Non-normal operators underlying legged locomotor dynamics resolve the local/global stability paradox

Locomotor dynamics present a fundamental modeling paradox: while local stability analyses suggest that legged locomotion is dynamically unstable, humans and animals maintain global stability and rarely fall under typical circumstances. We resolve this apparent contradiction by modeling locomotor dynamics as non-normal linear systems using dynamic mode decomposition (DMD) models. In non-normal systems, nearly parallel dynamical modes create transient energy amplifications that can lead to effective instabilities, despite the system exhibiting global stability at longer timescales. Analyzing human gait data from able-bodied individuals and stroke survivors, we find that pathological walking patterns exhibit stronger mode overlaps, leading to greater energy amplification from motor commands, but also larger transient instabilities that bring the system closer to failure under perturbation. Standard analysis tools fundamentally misidentify these structures because they assume normal dynamics. We demonstrate the effectiveness of alternative decomposition methods that correctly capture the relevant dynamical structures in both simulated and real locomotor data, providing a framework for understanding neural control strategies and predicting fall risk and rehabilitation strategies in clinical populations.