Optimization-based simulation of the motion of a human performing a horizontal drop jump

Abstract

The ‘Hybrid Predictive Dynamics Method for Digital Human Modeling’ is used in this work to analyze the dynamics of a human performing a “Drop Jump” task. The ‘Hybrid’ prefix mentioned in the literature recently [1] refers to the use of motion capture data for improving human motion simulations. This use of motion capture compensates for the inherent weaknesses of purely theoretical motion prediction due to deficiencies in computational power or available theoretical backgrounds. In this work, using motion capture data, an optimization based 3-D motion tracking of a human model performing a “Horizontal Drop Jump” is presented, as the first step in the simulation/ prediction of such a motion. Based on the evaluation of the motion, dynamics properties of the motion are calculated which include ground reaction forces, joint torques and metabolic energy. The human model starts in a standing posture on top of a small box (low elevation from the ground), while jumping down the box, he changes his posture into a ready to jump pose with his two feet on the ground in-line and parallel to each other. After a brief recoil, he accelerates his center of gravity in the upward and forward direction and lifts off from the ground with an initial velocity in the same direction as his past acceleration. In the air, he will have a projectile motion and then he lands in his final position. The human model is a 55 degree of freedom (DOF) robot defined by Denavit-Hartenberg parameters. The base of the model is considered to be the hip point of a human. The orientation and position of this base in the global reference frame is defined by 6 DOF (3 position and 3 orientation). The robot includes 5 open-loop kinematic branches all originating from the base of the robot and ending in left hand, left foot, head, right hand and right foot. The remaining 49 DOF of the robot are revolute joints used in these 5 branches. Based on a motion capture set of data, motion is generated by a multi-objective optimization approach minimizing the difference between the location of markers on an actual human and the location of those same markers on the digital human model. All the forces, inertial, gravitational as well as external, are known, except the ground reaction forces are known. Therefore, it will be possible to calculate the total sum of ground reaction forces and moments. In the next step, joint torques are calculated using Lagrange’s equations.