Biomedical Engineering Reference
In-Depth Information
TABLE 4.1 Definitions and typical values assumed for the muscle and limb parameters.
Parameter
Description (Units)
Value
β
Fraction of activation state
0
τ act
Activation time constant (s)
0.015
Coefficient of viscous damping in limb (Kg.m 2 .s)
1 × 10 04
B e
I c
Moment of inertia of limb (Kg.m 2 )
2 × 10 05
τ ε
Relaxation time for constant strain (s)
0.1
τ σ
Relaxation time for constant stress (s)
0.077
r te
Ratio of final to initial extensor tendon length
1.3
ml c
Limb unbalance (N.m)
0.005
α s
Reference limb rotation angle
π /2
TABLE 4.2 Typical initial values assumed for the muscle and limb dynamic states.
State
Description (Units)
Initial Value
q f
Flexor muscle activation state
0
q e
Extensor muscle activation state
0
α
Limb rotation angle (rad)
0.2
ω
Limb rotation rate (rad/s)
0
L tf
Flexor muscle tendon length (m)
0.1
L te
Extensor muscle tendon length (m)
0.1
d f
Flexor muscle force moment arm (m)
0.3
d e
Extensor muscle force moment arm (m)
0.25
d p
Proximal distance of muscle origin to joint (m)
0.2
d d
Distal distance of muscle insertion point to joint (m)
0.3
F max
Maximum muscle force (N)
0.01
L tf 0
Flexor muscle initial tendon length (m)
0.1
L te 0
Extensor muscle initial tendon length (m)
0.1
state response simulated by numerical integra-
tion of the equations in MATLAB. The assumed
set of parameters is listed in Table 4.1 . Table 4.2
lists the initial values of the states, that were
estimated by the adaptive UKF estimator. Of
these states, the last seven are assumed to be
constants. All the equations are assembled and
expressed in discrete form to facilitate the appli-
cation of the adaptive UKF.
In the first instance, the UKF was imple-
mented without any adaptation of the process
noise or measurement noise covariance matri-
ces. The first activation inputs used to determine
the limb response over a 10-second timeframe
corresponding to 10,000 time steps are obtained
from real measured EMG data available on the
Web [84] . The subject did a protocol of 30 seconds
water cycling in a 100 bpm cadence. The second
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