Rethinking margin of stability: Incorporating step-to-step regulation to resolve the paradox

Derived from inverted pendulum dynamics, mediolateral Margin of Stability (MoS_ML) is a mechanically-grounded measure of instantaneous frontal-plane stability. However, average MoS_ML measures yield paradoxical results. Gait pathologies or perturbations often induce larger (supposedly "more stable") average MoS_ML, despite clearly destabilizing factors. However, people do not walk "on average" - they walk (and sometimes lose balance) one step at a time. We assert the paradox arises because averaging MoS_ML discards crucial step-to-step dynamics. We present a framework unifying the inverted pendulum with Goal-Equivalent Manifold (GEM) analyses. We identify in the pendulum's center-of-mass dynamics constant-MoS_ML manifolds, including one candidate "stability GEM" signifying the goal to maintain some constant MoS_ML^∗. We used this framework to assess step-to-step MoS_ML dynamics of humans walking in destabilizing environments. While goal-relevant deviations were readily corrected, people did not exploit equifinality by allowing deviations to persist along this GEM. Thus, maintaining a constant MoS_ML^∗ is inconsistent with observed step-to-step fluctuations in center-of-mass states. Conversely, the extent to which participants regulated fluctuations in mediolateral foot placements strongly predicted their regulation of center-of-mass fluctuations. Thus, center-of-mass dynamics may arise indirectly as a consequence of regulating mediolateral foot placements. To help resolve the paradox caused by averaging MoS_ML, we present a new statistic, Probability of Instability (PoI_L), used here to predict lateral instability likelihood. Participants exhibited increased PoI_L when destabilized (p = 9.45 × 10^-34), despite exhibiting larger ("more stable") average MoS_ML (p = 1.70 × 10^-15). Thus, PoI_L correctly captured people's increased risk of losing lateral balance, whereas average MoS_ML did not. PoI_L also helps explain why people's average MoS_ML increased in destabilizing contexts.