## 5 Conclusions  
The study explored the intricate relationship between gait nonlinearities and the metabolic cost, hypothesizing that specific nonlinear gait parameters significantly influence the metabolic cost during walking. The research utilized advanced analytical models such as ANNs and MLR to decipher the complex dynamics of human gait, mainly focusing on variables such as the ankle velocity, COM velocity, ground reaction forces, and joint moments. The hypothesis was grounded in the premise that a deeper understanding of these nonlinear dynamics could enhance the predictive accuracy of the metabolic cost, thereby offering novel insights into gait optimization, especially for individuals using assistive devices like hip exoskeletons. In conclusion, the study's findings robustly support the initial hypothesis, revealing that DFA and the LyE\({}_{\text{R}}\) exhibit the highest explanatory power for the metabolic cost among the array of nonlinear gait measures examined. The R\({}^{2}\)\({}_{\text{MLR}}\) values obtained from the multiple linear regression analyses--72% for the LyE\({}_{\text{R}}\) and 63% for DFA--underscore the significant variance in the metabolic cost these measures can explain. ANN models tailored to the LyE\({}_{\text{R}}\), DFA, and ApEn outperformed others, showcasing low MSE and high R\({}^{2}\)\({}_{\text{ANN}}\) values. This superior performance suggests these models' efficacy in capturing the variability in gait that correlates closely with the metabolic cost. The ANN models developed in this study offer a unique advantage over traditional approaches by enabling potential real-time implementation alongside monitoring systems. By detecting deviations from expected gait patterns, these models could facilitate immediate adjustments to gait parameters, thus mitigating the risk of injury or strain. This adaptability provides a foundation for innovative applications in personalized rehabilitation and assistive device optimization, making our approach distinct in its ability to support safe, individualized gait interventions. The study recommends a focused examination of the variables with significant coefficients within these models, as they are potent predictors of the metabolic cost and pivotal in optimizing gait parameters for metabolic efficiency in assistive devices like hip exoskeletons. Our results offer valuable insights for exoskeleton robot design, especially optimizing control strategies. By accurately predicting the metabolic cost and key gait parameters, the ANN models can guide real-time adjustments in the torque, alignment, and support, reducing user fatigue, enhancing stability, and enabling more responsive, individualized gait assistance for safer and more effective rehabilitation. The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app142311026/s1](https://www.mdpi.com/article/10.3390/app142311026/s1)]([https://www.mdpi.com/article/10.3390/app142311026/s1](https://www.mdpi.com/article/10.3390/app142311026/s1)): Exprehensive regression analysis of the net\({}_{\text{JER}}\) model; Figure S2: Comprehensive regression analysis of the net\({}_{\text{JER}}\) model; Figure S3: Comprehensive regression analysis of the net\({}_{\text{CED}}\) model; Figure S5: Comprehensive regression analysis of the \({}_{\text{SPEn}}\) model; Figure S6: Comprehensive regression analysis of the \({}_{\text{LYEW}}\) model; Figure S7: Error histograms for the nonlinear models. Figure S8: Comprehensive Regression Analysis of the Multiple Linear Regression Models (MLR). Figure S9: Error Histograms for the Multiple Linear Regression Models (MLR). Table S1: 95% Confidence Intervals (CI) for Multiple Linear Regression (MLR) coefficients and Artificial Neural Network (ANN) models across six different gait nonlinearity measures. Conceptualization, A.M.G. ; methodology, A.M.G. and F.F. ; software, A.M.G. ; validation, A.M.G. ; formal analysis, A.M.G. ; investigation, A.M.G. and F.F. ; resources, A.M.G., F.F. and J.M.B. ; data curation, A.M.G., F.F. and J.M.B.