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

Derived from inverted pendulum dynamics, mediolateral Margin of Stability (MoS) is a mechanically-grounded measure of instantaneous frontal-plane stability. However, average MoS measures yield paradoxical results. Gait pathologies or perturbations often induce larger (supposedly "more stable") average MoS, 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 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 manifolds, including one candidate "stability GEM" signifying the goal to maintain some constant MoS. We used this framework to assess step-to-step MoS 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 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, we present a new statistic, Probability of Instability (PoI), used here to predict lateral instability likelihood. Participants exhibited increased PoI when destabilized (p = 9.45 × 10), despite exhibiting larger ("more stable") average MoS (p = 1.70 × 10). Thus, PoI correctly captured people's increased risk of losing lateral balance, whereas average MoS did not. PoI also helps explain why people's average MoS increased in destabilizing contexts.