## 3 Results  
Multidimensional gait tubes, constructed by pooling strides across all participants for each condition, provided a comprehensive visualization of COM dynamics (Figure 1). Compared to the NoExo and PowerOff conditions, powered conditions exhibited more dispersed trajectories, particularly in the vertical (Vy) and mediolateral (Vz) directions. This dispersion was most pronounced during late stance phases (50-60% of the gait cycle), aligning with the timing of peak torque application in powered conditions (Figure 1). Phase-specific ellipsoid volumes confirmed that variability evolved dynamically over the gait cycle and was modulated by the exoskeleton's torque assistance profile (Figure 3A). Most powered conditions exhibited elevated variability during early and mid-stance phases (10-50% of the gait cycle) compared to NoExo. For instance, HighLater and HighLatest showed prominent peaks in ellipsoid volume between 10 and 50%, corresponding to their respective torque profiles (Figure 3B). Statistical significance (Wilcoxon signed-rank test) was indicated by \(p\)-values in the legend, with significant differences from NoExo observed for most powered conditions (\(p<0.05\)). Ground reaction force (GRF) trajectories, normalized to body weight, remained consistent across conditions in the anteroposterior, mediolateral, and vertical directions (Figure 3C), suggesting that changes in variability were not driven by altered external loading but rather by the exoskeleton's assistive torque. Group-level comparisons revealed that all powered and PowerOff conditions led to significantly different mean ellipsoid volumes than NoExo (\(p<0.05\)). The HighLater condition exhibited the most excellent mean ellipsoid volume (99,937 mm\({}^{3}\)/s\({}^{3}\); z = 2.3), indicating heightened variability, whereas PowerOff yielded the lowest (47,285 mm\({}^{3}\)/s\({}^{3}\); z = \(-1.7\)), reflecting constrained trajectories in the absence of active assistance (Figure 4A). Across directional components, vertical variability (VT) was consistently elevated under powered conditions, with 11 of 12 comparisons reaching significance (\(p\leq 0.0059\)). In contrast, ML and AP variability showed condition-specific responses. HighLater was the only powered condition with significantly increased AP variability (\(p=0.0371\)), while PowerOff was the only condition with significantly reduced ML variability (\(p=0.0488\)) (Figure 4B-D). These findings suggest that VT is particularly sensitive to the presence and timing of exoskeleton assistance. Z-scores and Pearson correlation coefficients were calculated between ellipsoid volume and total variability (sum of ML, AP, and VT variances) to evaluate the alignment between multidimensional and univariate variability measures. Z-scores were positive in most powered trials, indicating increased variability relative to NoExo (Figure 5B). Correlationanalysis revealed strong associations (r \(\geq\) 0.65, \(p\) < 0.05) between ellipsoid volume and total variability in all but one powered condition, with the strongest relationship observed in HighLatest (r = 0.91, \(p\) = 0.0002) (Figure 5C). These results confirm that ellipsoid volume is a robust surrogate for summarizing total variability under varying assistance conditions. Figure 5A presents raw values of ellipsoid volume and total variability, while Figures 5B and 4C show z-scores and correlation coefficients, respectively, with dashed bars indicating reference conditions (NoExo and PowerOff). A comprehensive summary of extracted metrics is provided in Table 1, including ellipsoid volumes, direction-specific variability (AP, ML, VT), z-scores, statistical significance, correlation results, and metabolic cost [4]. Consistent with visual data, HighLater and HighLatest emerged as the most variable conditions, while PowerOff exhibited the most constrained trajectories. The table quantitatively reinforces the trends observed in Figures 1-5, offering a detailed overview of how exoskeleton assistance modulates gait variability across the gait cycle.