IEEE Robotics & Automation Magazine - September 2022 - 120

For question 3, in the optimization
50
40
20
20
01020300
(e)
10
5
4
2
01020300
(g)
2.5
2
0.72
0.7
01020300
(i)
10
Simulation Steps
(j)
Figure 18. A comparison of the estimated 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 the
normal planning, the solid line signifies the tension-optimization planning, and the
horizontal line is the respective mean.
20
30
10
(h)
20
30
10
(f)
20
30
50
01020300
(a)
20
01020300
(c)
14
12
10
8
6
10
(d)
20
30
10
(b)
20
30
search, the result mainly depends on
the fitness function. Therefore, the
goal of reducing the cable length can
be achieved by constructing a new fitness
function. First, under the
assumption that there are no other
restrictions, such as obstacles, we can
calculate the root position of the link
that makes the selected cable have the
shortest length, defined as .Jt
Subsequently,
in the optimization search,
for the position of
closer to Jt
J ,new making it
shortens the corresponding
cable length.
Therefore, in the fitness function, a
variable that measures the distance
between Jnew
and Jt
can be used to
represent the degree of the cable length
reduction, that is, the degree of the
cable tension reduction.
For the fitness function of general
link planning, an angle is used to represent
the amount of linkage movement.
To ensure the comparability of
these two variables, the angle X
between vectors JJ()()
newnew
+
kk1
JJ is used to represent the distance
between Jnew
() ()
t
new
+
k
1
k
and J . t Finally, the
new fitness function in general link
planning is as follows:
Qd
fit = *
∞
ha h X
12
))
+
forward
reverse
collision
.
(20)
For root planning, because the root
joint can move along the slider segment,
its possible location Jt
is not
fixed. The original fitness function
uses the distance of some position to
the slider segment. Thus, the distance
from this position to a line is also used
here to represent its proximity to .Jt
This line passes through
J ,t and it is
(a)
(b)
Figure 19. The (a) snake-like manipulator and (b) obstacle environment.
the cable tension is positively correlated with the change in its
length: when the cable becomes longer, the tension becomes
larger; when the cable becomes shorter, the tension decreases.
Therefore, when planning the link position, the adjustment of
the posture in the direction of reducing the length of the
selected cable can be used to reduce the cable tension.
120 * IEEE ROBOTICS & AUTOMATION MAGAZINE * SEPTEMBER 2022
Q ∞.
dd
fit = *
∞
hh line
))
slider +
collision
notinthe bulletarea
12 othersituation
parallel to the slider segment. Finally,
during root planning, the fitness function
is updated:
(21)
Because any secondary goals will consume the redundancy,
and the joints in the different positions have different
and
Tension (kgf)
IEEE Robotics & Automation Magazine - September 2022

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