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

In human walking, linear and angular momentum follow quasi-periodic functions with similar periodicity and phase.

• This observation was central to the theoretical framework linking CoP-to-CoM distance with horizontal ground reaction forces.
• The quasi-periodic nature of both linear and angular momentum with similar periodicity and phase is a key mechanical condition enabling simultaneous control.
• This finding was derived from both theoretical analysis and experimental data of participants walking at normal and slow speeds.

CoP shifts do not cause changes in linear CoM momentum but do cause changes in whole-body angular momentum.

• This mechanical relationship is established from the equations of linear and rotational motion for a system of linked rigid segments.
• Previous studies that linked deviations in linear momentum to subsequent CoP shifts had mechanically misattributed the effect of CoP shifts.
• The horizontal distance between CoP and CoM should be correlated to horizontal force in the corresponding direction when linear and angular momentum are quasi-periodic with similar periodicity and phase.

Deviations in horizontal ground reaction forces could be predicted from deviations in the preceding linear momentum in experimental walking data.

• Regression models were fitted to experimental data of participants walking at normal and slow speeds.
• The models predicted deviations in horizontal ground reaction forces from deviations in preceding linear momentum.
• This predictive relationship was observed across both normal and slow walking speeds.

Deviations in moments of the ground reaction force about the sagittal and transverse axes could be predicted from deviations in preceding angular momentum.

• Regression models fitted to experimental data demonstrated that ground reaction force moments about the sagittal and transverse axes were predictable from angular momentum deviations.
• This was observed for participants walking at both normal and slow speeds.
• The finding supports simultaneous control of both linear and angular momentum during human walking.

The theoretical framework combining equations of linear and rotational motion explains the success of preceding studies that correlated CoM states to CoP or foot locations.

• When linear and angular momentum are quasi-periodic with similar periodicity and phase, the horizontal CoP-to-CoM distance is mathematically correlated to horizontal force.
• This mechanical relationship provides a unifying explanation for why CoP-relative-to-CoM correlations with linear momentum have appeared stabilizing in prior literature.
• The authors conclude this may explain 'the success of preceding studies that correlated CoM states to CoP or foot locations.'

The analyses support that linear and angular momentum are indeed simultaneously controlled in human walking.

• Both theoretical derivation and experimental regression analyses converged on this conclusion.
• Participants walked at normal and slow speeds, providing evidence across locomotion conditions.
• The simultaneous control framework reconciles the mechanical reality that CoP shifts affect angular rather than linear momentum with the empirical success of CoM-based control models.