## 3 Results
Raw values of these stability metrics were compared directly with ellipsoid volume to highlight phase-independent trends across conditions (Figure 7). This figure plots ellipsoid volume on the left \(y\)-axis against each of the other six metrics on the right \(y\)-axis for subplots A through F, respectively: Lyapunov exponent, local dynamic stability, Hurst exponent, sample entropy, maximum Floquet multiplier, and Poincare variance. Across all subplots, conditions such as HighLater and HighLatest exhibited elevated values for both ellipsoid volume and the paired metric, particularly during early-to-mid stance, consistent with the phase-specific variability peaks observed in Figure 3A. For instance, HighLater showed the highest raw ellipsoid volume (99,937 mm\({}^{3}\)/s\({}^{3}\)) alongside a local dynamic stability value of 0.092, reinforcing the destabilizing effect of high-magnitude, late-timed torque. At the same time, PowerOff consistently displayed the lowest values across metrics, with an  
Figure 6: **Z-scores and correlations of gait stability metrics across twelve walking conditions. ** (**A**) Z-scores of ellipsoid volume, Lyapunov exponent, local dynamic stability, Hurst exponent, sample entropy, maximum Floquet multiplier, and Poincaré variance, all computed relative to the NoExo condition. The legend identifies each metric. (**B**) Pearson correlation coefficients (r) between ellipsoid volume and each of the six alternative stability metrics. (**C**) Corresponding \(p\)-values for these correlations across conditions. ellipsoid volume of 47,285 mm\({}^{3}\)/s\({}^{3}\) and a local dynamic stability value of 0.039, reflecting its stabilizing but metabolically costly nature. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Condition**} & \multirow{3}{*}{**Ellipsoid (mm\({}^{3}\)/s\({}^{3}\))**} & \multicolumn{6}{c}{**Variability (mm/s)**} \\ \cline{2-9}  & & \multicolumn{2}{c}{**Anteroposterior (AP)**} & \multicolumn{2}{c}{**Mediolateral (ML)**} & \multicolumn{2}{c}{**Vertical (VT)**} \\ \cline{2-9}  & \multicolumn{2}{c}{**CI**} & \multicolumn{2}{c}{**CI**} & \multicolumn{2}{c}{**CI**} & \multicolumn{2}{c}{**CI**} \\ \hline
**Low Early** & 72,385.14 & 74,342.55 & 14.30 & 38.32 & 21.13 & 50.41 & 9.95 & 40.23 \\ \hline
**Low Earlier** & 62,600.66 & 62,657.68 & 13.43 & 34.61 & 19.81 & 51.82 & 8.28 & 39.24 \\ \hline
**Low Mid** & 70,521.85 & 70,600.06 & 11.56 & 35.63 & 19.85 & 49.10 & 8.14 & 43.66 \\ \hline
**Low Later** & 78,548.18 & 78,576.63 & 14.06 & 35.21 & 21.03 & 49.81 & 8.65 & 45.68 \\ \hline
**Low Latest** & 69,858.14 & 69,902.69 & 13.32 & 36.15 & 19.74 & 46.41 & 8.79 & 41.56 \\ \hline
**High Early** & 67,194.32 & 67,251.67 & 13.22 & 31.70 & 22.03 & 49.40 & 8.11 & 39.49 \\ \hline
**High Earlier** & 64,386.53 & 64,431.67 & 12.64 & 33.25 & 21.18 & 51.36 & 8.53 & 36.37 \\ \hline
**High Mid** & 72,614.53 & 72,673.19 & 12.17 & 35.07 & 21.32 & 48.54 & 9.86 & 43.96 \\ \hline
**High Later** & 99,915.70 & 99,959.18 & 13.66 & 35.34 & 26.15 & 59.74 & 8.73 & 47.25 \\ \hline
**High Latest** & 71,921.06 & 71,982.23 & 12.20 & 34.32 & 22.39 & 52.82 & 8.61 & 37.81 \\ \hline
**No Exo** & 52,053.73 & 52,139.39 & 9.91 & 26.88 & 18.66 & 57.82 & 6.55 & 35.82 \\ \hline
**Power Off** & 47,259.04 & 47,311.88 & 10.43 & 30.68 & 17.41 & 47.19 & 7.86 & 33.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: 95% confidence intervals (CIs) for gait stability metrics across powered, unpowered, and baseline walking conditions. Confidence intervals are provided for ellipsoid volume, mediolateral variability, anteroposterior variability, and vertical variability. These intervals help interpret the precision of the observed differences and complement the \(p\)-values reported in Table 1.  
Figure 7: **Raw values of gait stability metrics compared to ellipsoid volume across twelve walking conditions. Each subplot displays ellipsoid volume (left \(y\)-axis) alongside a secondary stability metric (right \(y\)-axis), allowing for visual comparison of condition-specific trends. (A) Lyapunov exponent.