## 1 Introduction
In contrast, the mediolateral (ML) MoS is usually positive and offers a more precise representation of lateral balance control, with smaller values indicating reduced margins and increased demands on neuromuscular control to prevent falls [3]. This directional asymmetry in MoS interpretation is essential when evaluating the effects of assistive devices like hip exoskeletons, which can alter COM dynamics in complex ways. Additionally, step width and ML MoS are closely linked; wider steps typically correspond to increased ML MoS and may reflect compensatory strategies to enhance lateral stability [3]. Recent work has also highlighted the potential of combining biomechanical signals with data-driven models for gait pattern recognition and classification. For example, [PERSON] et al. [17] introduced a novel method to identify gait patterns based on joint motion signals, offering insights applicable to both sports and clinical rehabilitation settings [17]. While their approach focuses on identifying movement patterns, our work extends this direction by offering a continuous, phase-dependent metric of stability rather than discrete classification, complementing such approaches and supporting applications in exoskeleton control, real-time feedback, and individualized therapy planning. In addition to MOS, other model-based and dynamical systems approaches, such as Lyapunov exponents [1; 3; 18; 19], Floquet analysis [18], and Poincare maps [19], have been used to quantify gait stability [1; 3; 18; 19]. Specifically, Local Dynamic Stability, measured as the short-term Lyapunov exponent, captures the immediate divergence of gait trajectories, reflecting sensitivity to small perturbations during walking [1; 3; 18; 19; 20; 21]. Additionally, the Hurst exponent has been employed to assess the long-range correlations and persistence in gait dynamics, providing insights into the fractal structure of walking patterns and their stability over time [22]. Sample entropy, another dynamical systems metric, quantifies the complexity and predictability of gait time series, offering a measure of irregularity that can indicate underlying stability challenges in locomotor control [23; 24; 25]. These methods provide insight into walking dynamics' average local divergence or return map properties over time. While mathematically robust, they often lack intuitive visualization and are not easily interpretable in real-time applications or clinical environments. While traditional metrics such as MoS, Lyapunov exponents, or entropy provide valuable insights, they are typically constrained to single dimensions or isolated events within the gait cycle. These approaches may overlook how stability evolves continuously in three dimensions, particularly in response to dynamic inputs like assistive torque. Moreover, unidimensional metrics may not fully capture the coupled variability between directions (e.g., vertical and mediolateral sway), which can be critical for maintaining balance. A method capable of continuously characterizing gait variability in all three directions throughout the stride would allow for richer interpretation of stability mechanisms and a better understanding of how assistive devices influence balance across different gait phases. To address these limitations, this study presents the first application of gait tube analysis for evaluating gait stability under robotic exoskeleton assistance. Gait tube analysis is a continuous, phase-resolved approach that visualizes COM velocity trajectories in three-dimensional state space and quantifies variability through covariance-based ellipsoids computed across the gait cycle. By computing ellipsoid volumes at each gait phase, gait tubes offer a temporally resolved representation of locomotor stability, capturing the magnitude and orientation of COM variability. This approach is particularly suited for detecting subtle changes in stability induced by external perturbations or assistive interventions, providing a more detailed understanding than traditional metrics.