## 4 Discussion
Correlation analysis in Figure 6B further underscores this trend, with ellipsoid volume showing weak and non-significant correlations with Lyapunov exponent (r = 0.29, \(p\) = 0.41 in HighLatest; r = 0.37, \(p\) = 0.29 in HighLater) and sample entropy (r = \(-\)0.21, \(p\) = 0.55 in HighLater; r = \(-\)0.18, \(p\) = 0.62 in HighLatest), contrasting with the strong correlations (r \(\geq\) 0.65) observed for total variability (Figure 5C). This discrepancy highlights the gait tube method's strength in capturing multidimensional variability. At the same time, individual metrics like Lyapunov exponents may be more sensitive to specific perturbation responses, as noted in studies of exoskeleton-assisted gait where short-term Lyapunov exponents showed variable responses to torque assistance depending on stride length and timing adaptations [43; 44]. The reduced sensitivity of Hurst exponent, Lyapunov exponent, sample entropy, and maximum Floquet multiplier in this dataset may stem from their dependence on longer time series for reliable estimation, which could be limited by the short adaptation period (\(\sim\)4 min) per condition, potentially  
masking condition-specific effects as observed in other studies with extended walking trials [45; 46]. From a computational standpoint, gait tube analysis requires high-quality, time-normalized kinematic data and the construction of covariance matrices and ellipsoids at each phase, making it more resource-intensive than scalar metrics like MOS or Lyapunov exponents. However, this additional complexity allows for richer phase-specific insights and the visualization of multidimensional COM variability that event-based methods cannot provide. Practically, the gait tube method may not yet be well suited for real-time applications or clinical environments without automation and streamlined preprocessing tools. Nevertheless, its intuitive 3D visual outputs and potential to capture subtle stability changes make it a powerful complement to traditional metrics in research and potentially in high-resolution rehabilitation contexts. The raw value comparisons in Figure 7 further illustrate condition-specific trends, with HighLater's peak ellipsoid volume (99,937 mm\({}^{3}\)/s\({}^{3}\)) coinciding with elevated local dynamic stability (0.092), consistent with the gait tube method's indication of destabilization during early-to-mid stance (Figure 3A), while PowerOff's low values (e.g., ellipsoid volume at 47,285 mm\({}^{3}\)/s\({}^{3}\), local dynamic stability at 0.039) mirror its reduced ML variability (\(p\) = 0.0488, Figure 4B), reflecting a stabilizing effect of passive structure. In contrast, metrics like sample entropy and maximum Floquet multiplier showed limited variation across conditions (e.g., sample entropy: 0.83 in HighLatest vs. 0.84 in NoExo; maximum Floquet multiplier: 1.0616 in HighLatest vs. 1.0665 in NoExo), reinforcing their relative insensitivity to the exoskeleton conditions in this study. These findings align with prior research showing that passive exoskeletons can constrain lateral dynamics at a metabolic cost [4; 47; 48]. Still, they also underscore the gait tube method's advantage in resolving phase-specific effects that raw value averages may obscure, as supported by studies highlighting the importance of temporal resolution in stability analysis [49]. Moreover, studies using short-term Lyapunov exponents and Floquet multipliers have reported similar increases in local dynamic stability under high-torque assistance during stance transitions, corroborating our observations [50]. Yet, the lack of sensitivity in Hurst exponent and sample entropy may be attributed to their sensitivity to noise and short data lengths, which can dilute condition-specific effects in controlled treadmill settings [51; 52].