Optimization-based dynamic simulation of human jogging motion

Mathematical modeling and realistic human simulation of human jogging motion is a very challenging problem. Majority of the current literature is focused on studying walking or running. This work is aimed at bridging the gap in literature due to the lack of research work in three main areas: (1) simulations and experiments on running at speeds lower than 3 m/s, (2) Kinetics of fore-foot strike pattern in jogging and running and (3) the existence of a double support phase in running at slower speeds and its effects. Formulations to simulate natural human jogging are studied and developed. The digital human model used for this work includes 55 degrees of freedom, 6 for global translation and rotation and 49 for the revolute joints to represent the kinematics of the body. Predictive Dynamics methodology is used for dynamic analysis where the problem is formulated as a nonlinear optimization problem. Both, displacement and forces are considered as unknowns and identified by solving the optimization problem. The equations of motion are satisfied by applying them as equality constraints in the formulation. Kinematics analysis of the mechanical system is performed using the Denavit-Haretneberg (DH) method. The zero moment point (ZMP) condition is satisfied during the ground contact phase to achieve dynamic stability. The joint angle profiles are discretized using B-spline interpolation method. The joint torque squared, also termed dynamic effort, and the difference between predicted motion and motion capture data are used as performance measures and minimized in the optimization formulation. The formulation also includes a set of constraints to simulate natural jogging motion. Two formulations are discussed for jogging on a straight path: (1) one-step jogging formulation and (2) one-stride jogging formulation. The one-stride formulation is discussed for clock-wise and counter clock-wise jogging along a curved path. Cause and effect is shown by obtaining simulation results for different loading conditions. The proposed formulation provides realistic human jogging motion and is very robust.