## 3 Results
This increased dispersion was quantified by greater ellipsoid volumes, with powered conditions exhibiting an average volume of 75,232 mm\({}^{3}\)/s\({}^{3}\), compared to 52,097 mm\({}^{3}\)/s\({}^{3}\) in the NoExo condition and 47,285 mm\({}^{3}\)/s\({}^{3}\) in the PowerOff condition. Additionally, vertical variability (standard deviation of vertical COM velocity) was consistently higher in powered conditions, particularly during early-to-mid stance phases (see Table 1). These quantitative differences reflect greater stride-to-stride deviations in COM control during exoskeleton-assisted walking. Figure 3: **Phase-dependent metrics and supporting signals across walking conditions. ****(A)** Phase-dependent ellipsoid volumes across the gait cycle for all walking conditions. Based on Wilcoxon signed-rank tests, statistically significant differences from the NoExo condition are indicated by corresponding _p_-values in the legend. (**B**) Torque assistance profiles for powered conditions, showing the magnitude and timing of applied hip torque. (**C**) Mean normalized ground reaction force (GRF) trajectories averaged across subjects and strides in the anteroposterior, mediolateral, and vertical directions. Figure 4: **Summary of gait tube metrics averaged across the gait cycle. (A) Mean ellipsoid volume. (B) Mediolateral variability. (C) Anteroposterior variability. (D) Vertical variability. Bars represent condition-wise means across subjects, and error bars indicate standard deviations. Statistical significance is determined using Wilcoxon signed-rank tests relative to the NoExo condition. **  
Figure 5: **Summary of variability metrics and correlations across walking conditions. (A) Raw values of ellipsoid volume and total variability for each condition. (B) Z-scores computed relative to the NoExo condition for both metrics. (C) Pearson correlation coefficients (r-values) and corresponding \(p\)-values comparing ellipsoid volume and total variability across conditions. Dashed bars indicate reference conditions (NoExo and PowerOff). **  
In addition to the reported \(p\)-values in Table 1, we provide 95% confidence intervals for the main stability metrics in Table 2 to further clarify the range and reliability of condition-wise differences. To further elucidate the impact of hip exoskeleton assistance on multidimensional gait stability, z-scores and correlations of additional stability metrics were analyzed across all conditions (Figure 6). Figure 6A presents the z-scores of seven gait stability  
\begin{table}
\begin{tabular}{p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt} p{11.3 pt}} \hline \hline  & & & & & & & & & & & & & & & \\ \cline{3-14} \multicolumn{1}{c}{**Ellipsoid**} & \multicolumn{1}{c}{**Anteroposterior (AP)**} & \multicolumn{1}{c}{**Mediolateral (ML)**} & \multicolumn{1}{c}{**Vertical (VT)**} & \multicolumn{1}{c}{**Total (Ap+ ML+ VT)**} & \multicolumn{1}{c}{**Correlation**} \\ \hline  & & & & & & & & & & & & & \\ \cline{3-14} \multicolumn{1}{c}{**Correlationmetrics--ellipsoid volume, Lyapunov exponent, local dynamic stability, Hurst exponent, sample entropy, maximum Floquet multiplier, and Poincare variance--relative to the NoExo condition, revealing that powered conditions like HighLater and HighLatest exhibited distinct variability patterns, with z-scores peaking for ellipsoid volume in HighLater (z = 2.33) and for local dynamic stability in HighLatest (z = 1.30). Figure 6B,C display the correlation coefficients (r) and corresponding \(p\)-values between ellipsoid volume and the other six metrics, demonstrating varied relationships across conditions; for instance, the correlation for Lyapunov exponent in HighLatest was moderate (r = 0.29, \(p\) = 0.41), and for sample entropy in HighLater, it was weakly negative (r = \(-\)0.21, \(p\) = 0.55), indicating that these relationships were not statistically significant and highlighting the complexity of stability interactions under exoskeleton assistance.