Biomedical Engineering Reference
In-Depth Information
Since force is the control variable along the moving direction, position can not
be controlled and the subject can move with an individually preferred speed. In
the scheme, the direction of force control (S
T
) is determined first by a selection
matrix (
S
S
) and the direction of position control (S
N
) is determined accordingly by
another selection matrix (
I
-
S
S
)
,where
I
is the identity matrix.
The end position error along S
N
is calculated first and transformed into the
equivalent end force error (F
N
)
by a predefined stiffness constant(K
s
)
, i.e.,
F
N
=
Ks
·
Δ
X
N
(9.5)
Δ
where
X
N
is the end position error along S
N
in one time step.
F
N
is transformed
Δ
Δ
to the needed torque acting on joints by the Jacobian matrix (J),
τ
N
=
J
T
J
T
·
Δ
F
N
=
·
·
Δ
Ks
X
N
(9.6)
where
−
.
l
1
·
sin
(
θ
1
) −
l
4
·
sin
(
θ
2
+
π
)
J
=
(9.7)
l
1
·
cos
(
θ
1
)
l
4
·
cos
(
θ
2
+
π
)
Δ
τ
N
are the inputs to the fuzzy logic and are regarded as error and error
change in the logic, respectively. In the fuzzification process, inputs (
τ
N
and
Δ
τ
N
)
are scaled and mapped to the five triangle-shaped membership functions. One
membership degree is obtained for each scaled input and membership function
combination. Then, each combination of mapped inputs activates one control
action according to the inference rule table. The control rule table was determined
based on the step response of a presumed second-order system. The final output
of the position fuzzy controller is obtained in the defuzzification process by using
the center-of-gravity method.
Force control is implemented in the tangent direction of actual movement. By
this convention, the robot is able to provide a desired resistive or assistive force to
the subjects (Chou, 1997). Since the properties of the subject are unknown a priori,
it is impossible to determine the optimal control parameters exactly. Therefore we
combine a conventional linear PI (proportional-integral) controller and a fuzzy PI
tuner as the force controller. The purpose of the fuzzy PI tuner is to compensate
for the nonlinear dynamics (joint friction) of the robot and the unknown disturbing
force from the subject. The force error along S
T
direction (
τ
N
and
Δ
F
T
)
is transformed into
by J
T
.
joint torque error (
are fed to the fuzzy PI tuner.
The fuzzy PI tuner has separate fuzzy logics for P and I parts, and each operates
in a similar way as in the position controller. The outputs from the fuzzy logic
(K
Pc
for P part and K
Ic
for I part) are linearly combined with the conventional PI
controller,
τ
T
)
τ
T
and change of it (
Δ
τ
T
)
τ
F
=
τ
T
· (
K
P
+
K
Pc
)+
τ
T
· (
K
I
+
K
Ic
)
dt
,
(9.8)
where K
P
and K
I
are the parameters for the conventional PI controller respectively
and
τ
F
is the final output of the force control. The maximal values of K
Pc
and K
Ic
are set to be equal to K
P
and K
I
, respectively.
