Biomedical Engineering Reference
In-Depth Information
Determine:
Joint Profiles q
Torque profiles t
Minimize:
J
(q,
τ
,t)
Example: Energy and Effort
Subject to:
- Equations of motion
τ
-
f
(q, t) = 0
- Variable information constraints
g(
ϒ
)
-
0
q
L
-
q
-
q
u
- Joint Limits
- Strength constraints
τ
L
-
τ
-
τ
u
FIGURE 5.3
Illustration of the optimization problem in three main components.
q
Predictive
Dynamics
unknown
ϒ
known
τ
(Optimization)
unknown
FIGURE 5.4
Flow chart of predictive dynamics.
others;
f ð
q
;
q
;
q
;
are subject to their
lower and upper bounds, respectively. This is called the predictive dynamics
approach and is formulated for the system M as follows:
tÞ
5τ
are the equations of motion; and q and
τ
min
q
Jð
q
;
τ
;
t
Þ
; τ
s:t:
:
τ
-
f
ð
q
;
q
;
q
;
t
Þ
5
0
g
ðϒÞ
#
0
q
(5.2)
L
U
#
q
#
q
L
U
τ
#τ#τ
For the biosystem, the objective function is usually called the performance
measure. The flowchart of predictive dynamics is shown in
Figure 5.4
.
Two challenging problems naturally arise for
the predictive dynamics
approach:
1.
The functional form of the performance measure is unknown
2.
The constraints are undetermined.
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