Modelling the dynamic margins of stability for use in evaluations of balance following a support-surface perturbation

The dynamic margin of stability provides a method that captures the center of mass (CoM) state (position-velocity) in relation to the base of support (BoS). However, the model upon which this concept was derived does not consider how the inertial characteristics of forced support-surface perturbations would influence balance control. Within the current article, the inverted pendulum model was restructured to account for fixed, piecewise accelerations of the BoS. From this logic, two variations of the adjusted margin of stability, each maintaining a similar definition of extrapolated CoM, are proposed; one ignoring horizontal ground contact and inertial forces applied to the BoS, the other incorporating these forces. Unique within the proposed models is the time-variant BoS boundaries that depend on the perturbation applied. Verification of the solution for each model is provided, along with a comparison of obtained values to previous methods of defining CoM position-velocity stability metrics using a computational model and optimal control. For the simpler model variation (ignoring forces), we also assessed how CoM position and perturbation parameter selection over/underestimate the predicted maximal permissible velocity. The results of these analyses suggest that factors which increase the acceleration impulse decrease the difference between the two models; the opposite was observed for factors increasing displacements between the CoM and BoS boundary. Lastly, use of the proposed adjusted margin of stability within an experimental data set highlights the ability of our model to predict instability (stepping strategies; negative margin of stability) relative to the use of the extrapolated CoM alone.