Alternative Formulations for Optimization-based-Digital Human Motion Prediction

Simulating human motion is a complex problem due to redundancy of the human musculoskeletal system. The concept of task-based motion prediction using single- or multi-objective optimization techniques provides a viable approach for predicting intermediate motions of digital humans. It is shown that task-based motion prediction is in fact a numerical optimal control problem. Alternative formulations for simulation of human motion are possible and can be solved by modern nonlinear optimization methods. Three techniques based on state variable elimination, direct collocation and differential inclusion are presented and compared. The basic idea of the formulations is to treat different combinations of the state variables, such as the joint profiles and torques or their parametric representations as independent variables in the optimization process. Different ways to discretize the equations of motion are also presented, namely finite difference, piecewise polynomial interpolation and series expansion. The advantages and disadvantages of different formulations are discussed. A numerical example is used to illustrate the basic ideas, and is solved by a large-scale sparse nonlinear programming solver. It is concluded that with the aid of motion tracking for validation, optimal control techniques based on nonlinear optimization have great potential to provide a useful tool for realistic human motion prediction.