IEEE Robotics & Automation Magazine - September 2023 - 59

changing the position and orientation " PR ,II, of the haptic
3
device's control bar, described by position vector P RI
I ! ^h A transformation matrix
!
and rotation matrix RS .O 3
TSE 3
IE ! ^h is used to map the haptic device workspace in
the robot end-effector workspace as position vector
P RE
! 3 and rotation matrix RS .O 3
device as
;;=EE (1)
EE
RP
01
ll
,, ,,
TIE
RP
01
II
.
Then, to drive the actuators of the robot, the joint positions
" 12 lnf , where n is the number of degrees of
freedom (DoF) of the robot, are calculated according to the
robot inverse kinematics. This command process is shown
in Figure 3(a).
A mismatch between the desired position (defined by the
haptic input) and the output motion of the follower robot signals
that the user is sending an unexpected command that is
out of the robot's motion range in either position or velocity.
Hence, this error between the commanded and current position
of the robot is monitored in real time, and a proportional
force feedback is generated to dampen or inhibit any motion
that would increase the error. In every control loop of the
robot motion control mode (in block C in Figure 2), the haptic
device sends its current position
"
PR , I
M
M, as a motion comI
mand
to the robot and then reads the current position of robot
C.
Human
Operator
Motion
Input
User and Haptic Interface
2
Sound Signal Processing
B.
Forward
Kinematics
Force Feature
Scaling
Signal
Processing
Microphone
A.
Robot Control
Robot
FIGURE 2. The control architecture of the proposed system: the robot motion control is in block A, the sound signal acquisition and
processing are in block B, and the haptic interface is in block C, with a switch between motion control without sound feedback (line 1) and
motion control with sound feedback (line 2).
SEPTEMBER 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
59
Robot
Actuation
Force
Feedback
Haptic
Device
Spring Force
Scaling
1
Robot to Haptic
Coordinate
Sound
Transformation
E ! ^h Thus, the commanded
end-effector position in the robot coordinate system
" PR
,EE, can be calculated from the pose of the haptic
actuators ll " 12 f , to obtain the current position of robot
SS ln
S
,, ,
end effector.
In block B (Figure 2), a user can choose how much
he or she wants to " feel " this pose discrepancy with the
haptic device through the virtual coupling method that is
used to generate the force feedback. As detailed in Figure
3(b), based on the inverse process of Figure 3(a) and
the current position of the robot's actuators
" 12 f ,
ll
"
PR ,I
S
I
S
user-adjustable stiffness matrix AA ,AI
M
F
I
"
M, and ,,
I
"
PRI
S
I
S
is generated as
FA PP
MA RR
I ^h
M 1
I
==
F
I
M
I
I
S
I
S
-
I
M
I
(2)
where
F I is the feedback force and MI is the feedback
moment.
TOUCHING THE SOUND
When the robot is executing a sound-generating task,
such as machining, grinding, and polishing, some audible
features (e.g., frequency and amplitude) are due to the
interaction force between the robot's end effector and the
workpiece, as reported in the examples in [18], [22], and [23].
The wrench applied to the robot's end effector is defined
as
WF ,,MEE E, where FE and ME are, respectively, the
= "
Haptic to Robot
Coordinate
Transformation
SS ln
S
,, ,,
the current pose of the robot's end effector is mapped into
the haptic device coordinate system as
I = "
, a feedback wrench WF , MII I,
= "
,. Using a
M, to scale the
springlike force generated by the position error between
PR ,I
Inverse
Kinematics
-
IEEE Robotics & Automation Magazine - September 2023

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