Biomedical Engineering Reference
In-Depth Information
Before turning to these two important issues, the evaluation criterion for pre-
dictive dynamics is first proposed, i.e., how to validate the predictive dynamics
solution of model M with that of the real system S.
Suppose q and
τ represent the natural motion of the biosystem S. One way
to quantify the accuracy of the predictive dynamics solution for the biosystem is
to evaluate the percentage error of the residuals of the predicted force and dis-
placement histories in a norm, as follows:
Ð 0 ðjj q-q jj 1 jj τ
τ jjÞdt
Ð 0 ðjj q jj 1 jj τ jjÞdt
-
ε 5
(5.3)
where q and
are optimal values obtained from the predictive dynamics in
Equation (5.2) ; T is the total time.
For human motion validation, some well-studied kinematics variables (angles
and displacements) have been chosen as determinants to define a specific motion
such as walking and running. For example, in walking motion the six determi-
nants have been identified corresponding to the lower extremities and pelvic
motion ( Saunders et al., 1953 ). Therefore, instead of using all the joint angle and
torque profiles in Equation (5.3) , only the determinant and the corresponding tor-
que profiles may be used to validate the task.
Furthermore, the predictive dynamics structure has very flexible optimization
formulation in terms of constraints and performance measures for dynamic human
motion prediction. For instance, the constraints allow one to model the boundary
conditions and state response of the problem, and the performance measure allows
one to study what drives human behavior. However, this assumes that the perfor-
mance measure represents a physically significant quantity, not just a curve fit to
predetermined data. Therefore, once the simulation model is validated, it can be
used to show cause and effect, study an injury problem (reduce joint limit), ana-
lyze pathological motion, and so on.
τ
5.3 Dynamic stability: zero-moment point
Dynamic stability of the human model is an important aspect of almost every
task. Some tasks, such as rolling on the ground, may not require a stability crite-
rion, but in most cases it is required.
Balance of the skeletal model is achieved by satisfying the zero-moment point
(ZMP) constraint throughout the motion, if applicable. ZMP is briefly explained
below and used in detail in the following chapter. In a balance state, ZMP coin-
cides with the center of pressure (COP) where the resultant GRF acts ( Xiang
et al., 2010a,b ).
The ZMP is a point on the ground at which the resultant tangential moments
of the active forces are zero ( Vukobratovic and Borovac, 2004 ). It is used as the
balance criterion for human walking. The forces on the system are divided into
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