## 4 Discussion
This suggests that while powered assistance amplifies COM variability, particularly during early-to-mid stance, it may simultaneously alleviate muscular effort, potentially at the expense of stability. Conversely, the PowerOff condition, with the lowest ellipsoid volume (47,285 mm\({}^{3}\)/s\({}^{3}\)) and reduced ML variability (\(p\) = 0.0488), showed a higher metabolic cost, likely due to the added inertia of the passive exoskeleton constraining natural gait dynamics [4]. The strong correlations between ellipsoid volume and total variability (r \(\geq\) 0.65) across conditions further indicate that metabolic cost reductions may be linked to increased multidimensional variability, highlighting a trade-off between energy efficiency and dynamic stability. These findings underscore the need for exoskeleton controllers to balance metabolic benefits with stability requirements, particularly by optimizing torque timing to minimize variability during critical stance phases, enhancing safety and efficacy in rehabilitation and performance applications. Based on these findings, we recommend that exoskeleton controllers incorporate phase-specific modulation strategies to reduce torque during early stance (10-30%), where vertical variability was elevated, and apply assistance more conservatively during mid-stance transitions. Adaptive controllers that monitor real-time stability indicators--such as vertical COM fluctuations or variability thresholds--could dynamically adjust torque delivery to prioritize safety without fully sacrificing energetic gains. This phase-aware approach may be particularly beneficial for clinical populations who are more sensitive to balance perturbations. From a biomechanical perspective, vertical COM control is closely linked to managing ground reaction forces, trunk posture, and head stabilization during stance. The increased VT variability observed under powered conditions may reflect perturbations in the force generation and absorption mechanisms responsible for smooth vertical motion. Hip torque assistance--especially during push-off--can alter leg stiffness and disrupt the neuromuscular coordination of proximal and distal joints, amplifying fluctuations in vertical displacement. This result suggests that exoskeleton designs should consider how vertical force control is affected during late stance to avoid destabilizing the upper body. Notably, vertical ground reaction force analysis during powered exoskeleton walking has shown distinctive loading patterns in such devices, linking vertical loading control to stability maintenance [40; 41; 42]. Moreover, studies modeling the vertical stiffness of the hip and knee during gait demonstrate that vertical stiffness varies significantly across the gait cycle and is critical for attenuating vertical oscillations [40]. Figures 6 and 7 extend the gait tube analysis by incorporating a broader suite of dynamical stability metrics, revealing nuanced patterns that complement and contrast with the phase-specific variability observed in ellipsoid volumes (Figures 1-3). The z-scores in Figure 6A show that powered conditions like HighLater (z = 2.33 for ellipsoid volume, z = \(-\)0.34 for local dynamic stability) and HighLatest (z = 0.21 for ellipsoid volume, z = 1.30 for local dynamic stability) amplified variability in ellipsoid volume and local dynamic stability, aligning with the gait tube findings of heightened VT variability during early-to-mid stance (\(p\leq\) 0.0059, Figure 4D). In contrast, metrics like Hurst exponent (z = 0.12 in HighLater, z = 0.40 in HighLatest), sample entropy (z = \(-\)1.01 in HighLater, z = \(-\)0.16 in HighLatest), and maximum Floquet multiplier (z = \(-\)0.29 in HighLater, z = \(-\)0.30 in HighLatest) exhibited minimal deviation across conditions, indicating lower sensitivity to exoskeleton assistance.