Information Technology Reference
In-Depth Information
−
3
q
d
(0)]
(3.11)
1
2
t
b
t
b
[2
c
a
−
k
4
=
30 [
q
b
−
q
d
(0)] +
t
b
[14
c
v
+16
q
d
(0)]
−
12 [
q
b
−
q
d
(0)]
1
2
t
b
6
t
b
[
c
v
+
q
d
(0)] +
t
b
[
c
a
−
k
5
=
q
d
(0)]
−
(3.12)
where
c
v
,
c
a
represent arbitrary vectors. If the hitting time and swing time are con-
stant during the swing motion, the vectors are represented by
c
v
=
q
d
(
t
b
)
c
a
=
q
d
(
t
b
)
respectively. Thus we can set the speed of the manipulator at the hitting point by ad-
justing the arbitrary vectors.
To increase the velocity of the end-effector in the serial link mechanism, it is
necessary to speed up the velocity of the joints on the bottom side. Then it is easy to
modify the trajectory of the joints on the top side during the swing motion, so that
the manipulator can track an unpredictable target motion. This is because the inertia
of the top side is lower than that of the bottom side. For this reason, the bottom side
is controlled only in the SW mode, and the top side is controlled in the HT mode.
Define the vector
q
s
b
,
as
q
s
b
=
l
−
1
p
01
(
t
b
)
,
φ
d
(
t
b
)
.
(3.13)
It is the desired joint angle at the hitting time in the case that the target trajectory is
estimated only by using one sample
p
0
(
t
1
), and it means that the desired trajectory
of the manipulator is not modified during the swing motion. Next, define the vector
q
int
b
q
top
q
top
q
top
=[
q
s
b
1
,
q
s
b
2
,
b
5
]
t
,where
q
s
b
1
and
q
s
b
2
b
3
,
b
4
,
are respectively the first and
. The parameters
q
top
b
3
,
q
top
b
4
,
q
top
b
5
second element of the vector
q
s
b
are decided so that
the following equation holds:
q
in
b
=
l
−
1
(
p
d
(
t
b
)
,
φ
d
(
t
b
))
.
(3.14)
By using
q
in
b
instead of
q
b
in (3.6), the joints 1 and 2 are controlled in the SW mode,
and the joints 3, 4, and 5 are controlled in the integration of the SW and HT mode.
3.2.4
Experiment
In the experiment, a human threw a styrofoam ball with radius 5 cm toward the ma-
nipulator from 2
.
5 m distance, and the manipulator hits the ball toward the objective
3]
T
,and
q
(0)=
q
(0)=
0
, the hitting time
t
b
= 0
point
p
d
=[1
.
90
.
01
.
.
25 s, and the
whole swing time is 0
85 s. In addition, we use a proportional derivative (PD) con-
troller to track the desired trajectory of the manipulator, and the second joint
q
2
is
fixed during the swing motion for safety. After the hitting, the trajectory of the ma-
nipulator is also generated by another fifth order polynomial for the follow-through.
This allows the manipulator to stop smoothly.
From the moment the vision system finds the ball, it takes the ball 0
.
4sto
reach the hitting point. In this experiment, the manipulator must immediately start
to swing just after the vision sensor recognizes the ball, and its period is only 0
.
3
∼
0
.
.
1s.
Search WWH ::
Custom Search