## 4 Discussion
High \(\mathrm{LyE_{w}}\) values for the ankle moment indicate its sensitivity to initial conditions, reflecting the ankle's responsiveness in maintaining propulsion and balance, especially in exoskeleton-assisted gait. The lower \(\mathrm{LyE_{w}}\) values for the hip angle highlight the unique control demands placed on the ankle compared to other joints during assisted walking. This sensitivity to initial conditions indicates that small variations at the start of the stride cycle can lead to significant differences in gait patterns, particularly for the ankle moment. In contrast, the hip angle's lower sensitivity suggests more consistent and stable behavior throughout the gait cycle, making it less influenced by small changes at the beginning. In contrast, the \(\mathrm{LyE_{R}}\) of the GRF\({}_{\mathrm{Ver}}\) (0.271) was the highest. The \(\mathrm{LyE_{R}}\) of the COM displacement and COM velocity showed negative values. A negative value of a Lyapunov Exponent, when calculated using the Rosenstein method, implies that the trajectories of the system converge over time. This convergence suggests that the system is stable, and its future behavior is predictable over the long term [50]. In practical terms, minor differences in initial states will diminish over time, leading to similar outcomes or states. This stability is characteristic of non-chaotic systems, where, despite slight variations at the start, the system evolves predictably without sensitive dependence on those initial conditions. In Table 5, regarding the ANN prediction errors, the ApEn has the highest error for the COM velocity (29.306%) and the lowest for the hip velocity (14.893%), indicating varying degrees of predictability across gait parameters. The SpEn's prediction error is greatest for the GRF\({}_{\mathrm{Ver}}\) (33.525%) and lowest for the hip velocity (9.863%), suggesting that vertical force predictions are less reliable. The CD model's error is highest for the ankle moment (38.107%)and lowest for the GRF\({}_{\text{Ver}}\) (12.112%), aligning with the complexity noted in CD values. DFA models have the most substantial prediction error for the COM velocity (51.333%) and the smallest for the knee angle (10.430%), indicating a challenge in accurately predicting the metabolic cost based on COM movement. Errors from the LyE\({}_{\text{w}}\) model are most significant for the ankle velocity (24.799%) and least for the hip velocity (17.627%), while the LyE\({}_{\text{R}}\) model shows the highest error for the hip angle (15.897%) and an impressively low error for the COM velocity (5.834%), which is interesting considering its negative value in nonlinearity measures. These prediction errors are crucial for understanding the reliability of each nonlinearity measure in estimating the metabolic cost and can guide the development of more sophisticated models for gait analysis. In analyzing the influence of various biomechanical variables on the prediction of the metabolic cost using ANN models, as outlined in Table 5, certain variables stand out due to their higher prediction errors across different nonlinearity measures. For instance, the ankle velocity and COM velocity demonstrate significant prediction errors (ApEn, LyE\({}_{\text{w}}\), and SpEn for the ankle velocity and the ApEn and DFA for the COM velocity), underscoring their critical influence in the models. ApEn errors suggest that the model struggles with the complexity and adaptability of the ankle and COM velocity, as the ankle velocity is essential for propulsion and balance, and the COM velocity requires frequent adjustments for stability. LyEw errors for the ankle velocity indicate potential challenges in capturing sensitivity to small perturbations, contributing to nonlinear variability. High SpEn errors point to the irregularity in ankle force generation needed for propulsion. In contrast, DFA errors in the COM velocity reflect the complexity of long-range correlations required for balance control.