IEEE Robotics & Automation Magazine - March 2023 - 54

Ftgt
Fe_c
-
Converting to Force: (1)
eF
PD
δ
→
Fe Fe
Fe
Updating
e→
PI
Ptgt
-
IK
φg_j-adj
δ
δ
→
δ
→
φs_j-adj
JT -1
-
Calculating Gravity Compensation: (14)
Updating Jacobian J
Lrb-d
9L
j φtgt -adj
,τg2
T
As_j · As_j · Ks_ j
T
As_j · As_j · Ks_ j
τg1
,...,τg6
- Lrb-a
φs_j-adj
φg-adj
Rb
φtgt -adj
φtgt-comp
θeef-a
Spring Compression Sensor of the End Effector
θeef
.
End Effector
Converting to Torque: (1) and (2)
φs_j
φm
Fe_c
Spring Compression Sensors of
the First Through Sixth Joints
Motor Sensors of
the First Through Sixth Joints
Angle Sensor
Pact
Compliant Control: (8)
Robotic Arm
FIGURE 3. The control block diagram. IK: inverse kinematics; PD: proportional derivative; PI: proportional integral.
Figure 5 shows the results of a comparison of the workspace
with and without the strategy. Two postures of an injured arm
are set for comparison, including being parallel to the x-axis
and having yaw angle of 45°. The workspace increases by
almost 50% on average. The enlarged workspace ensures that
the robot arm is able to follow the patient's arm even when it
undergoes relatively large swaying.
COMPLIANT CONTROL ALGORITHM
The control algorithm is designed to allow the joint to maintain
the desired stiffness during motion. The algorithm is
based on the position control strategy, which is to control the
Robot Arm
-200
-400
400
-200
y (mm)
-200
i =
m
(a)
-200
-400
400
-200
y (mm)
-200
(b)
FIGURE 4. A comparison of the bandaging trajectory: (a) bandaging
without swaying and (b) the swaying process of the bandaging
trajectory.
54 IEEE ROBOTICS & AUTOMATION MAGAZINE MARCH 2023
200
x (mm)
400
where tgtcomp represents the target position of the joint with
i
-
compensates for gravity and tension of the end effector. More
details are provided in the " Following Strategy. "
BANDAGE TENSION CONTROL OF THE END EFFECTOR
The tension of the bandage is measured by the SEA of the
end effector. Different from others joints' SEAs, the end
200
x (mm)
Equation (7) describes the control relationship of the motor
output angle for the case where the desired joint angle is zero.
When the desired joint angle is not zero, the output angle of
the joint motor is given by the following equation:
ii kk
i =
m
tg sdtcomp
kd
- --^h
(8)
400
Forearm
motor output angle by a given control law to obtain the
desired stiffness. Equation (4) describes the kinetic model of
the joints under Laplace transform, while (5) is the designed
control law of the motor's output angle.
I ,l xl , im , il , D, k,
and kd are the equivalent inertia of the load on the joint,
external torque, output angle of the motor, output angle of the
joint, damping of the joint, stiffness of the SEA, and desired
stiffness. Equation (6) is the equivalent model after bringing
in the control law of (5). As the model shows, the system's
equivalent stiffness is changed to :kd
Is Ds k^hii ii x++ -= 1
^hll
ll m
2
i =
m
i kk
k
Is Ds kii2
ll
ld
ll ++ ix= l
dl
.
ii i=sl
:m
(4)
(5)
(6)
The sensor of the SEA measures the compress angle of
spring si rather than the joint's output. Equation (5) is changed
to (7) according to the relationship of
i kk
sd
kd
^h.
(7)
z
(mm)
z (mm)
IEEE Robotics & Automation Magazine - March 2023

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2023
