Simultaneous stabilizing feedback control of linear and angular momentum in human walking

Stabilizing bipedal gait is mechanically challenging. To analyze how gait is stabilized, previous studies have focused on the control of the body center of mass (CoM). These studies often linked deviations in linear momentum of the CoM to subsequent shifts in position of the center of pressure (CoP), or of the foot, relative to the COM, and interpreted these as stabilizing responses to correct linear CoM momentum. Mechanically, however, CoP shifts do not cause changes of linear CoM momentum, whereas they do cause changes in whole-body angular momentum. We hypothesized that experimentally observed correlations between CoP to CoM distance and horizontal ground reaction forces are related to the need to control both linear and whole-body angular momentum. We show that, in human walking, linear and angular momentum follow quasi-periodic functions with similar periodicity and phase. Combining the equations of linear and rotational motion for a system of linked rigid segments shows that, in this case, the horizontal distance between CoP and CoM should be correlated to horizontal force in the corresponding direction. This suggests that linear and angular momentum are simultaneously controlled and may explain the success of preceding studies that correlated CoM states to CoP or foot locations. Regression models fitted to experimental data of participants walking at normal and slow speeds showed that deviations in horizontal ground reaction forces and in moments of the ground reaction force about the sagittal and transverse axes could be predicted from deviations in the preceding linear and angular momentum respectively. Our analyses support that linear and angular momentum are indeed controlled simultaneously in human walking.