Biomedical Engineering Reference
In-Depth Information
As stated earlier, the most important benefit of this optimization formulation
is that the equations of motion are not explicitly integrated, but are evaluated by
inverse dynamics. The dynamic effort (performance measure) that is represented
as the integral of the squares of all the joint torques is minimized. Indeed,
dynamic balance is achieved by satisfying the ZMP constraint throughout the
walking motion. Subsequently, the sequential quadratic programming algorithm is
used to solve the nonlinear optimization problem. The results of the optimization
problem, torque and joint profiles, are shown to be realistic when compared with
the experimental data for normal walking. Besides normal walking, three other
cases of walking with a shoulder backpack are simulated.
The objective of formulating the gait using predictive dynamics is to enable
the prediction of natural motions, and to be able to simulate cause and effect,
whereby a user can input various parameters, observe the simulated motion, and
calculate the parameters of the motion (forces, torques, motion profiles, ground
reaction forces [GRFs], and balance issues).
Because of the use of optimization to model the behavior and the biomechan-
ics, it is believed that the algorithm drives the motion towards a more naturalistic
and higher-fidelity motion. As a result, our objective is to obtain a high-fidelity
motion with a model of a large DOF human skeleton. Because we use the joint
space (not muscle space), we shall use the strength limits (strength surfaces) as
the limits of what a person can do.
7.4
Spatial kinematics model
As detailed in Chapter 2, we shall use the DH parameterization method to model
the full kinematics of the human body. Recall that the DH transformation matrix
includes rotation and translation and is a function of four parameters,
θ
i
,
d
i
,
α
i
,
and
a
i
, which relate coordinate frames
i
and
i
-1, depicted in
Figure 7.1
.
7.4.1
A kinematic 55-DOF human model
The spatial kinematic skeletal model with 55 DOFs (the z's), shown in
Figure 7.2
, will be used throughout this chapter to illustrate the principles. The
model consists of six physical branches and one virtual branch. The physical
branches are: the right leg, the left leg, the spine, the right arm, the left arm, and
the head. In these branches, the right leg, the left leg and the spine start from the
pelvis (
z
4
,
z
5
,
z
6
), while the right arm, left arm, and head start from the spine end
joint (
z
30
,
z
31
,
z
32
).
The spine model includes four joints, and each joint has three rotational DOFs
([
z
21
,
z
22
,
z
23
], [
z
24
,
z
25
,
z
26
], [
z
27
,
z
28
,
z
29
], [
z
30
,
z
31
,
z
32
]). The legs and arms are
assumed to be symmetric with respect to the sagittal plane y-z. Each leg consists
of a thigh, a shank, a rear foot, and a forefoot. There are seven DOFs for each
leg: three at the hip joint (
z
7
,
z
8
,
z
9
), one at the knee joint (
z
10
), two at the ankle
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