IEEE Robotics & Automation Magazine - March 2023 - 57

angle of the joint motor requires a compensation term in addition
to the described solution (21). The compensation includes
the spring deflection angle due to the end-effector tension and
gravity. The compression caused by the end-effector tension
()_sj adj
z
-
pression caused by gravity ()g adjz -
ing to (23). A _sj and K _sj are the center distance matrix and
stiffness matrix of each joint, respectively:
z--= InverseKinematics Ptgtadj
zz zz=+ + g
tgtadj
tgtcomptgt adjadj
JFtgt
-
sj-adj =
zg-adj =
6xx x
^h
gg g @T
AK_
^ AK h
,, ,
sj sj
2
sj sj
_
_
12 6
2
f
.
_
EXPERIMENTS
Four experiments are conducted to evaluate the proposed
method. In the first experiment, the performance of the proposed
method for estimating the tension direction was tested.
In the second experiment, the tension control effect of
the end effector was verified independently. In the third
experiment, the effectiveness of the proposed force-position-decoupling
control strategy was demonstrated. In the
final experiment, the effectiveness of the proposed force-
position-decoupling control strategy in the bandaging task
was validated. Ethics approval and informed consent were
obtained from all participants, and the protocol was
approved by the Ethics Committee of Guangdong University
of Technology (Gdutxs2022104).
Sawyer, a collaborative robot built by Rethink Robotics
GmbH, was used instead of a human arm, and the prosthesis
was fixed to the end of Sawyer. The main function of the
Sawyer robot is to use the flexibility of its joints to simulate
the movement of a human arm. In the experiments, the stiffness
of the Sawyer joints was used as the default stiffness of
its system. The experimental conditions were set up as shown
in Figure 7, divided into two situations: an adult male and
Sawyer. Sawyer was used to analyze repeatable positioning
accuracy, and the adult male was used to prove that the
robot arm, using this algorithm, can complete the bandaging
task. In addition, the force of the band was set to 2.5 N in the
experiments. Please notice that the tension
of the bandage was measured with
the end effector of the robot proposed
in this article.
The algorithm ran on a PC with an
Intel Core i7-7700HQ (2.8 GHz) with
MATLAB version 2016 b, which performs
the upper control. The lower control
is fitted into an STM32F4, which
can receive and send motor commands
and sensor system information. The
communication frequency between the
upper and lower computers is 200 Hz.
360
270
180
90
(23)
FORCE CONTROL OF THE END EFFECTOR
In this section, experiments were implemented to independently
verify the force control performance of the end effector. The initial
position of the prosthesis (in the workspace) and the target
force of the band are selected as the input of the force control
method. The first through sixth joints are set in the locked state,
and the prosthesis is required to move according to a preset trajectory
(the speed of the prosthesis is set to 50 mm/s) to simulate
the human limb moving. The proposed force control (.S 05=
and
K 800ul =
z _
-- --sj _
^ ^ztgtadjhhT
adj
^h (20)
(21)
(22)
is compensated for according to (22), while the comis
compensated for accordESTIMATION
OF THE FORCE DIRECTION
In this section, experiments were designed to verify the effectiveness
of the estimation method. The first through sixth
joints of the robot arm were locked, and the end effector performed
the force control (see the " Bandage Tension Control
of the End Effector " section for details). The prosthesis
moved along a circular trajectory in the cross section of the
end effector. The effectiveness of this method is verified by
comparing the estimated direction with the direction measured
by the motion capture system (OptiTrack Co., Ltd.). As
shown in Figure 8, the results show that the estimated
direction roughly coincides with the visually measured direction.
The mean error is 2.85°.
) and the traditional PD control ()P 5= are compared.
For both methods, the gain of damping K _de is set to
0.01. The target tension is set to be 2.5 N. The results are shown
in Figure 9. The peak tension error of the proposed method is
0°/360°
270°
90°
Force
Direction
180°
(a)
(b)
FIGURE 7. The experimental conditions. (a) An adult male: the robot
arm was connected to the arm of an adult male through a band to
finish the fourth experiment. (b) Sawyer: the prosthesis was fixed to
the end of Sawyer to finish the first, second, and third experiments.
Visual Measurement
Indirect Measurement 1
Indirect Measurement 2
θδ = 180°
θδ1 = 169°
θδ2 = 165°
05 10
15
Times (s)
FIGURE 8. A comparison of indirect measurement and visual measurement. An
estimation of the force direction id
is measured by the motion capture system (OptiTrack
Co., Ltd.);
i 1d
t
and 2id
t
estimation method.
MARCH 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
57
are the angles of two different experiments estimated by using the
20
θδ = 270°
θδ1 = 290°
θδ2 = 277°
25
30
Angle (°)
"
"
"
"
IEEE Robotics & Automation Magazine - March 2023

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