJRR paper unified the definition: draw a line through the center of mass parallel to the ground-reaction force, and its intersection with the ground is the CMP. If the ground-reaction force happens to pass exactly through the center of mass — producing zero moment about it — the CMP coincides with the zero moment point; whenever the two separate, it means the body is experiencing a moment about its center of mass and its overall angular momentum is changing, with the separation distance equal to the moment's horizontal component divided by the vertical component of the ground-reaction force. Unlike the zero moment point, the CMP is not restricted to stay inside the support region, which makes it useful for describing balance strategies — like swinging an arm or twisting the torso — that rely on angular momentum.

ExamplePopovic and colleagues measured normal human walking on level ground and found the CMP never left the support region, staying only about 14% of a foot length away from the zero moment point on average — evidence that humans keep the angular momentum about their center of mass tightly controlled while walking.

Also called

CMP

Related

Zero Moment Point · Center of Pressure (CoP) · Angular Momentum · Capture Point · Centroidal Dynamics · Push Recovery

Sources

Popovic, Goswami, Herr: Ground Reference Points in Legged Locomotion（IntechOpen 开放获取版） (Chinese)
Popovic, Goswami, Herr: Ground Reference Points in Legged Locomotion (IJRR, 2005)