IEEE Robotics & Automation Magazine - December 2022 - 29

xt Tx tpp f
() ()
xt
+= -
=p()
where
iho
()t
u
f
dx t
dt
u
iho
p
dt pT
(( )( ))ii t
tho
-dx
tp()
represents the adaptation rate of x .p
As seen from Figure 3(a), generated from simulations, we
set original curve ()thi
as .().sin t +1508 and choose
=
0675
different prediction serial numbers ,,,,p 10 13 15 18 20 to
evaluate the effectiveness of the fitting method. We obtained
that when the value of p gets larger, the prediction step is farther,
but the error between the original value ()
the predicted value
ih tpT+
iho ()t
t
and
also becomes larger. Therefore,
choosing a proper prediction serial number is very important
in practice. From Figure 3(b) and (c), we can obtain that
adaptation weight xp
initial values of xp
and converge to the ideal x .p
Signal Filtering
Since the predicted elbow joint angle may include noises, we
propose a composite filter to filter the prediction value, which
combines a moving average filter and a dither removal filter.
The moving average filter is utilized to calculate the mean of the
data ().thoitr
rt
frame ().tThoi -
t
If the difference is less than the threshold c,
Otheriho
tTt
and
the current frame ().thoitr
The first output value of the filter is the average of
are compared with the output value of the previous
the value of the previous frame is kept as output ().thoit
wise, the output of the filter is the sum of the weighted average
of the previous frame ()
The mathematical form of the filter is described as follows:
()
rtho t =
ii
i
t ()ho t = ) rtho 1otherwise
tho
n +1 i =0
ho
ttr ho
ii i
di
t
diho
() |()( )
() () ()
-- -
+- -
tT tt Tc
tt T
;1
1 / tho(),tiT
-
n
(4)
where d denotes the weight.
Human motion predictions and filtering are always
subject to model overfitting, and this will influence the
control performance. Therefore, we propose a hybrid visual-haptic
framework to complement the advantages of
visual and force sensing to solve this issue, as introduced in
the next section.
Impedance Behavior
We consider impedance control for the robot with a desired
mass-damping-stiffness impedance model as follows:
xi ii ii i
rr rd rr dr rd
=- +- +pp
MD
K
where M ,r
D ,r and Kr
() () (),
oo
(5)
denote the desired mass, damping,
and stiffness matrices. di denotes the desired joint angle of
Figure 3. Simulation results of LR prediction method.
(a) Prediction performance with different prediction steps p.
(b) xp in different prediction serial numbers p. (c) xp in different
initial values in the same p.
DECEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
29
15
20
25
30
10
5
200
400
600
Initial Value = 5
Initial Value = 13
Initial Value = 20
Initial Value = 30
Train_Number
800 1,000 1,200
(c)
15
20
25
the first n frames, and n moving average values of each frame
iho ()t
10
5
200 400 600
Train_Number
(b)
Step = 20
Step = 18
Step = 15
Step = 13
Step = 10
800 1,000 1,200
can handle the situation for different
and different prediction serial numbers
h
,
()
()
the robot, and ri denotes the reference joint angle. We design
the desired trajectory di as () ()
positive scalar.
ii ax=-o
to
(3)
represents the prediction error, and f ! (, )01
2.2
1.2
1.4
1.6
1.8
2
0.6
0.8
1
0.4
Time (s)
(a)
Original
p = 10
p = 13
p = 15
p = 18
p = 20
51015202530
p Increasing
dhor
tt , where a is a
xp
xp
Angle (rad)
IEEE Robotics & Automation Magazine - December 2022

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