## 2 Materials and Methods
### Statistical Analyses  
To evaluate the effects of exoskeleton assistance on gait stability, non-parametric Wilcoxon signed-rank tests were used to compare each of the ten powered conditions and the PowerOff condition to the NoExo condition across multiple gait stability metrics [14; 27]. Phase-dependent comparisons were performed at each of the 100 normalized points across the gait cycle. For each participant and condition, ellipsoid volumes were smoothed using a five-point moving window, and differences from the NoExo condition were assessed at each time point using paired Wilcoxon tests. The minimum _p_-value across the cycle was recorded for each condition to summarize statistically significant deviations. To reduce the risk of false positives, we interpreted significant effects only if they persisted across multiple contiguous gait phases. For ellipsoid volume, phase-dependent comparisons were performed at each of the 100 normalized gait cycle points. Per-subject ellipsoid volumes were calculated using a five-point sliding window to smooth temporal variations, and pairwise comparisons were conducted at each phase. This window size (5% of the gait cycle) was chosen based on sliding-window practices in cyclic human movement analyses, which recommend small windows (\(\approx\)5% of the cycle) to balance noise reduction and temporal resolution [28]. It preserves meaningful phase-specific trends while attenuating high-frequency fluctuations that could obscure short-duration effects [28]. Larger windows were avoided to prevent over-smoothing of critical transient changes in gait stability [28]. The minimum _p_-value across the cycle was recorded to summarize condition-wise deviations from the reference (NoExo). To account for multiple comparisons across 100 gait phases, we applied a temporal clustering approach. Specifically, a condition was only considered statistically different from the NoExo reference if significant _p_-values (_p_ < 0.05) occurred across at least five consecutive gait points. This method balances sensitivity to  
Figure 2: **Gait tubes were pooled across subjects under NoExo walking condition. (A) Three-dimensional view of the center of mass (COM) velocity trajectories in velocity state space. (B) Sagittal view showing COM vertical versus anteroposterior components. (C) Transverse view showing COM mediolateral versus anteroposterior components. (D) The frontal view shows COM mediolateral versus vertical components. The NoExo condition is shown as a bold dashed line. Ellipsoids were computed at each gait phase and plotted to represent local variability in COM velocity across strides.**phase-dependent effects with control of family-wise error rate and has been applied in prior studies analyzing time-normalized biomechanical data. Direction-specific variability in the ML, AP, and VT directions was assessed by computing the standard deviation of stride-to-stride COM velocity for each axis, averaged across the gait cycle. These variability values were compared to the NoExo condition using the Wilcoxon signed-rank test. A total variability metric, defined as the sum of ML, AP, and VT variances, was also compared using the same statistical approach. To quantify the relationship between multidimensional ellipsoid volume and total linear variability, Pearson correlation coefficients (r) and associated \(p\)-values were calculated for each condition, providing insight into the consistency of variability patterns across metrics. All statistical analyses were implemented in MATLAB (MathWorks, Natick, MA, USA) using custom scripts, with a significance threshold of 0.05. Raw \(p\)-values for each metric were tabulated, and results were visualized using bar plots and phase-dependent line plots annotated with statistical significance. This approach ensured robust comparisons across conditions, accounting for the non-normal distribution of variability metrics and the paired nature of the experimental design.