Optimization of human gait using singular-value decomposition-based design variables

Age, walking speed, the presence of walking problems, the slope of the ground, and many other parameters affect human gait. Understanding gait variations and obtaining a reference behavior under different conditions is important for identifying abnormal walking behaviors and designing walking assistive devices, orthoses, and prostheses. Predictive dynamics can be used to determine a reference motion for a given task. In the predictive dynamics approach, the motion of a human is generated using design variables, and the equation of motion is considered a constraint. Several design variables were used to generate the motion, and the biological limits of the joints were considered additional constraints in previous studies. A foot-ground contact model was used to generate vertical and horizontal ground reaction forces using the nonlinear spring-damper model. This study proposed a singular value decomposition-based joint angle generation method to reduce the number of design variables and additional constraints. First, the joint angles were calculated using the motion capture data of 225 participants. Then, a joint angle matrix containing the joint angles of all participants in the experiments was created. The modes of the joint angles were extracted using singular-value decomposition. The joint angles were generated by summing the multiplication of the first nine modes of the joint angles and their corresponding design variables. Therefore, the number of design variables was significantly reduced. Moreover, the constraints related to the joint angle limits were intrinsically satisfied. Joint angles, moments, and power were obtained for the optimal energy and moment square cases at different walking speeds. The optimal results were found to be consistent with experimental results in the literature.