IEEE Robotics & Automation Magazine - September 2022 - 113

Finally, combining Vpull al
ing
speed
V .pull
l
VV V
pull
l=+h )-l
pull
apullpullb
,
(4)
where pullh is the pulling coefficient, and the initial value is
one. When the final speed is too small, it gradually increases
until it meets the requirements.
For multiple obstacles, there are various repulsive directions,
and they are often not orthogonal. If the pulling speed
is still decomposed in the way described, there will be a variety
of decomposition results. Therefore, we decomposed
each repulsive direction according to the direction of the
pulling velocity, as shown in Figure 7(b). The components
Vrepain
the direction of the pulling speed and V , which
repbis
perpendicular to the direction of the pulling speed, are calculated
by
|| )
V
repa
-
- =
hi 1h
h
offset ) cos()|| offset
Vpull
||
Vpull
|| offset
VVpull|,
repb =hi) sin()|
offset =
1
1
(5)
(6)
where i is the angle between the direction of the repulsive
speed and opposite direction of the pulling speed.
When considering Vrepafor
all of the obstacles, they are
merged as follows:
VV VV()
12 n
|| (),
()
repa
sum
--= max ||,|
With regard to Vrepbrepb
sum
repa
--repa|, ||,
()
f
()
repa
(7)
for all of the obstacles, they are
merged according to the normal vector summation method:
.
VV VV() ()
()
-- --repb
=+ g++repb
12 ()n
repb
(8)
The final pulling speed Vpulll can be determined as follows:
VV VV=+ h )+pulll
pull
()
a
rep
sum
pull
()
-
repb
sum
(9)
In
summary, starting from the initial point, the moving
point moves toward the target point step by step under the
combined action of the passive repulsive and pull speeds, and
it finally reaches the target point. By fitting all of the waypoints
as a curve, the final guide trajectory can be obtained.
Joint-Following Algorithm
Basic Idea
The second stage of path planning uses the end-guide trajectory
and joint-following method to obtain the obstacleavoidance
path. Joint following means that, when the end of
the manipulator moves along the guiding trajectory, the
Algorithm Flow
The obstacle-avoidance algorithm uses the current posture
of the manipulator as the initial condition and plans the
new positions of each link one by one to obtain a new posture
that can allow the end of the manipulator to reach the
target position. When planning each link position, the following
points should be considered: 1) obstacles must be
avoided, 2) the amount of movement should be as small as
possible, and 3) the root joint needs to meet the requirements
of the propulsion platform (such as moving along a
straight line).
The expected position of the end of the manipulator at
the beginning of the algorithm was derived from the trajectory
that was searched for in the previous section. This trajectory
guides the manipulator forward. Therefore, when
planning, the end of the manipulator does not need to fall on
this trajectory, but it allows a deviation. The joint-following
algorithm is divided into the forward and reverse planning
parts, as shown in Figure 8.
In forward planning, the position of each link is planned
from joint n to joint 1. While planning joint 1 and joint 2,
whether the constraint of the sliding table can be satisfied
must be considered, and, if it cannot be satisfied, reverse planning
is required.
The reverse planning design makes full use of the existing
plan results when the position of the root joint does not meet
the requirements. It adjusts the position of the root joint individually
according to the current planned pose, then it
reversely plans from the root to the end, and finally it checks
the position of the end joint.
The main process in forward planning is Jn-J3 and J2J1
planning. For Jn-J3 planning, as shown in Figure 8(b), general
link or root planning must be performed according to
SEPTEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
113
and Vpull byields
the final pullother
joints follow in turn and avoid the obstacles. Because
the manipulator can bend only at the joint, if the other
joints repeat the trajectory of the end joint in the joint
space, the manipulator posture in the actual workspace
will have unexpected situations, such as colliding with the
obstacles. At the same time, in this case, the potential flexibility
of the proximal joint will be lost. Therefore, it is necessary
to specially design the joint-following algorithm
Xiong et al. [18] proposed an improved algorithm that
moves each joint in turn according to the geometric constraints
of the joints to make the movement more reasonable
and flexible. This study learns from its idea and proposes the
following method with the obstacle-avoidance ability, and it
cooperates with the end-guide trajectory search algorithm
from the previous section to complete obstacle-avoidance path
planning for the hyperredundant manipulator.
In addition, due to the adoption of the optimization search
algorithm to move the joints, cable tension optimization can
also be easily introduced as a secondary goal of path planning.
By using the hyperredundancy of the manipulator,
obstacle avoidance and tension optimization can be realized
at the same time.
IEEE Robotics & Automation Magazine - September 2022

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