## 1 Introduction  
Falls due to gait instability are a leading cause of injury, costing billions annually and limiting mobility for millions, particularly among aging and clinical populations [1, 2, 3]. With advancements in wearable robotics, hip exoskeletons have emerged as promising tools to augment locomotion by providing targeted joint torque assistance, benefiting healthy individuals and those with mobility impairments [4, 5]. These devices aim to enhance gait performance, reduce metabolic cost, and support rehabilitation by assisting hip extension, a critical component of walking that accounts for up to 45% of mechanical power [2, 4, 5, 6, 7]. However, a comprehensive understanding of how exoskeleton assistance influences gait stability throughout the gait cycle remains limited, posing challenges for optimizing device design and control strategies. Lower-limb robotic exoskeletons have been utilized to support walking across various populations, including individuals with mobility impairments, military personnel, and industrial workers [8]. By providing external mechanical assistance, these devices can reduce muscular demands [8] and decrease the metabolic cost of walking [5; 9; 10; 11; 12], enhance self-selected walking speed [13; 14; 15; 16], and reduce fatigue during locomotion. While initial research has focused on improving energy efficiency and gait strength, expanding the functionality of exoskeletons to address stability control has become an increasingly important area of investigation. Notably, hip exoskeletons have attracted growing interest due to their ability to assist the hip joint, an essential contributor to propulsion and postural control during gait, thus potentially improving both gait performance and dynamic balance [3]. Several quantitative metrics have been developed to assess human gait and evaluate such stability improvements. Traditional approaches to assessing gait stability, such as the margin of stability (MOS), focus on discrete gait events, typically heel contact, using the extrapolated center of mass (XCoM) relative to the base of support [1; 3]. MOS integrates COM position and velocity through the linear inverted pendulum model, providing a biomechanically grounded estimate of instantaneous stability [1; 3]. However, its event-based nature limits its ability to capture the continuous, multidimensional nature of gait variability, particularly during transitions between gait phases. Furthermore, the interpretability of MOS in the anteroposterior (AP) direction is debated due to walking's inherently unstable forward-driven mechanics, where the COM often exceeds the base of support to propel the body forward [1; 3]. This raises questions about MOS's suitability as a global stability metric, especially under assistive conditions where compensatory adjustments may occur outside discrete events. Nonetheless, MOS remains a widely used and biomechanically grounded metric that provides valuable insights into stability at discrete gait events, particularly heel strike [1; 3]. It has been applied successfully in perturbation studies, clinical assessments, and investigations of fall risk where event-specific deviations are informative. Rather than replacing MOS, our approach offers a complementary tool that expands stability analysis to a continuous, multidimensional framework across the entire gait cycle [1; 3]. The interpretation of MoS varies by direction: in the AP plane, the MoS is typically negative, reflecting the \"fall forward\" mechanics inherent in normal gait, where the extrapolated center of mass (XCoM) moves beyond the anterior boundary of the base of support to enable forward progression. A more negative AP MoS may indicate a greater reliance on momentum-driven stepping, which is not necessarily indicative of instability unless compensatory mechanisms fail.