## 4 Discussion
Specifically, the ankle velocity has a coefficient of 0.3245 with a \(p\)-value of <0.0001, marking it as a key variable in the DFA model for predicting the metabolic cost. For the LyE\({}_{\text{R}}\) model, the hip velocity and hip moment stand out with significant \(p\)-values and large coefficients, suggesting their critical influence on metabolic cost predictions. The hip velocity has a coefficient of 1.2900 with a \(p\)-value of 0.0002, and the hip moment has a coefficient of \(-\)1.7930 with a \(p\)-value of 0.0003, highlighting their importance in the LyE\({}_{\text{R}}\) model. Nonlinear analysis tools serve distinct purposes for different gait metrics. For instance, using the DFA on the ankle moment time series uncovers the neuromuscular system's complexity and strategies for joint stability, adaptation to varied walking or running conditions, and injury risk through abnormal conditions. On the other hand, the DFA on GRF data sheds light on the fluctuation in external forces crucial for movement. While ankle moment analysis delves into joint mechanics and control, GRF analysis provides a broader perspective on the body's interaction with its environment, which is crucial for evaluating gait stability and efficiency. To deepen the biomechanical understanding of our ANN results, we interpret the role of specific nonlinear measures, such as DFA and the \(\mathrm{LyE_{w}}\), in capturing the fundamental dynamics of exoskeleton-assisted gait. DFA applied to the ankle moment provides insights into the neuromuscular complexity and joint stability strategies required to adapt to external support. This adaptability is essential for preventing joint strain and ensuring stability during varied gait conditions, where subtle, complex control adjustments are needed. Similarly, the DFA on GRF data highlights the fluctuation in external forces, emphasizing the body's interaction with its environment, which is central to maintaining movement stability and efficiency. In overall observations, GRF components seem consistently significant across models, especially in Tables 3 and 4, indicating their general importance in predicting the metabolic cost. In the \(\mathrm{LyE_{R}}\) and DFA models, variables related to hip and ankle movements (velocity, moment) are particularly influential, suggesting that specific lower limb dynamics aspects are crucial for metabolic cost estimation. These findings highlight the complexity of gait dynamics and their relationship with the metabolic cost. Variables related to ground reaction forces and specific joint dynamics (especially at the hip and ankle) are significant predictors, underscoring the importance of these factors in the context of gait analysis and metabolic cost estimation. Figure 2 and Table 5 offer a detailed summary of various nonlinear gait measures and their corresponding prediction errors from ANNs for a range of gait parameters. Regarding nonlinearity, the greatest value for the ApEn was observed for the ankle velocity (0.390), indicating the highest complexity, and the lowest ApEn was related to the hip angle (0.240), suggesting a more predictable pattern. The SpEn follows a similar trend, with the ankle velocity again showing the greatest (0.301) and the ankle moment the lowest unpredictability (0.103). The COM velocity presented the highest value for the CD (1.888), which signifies a complex dynamic, while the GRF\({}_{\mathrm{Ver}}\) has the lowest (0.075), implying a more straightforward structure. The highest DFA values were observed for the vertical GRF\({}_{\mathrm{Ver}}\) at 0.691 and the lowest for the COM velocity at 0.444. This indicates that the dynamics of vertical GRFs during gait may be more persistent than those of COM displacement. The \(\mathrm{LyE_{w}}\) of the ankle moment was highest among other gait measures (2.068), reflecting significant sensitivity to initial conditions, while the hip angle exhibited the least sensitivity (0.745).