IEEE Robotics & Automation Magazine - September 2022 - 122

requirements for the tension optimization, a different 1h and
h 2
to each joint could be presented to achieve a better balance
for the flexibility and tension optimization. The tension optimization
is not added to reverse planning because the highest-priority
goal at that time is to make the root joint meet the
constraints of the propulsion platform.
In summary, when tension optimization is enabled, the fitness
function in each phase of the joint-following algorithm is
shown in Table 2. In addition to the parameters in Table 1, in
Table 2, X is the angle between JJ()()
dline is the distance from J k
newnew
+
kk1
new
^h
Jt and parallel to the slider segment.
Simulation and Experiment
In this section, we establish simulations and actual experimental
environments for obstacle-avoidance path planning.
Simulation
This simulation mainly verifies the functional effectiveness of
the algorithm and effect of the tension optimization. We
designed a real environment based on this and configured the
obstacles as shown in Figure 15.
and JJ , and
() ()k
t
new
+
k
1
to the line that passes through
The manipulator was placed along the y-axis, and its end
was placed at the origin point. The manipulator has 10
joints, and each link is 140 mm in length and 60 mm in diameter.
It should be noted that the line in Figure 15 is the
central axis of the links, and the diameter of the link is not
shown; this is the same for subsequent figures as well. The
obstacle is a cylinder that is represented by spheres; its center
coordinate is (120, 430, -120), length is 60 mm, and radius
is 140 mm.
First, we simulated normal planning without tension optimization.
The moving process of the manipulator is shown in
Figure 16.
The joints near the end successfully avoided the obstacles.
The following process for the other joints was also
smooth and continuous, and the path of the manipulator
met expectations.
Next, we simulated another path-planning method by
38.5
38
050
(a)
10
20
050
(c)
20
15
10
050
(e)
10
5
050
(g)
6
4
2
050
(i)
33
32.5
100 050
(b)
20
10
100 050
(d)
15
5
10
100 050
(f)
10
5
100 050
(h)
4
2
100 050
(j)
Normalized Time
Figure 21. A comparison of the actual maximum cable tension for joints (a) 1, (b) 2,
(c) 3, (d) 4, (e) 5, (f) 6, (g) 7, (h) 8, (i) 9, and (j) 10. The dashed line represents normal
planning, the solid line signifies the tension-optimization planning, and the horizontal
line is the respective mean.
122 * IEEE ROBOTICS & AUTOMATION MAGAZINE * SEPTEMBER 2022
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100
100
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using tension optimization. According to the optimization
method, we assume that the load of the joint does not
change significantly every time the manipulator moves.
Therefore, we enable tension optimization only of the last
three joints to observe its effect. A comparison of the moving
process between normal planning
and tension-optimization planning is
shown in Figure 17.
After the enabled tension optimization,
the manipulator can still avoid
obstacles. At the same time, the postures
of the last three joints are different
from normal planning. The
postures of the other joints also
change relative to their situations in
normal planning, which becomes
more obvious after the end joint
enters the inside of the cylinder obstacle.
These changes show that the X in
the fitness function plays its role of
adjusting the postures of the joints
under the premise of satisfying obstacle
avoidance. In addition, it can be
seen that tension optimization has a
negative effect on the smoothness of
the overall path. This indicates that
any task that relies on posture adjustment
will " consume " the redundant
DoF of the manipulator, causing it to
lose a certain degree of flexibility.
The tension model was also used to
estimate the maximum cable tension of
each joint according to the posture of
the manipulator at each step. A comparison
of the path and tension-optimization
paths is shown in Figure 18.
When tension optimization was
enabled, the maximum cable tensions
of the last three joints were reduced to
Tension (kgf)
IEEE Robotics & Automation Magazine - September 2022

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