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Hybrid predictive dynamics: a new approach to simulate human motion

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Abstract

A new methodology, called hybrid predictive dynamics (HPD), is introduced in this work to simulate human motion. HPD is defined as an optimization-based motion prediction approach in which the joint angle control points are unknowns in the equations of motion. Some of these control points are bounded by the experimental data. The joint torque and ground reaction forces are calculated by an inverse algorithm in the optimization procedure. Therefore, the proposed method is able to incorporate motion capture data into the formulation to predict natural and subject-specific human motions. Hybrid predictive dynamics includes three procedures, and each is a sub-optimization problem. First, the motion capture data are transferred from Cartesian space into joint space by using optimization-based inverse kinematics (IK) methodology. Secondly, joint profiles obtained from IK are interpolated by B-spline control points by using an error-minimization algorithm. Third, boundaries are built on the control points to represent specific joint profiles from experiments, and these boundaries are used to guide the predicted human motion. To predict more accurate motion, the boundaries can also be built on the kinetic variables if the experimental data are available. The efficiency of the method is demonstrated by simulating a box-lifting motion. The proposed method takes advantage of both prediction and tracking capabilities simultaneously, so that HPD has more applications in human motion prediction, especially towards clinical applications.

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Abbreviations

q IK::

Joint angles from inverse kinematics

\(\tilde{X}_{i}^{k}\)::

Cartesian coordinates of key joint centers from motion capture

\(\tilde{X}_{i}^{g}\)::

Cartesian coordinates of guiding joint centers from motion capture

P i ::

Control points for ith DOF

\(t_{i}^{k}\)::

The ith key event time point

Ω::

Time interval of interest

ε IN::

The error of the interpolation function

F G::

Ground reaction forces

F A::

Applied external loads

g::

Task-based constraints

q::

Joint angle profile

τ::

Joint torque profile

t::

Time knot vector

B(t)::

B-spline basis function

\(\mathop{(\bullet )}\limits^{\bullet}\)::

The derivative with respect to time

N dof::

The number of degrees of freedom of the mechanical system

f i ::

The ith objective function

(P ∗,t ∗)::

The control points and knot vector from the mechanical model optimal solution

(\(\bar{\mathbf{P}}^{*}, \bar{\mathbf{t}}^{*}\))::

The control points and knot vector form the motion capture

e P::

The variation on control point P

e t::

The variation on knot vector point t

Φ(F G)::

A function of the contacting forces F G

c(F G)::

The friction constraints on each contacting point

DOF::

Degrees of freedom

GRF::

Ground reaction forces

ZMP::

Zero moment point

IK::

Inverse kinematics

PD::

Predictive dynamics

HPD::

Hybrid predictive dynamics

SQP::

Sequential quadratic programming

NLP::

Nonlinear programming

DH::

Denavit-Hartenberg method

MOO::

Multi-objective optimization

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Acknowledgements

This research is supported by projects from US Army TACOM, US Army Natick Soldier Systems Research Center, and US Navy. The authors would like to thank reviewers for their insightful and constructive comments. We would also like to thank all the colleagues at the University of Iowa for fruitful discussions on the subject of PD.

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  1. Virtual Soldier Research (VSR) Program, Center for Computer-Aided Design (CCAD), College of Engineering, The University of Iowa, Iowa City, IA, 52242, USA

    Yujiang Xiang, Jasbir S. Arora & Karim Abdel-Malek

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Xiang, Y., Arora, J.S. & Abdel-Malek, K. Hybrid predictive dynamics: a new approach to simulate human motion. Multibody Syst Dyn 28, 199–224 (2012). https://doi.org/10.1007/s11044-012-9306-y

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