The ‘extrapolated center of mass’ concept suggests a simple control of balance in walking

Next to position x and velocity v of the whole body center of mass (CoM) the ‘extrapolated center of mass’ (XcoM) can be introduced: ξ = x + v/ω0, where ω0 is a constant related to stature. Based on the inverted pendulum model of balance, the XcoM enables to formulate the requirements for stable walking in a relatively simple form. In a very simple walking model, with the effects of foot roll-over neglected, the trajectory of the XcoM is a succession of straight lines, directed in the line from center of pressure (CoP) to the XcoM at the time of foot contact. The CoM follows the XcoM in a more sinusoidal trajectory. A simple rule is sufficient for stable walking: at foot placement the CoP should be placed at a certain distance behind and outward of the XcoM at the time of foot contact. In practice this means that a disturbance which results in a CoM velocity change Δv can be compensated by a change in foot position (CoP) equal to Δv/ω0 in the same direction. Similar simple rules could be formulated for starting and stopping and for making a turn.