For a legged robot external force/moments may arise from gravity, ground contacts, additional contacts and interactions, or unexpected disturbances. The essence of our approach is schematically described in the figure below for a biped robot on a horizontal ground.

If the line of action of the GRF in Fig. b is linearly shifted, a time will come when the GRF will actually pass through the CoM. The point A on the ground through which this imaginary GRF now passes is called the centroidal moment pivot (CMP) point. The distance AP is a measure of rotational instability of the robot.

Human beings do not have a direct control over GRF but must modulate it through dynamic coupling. This coupling is performed rather judiciously to take advantage of gravity. In normal walking, depending on the part of the gait cycle, the GRF may or may not pass through the CoM. There are interesting human movement examples, such as the take-off phase of forward running somersault, in which GRF is deliberately shifted to an off-centroid direction. This is useful in creating a large rotational instability which is what is precisely required for the task.

Note that AP, the distance between CMP and CoP, is a measure of instability. It is meant to be primarily used as an analysis tool. It may be used as a control criteria with the following caveat. We, by no means, imply that to control CMP necessarily means to bring it to coincide with the CoP. In fact, a controller attempting to achieve this objective is likely to result in a rigid and restrictive gait. The fluidity of the human gait seems to come mostly from its cyclic regime of deliberate push to instability and a stability recapture.

The following figure shows the relationships between a few ground reference points pertaining to the dynamics and balance of humanoid robots.