## 4 Discussion  
This study aimed to investigate how hip exoskeleton assistance affects phase-dependent gait stability using gait tube analysis. We hypothesized that exoskeleton torque, particularly when applied with high magnitude and during late stance, would increase gait variability, with peak effects expected near 50-60% of the gait cycle. Additionally, we anticipated that ellipsoid volume would serve as a valid multidimensional metric for detecting subtle and temporally localized changes in gait stability. Our results revealed that the greatest variability occurred earlier than expected, primarily during early-to-mid stance (10-50%), with distinct peaks in ellipsoid volume observed during initial contact and toe-off (Figure 3A). These phases correspond to transitions between double and single limb support, where the COM trajectory and base of support rapidly shift [3; 29]. These findings are supported by vertical ground reaction force patterns in Figure 3C, suggesting that foot-ground contact events are key phases where gait stability is challenged [3; 29]. This earlier-than-expected variability peak may reflect biomechanical instability during weight acceptance and early single-limb support, where the body transitions from double to single support while managing vertical loading. These phases are characterized by rapid changes in limb stiffness, postural control demands, and motor coordination. Additionally, participants may have made anticipatory or compensatory adjustments in response to the onset of hip assistance, which could increase variability earlier in the cycle than the torque peak itself. These findings suggest that exoskeleton-induced perturbations can influence gait stability not only at the moment of maximal assistance but also during preceding preparatory phases when balance demands are already elevated. These early-to-mid stance increases in variability may reflect biomechanical challenges during weight acceptance and transition from double to single limb support. During these phases, the body's center of mass rapidly shifts over the stance limb while absorbing impact forces and maintaining forward progression. The presence of assistive torque from the hip exoskeleton may disrupt the natural timing and coordination of joint moments, thereby amplifying vertical excursions and postural adjustments. The observed increase in VT, particularly in conditions with late or high-magnitude torque, suggests a potential destabilizing effect on vertical balance control mechanisms, which are critical for trunk and head stabilization. These findings indicate that early stance is a sensitive period for stability disruptions under powered assistance and should be considered when designing exoskeleton controllers that adapt torque delivery in a phase-specific manner. This temporal pattern reinforces the rationale for traditional stability metrics like MOS being calculated at heel strikes [3; 30]. This timing corresponds to key biomechanical transitions within the gait cycle. Between 10% and 30%, the body transitions from double to single limb support, requiring coordinated control of vertical and lateral ground reaction forces--critical for maintaining trunk and head stability during weight acceptance and limb stiffness modulation [31; 32; 33]. During this phase, lower limb joints adjust stiffness to manage vertical loading and ensure smooth progression. The addition of hip torque assistance may alter typical joint moment patterns, introducing instability prior to the peak torque application later in the cycle [31; 32; 33]. From 30% to 50%, the limb continues weight support while preparing for push-off, a phase that is biomechanically sensitive to force and coordination perturbations [31; 32; 33]. These findings indicate that phase-specific adjustments in ground reaction force modulation and neuromuscular control underlie the observed early-to-mid stance variability, and they highlight that assistive torque strategies should consider stability demands beginning earlier in the gait cycle than traditionally expected.