Biomedical Engineering Reference
In-Depth Information
FIGURE 7.11
The general optimization formulation for walking.
7.9.3
Constraints
Two types of constraints are encountered for the walking optimization problem:
one is the time-dependent constraints, which include joint limits, torque limits,
ground penetration, dynamic balance, arm-leg coupling, and self-avoidance. These
constraints are imposed throughout the time interval. The second type is the time-
independent constraints, which comprise the symmetry conditions, ground clear-
ance, and initial and final foot positions; these constraints are considered only at a
specific time point during the step.
7.9.3.1
Time-dependent constraints
7.9.3.1.1
Joint limits
To avoid hyperextension, the joint limits are taken into account in the formula-
tion. The joint limits representing the physical range of motion are
q
L
q
U
T
(7.27)
where q
L
are the lower joint limits and q
U
the upper limits as presented later in
Table 7.3. A joint limit constraint is also used to “freeze” a DOF by setting its
q
ðtÞ
#
;
t
#
0
#
#
Search WWH ::
Custom Search