IEEE Robotics & Automation Magazine - September 2023 - 64

position in the haptic device coordinate
system, and
k RI ! is a linear scal.
ing
factor used to amplify the low
operation forces up to a value that an
operator can easily feel. In this example,
k 5 N/mm
I =
is selected as comfortable
for the user to operate.
When the robot starts machining, the
process sound frequency is detected, and
the force feedback is obtained as
Fk RFH
I
= $$
II
EtoH M .
(7)
In this stage, FM is the radial machining
force, RSO 3
EtoH ! ^h is the rotation
matrix from the robot's frame to the haptic
device's frame, and kII is an adjustable
scaling factor to amplify the force for an improved user
experience. For the experiments in this article, considering
the range of FM and haptic device specifications ( " 3D System, "
maximum feedback force of 3.3 N), kII is set to a standard
of 30 to amplify the feedback force to a suitable range in
which the operator can feel the feedback force variety clearly.
For improved sensitivity in a lower force range, higher values
(e.g., 100) can be selected, but they lead to force feedback saturation
in the higher force range.
Apart from the preceding stages, a third feedback mode
is introduced to prevent stalling. If the measured sound frequency
is lower than a critical limit frequency, close to the stall
position as measured in the calibration experiment or out of
the system detection range, our system creates a " virtual wall "
to stop the user from getting closer to stalling or uncontrolled
operation. The farther an operator moves the haptic joystick
in the critical direction, the stronger the haptic force added to
the stop motion. When moving in any other direction (thus,
farther from risk), no force is experienced. This haptic force
FH
I is defined as
F =)
H
I
kP Pr R
rR
III H
I
^h,
H
S
,
00$
#
signal
reaches the alert area, r R3
motion of the haptic device, R R3
!
$ 2 0
(8)
where PH
S is the haptic device position recorded when the
! is the direction of
is the force vector
mapped in the haptic reference frame, and k I =II 20 N/mm is
the stiffness of the haptic " virtual wall. " This force feedback
at different stages is summarized in Figure 7, where finitial
represents the lower boundary of the sound frequency when
Springlike Force
FI
H
f
finitial
falert
Machining Force Feedback
FI
H
FI
THE SYSTEM PROVED
CAPABLE OF REALIZING
STABLE AND ACCURATE
MOTION CONTROL, PREVENTING
THE USER FROM
STALLING OR MOVING
THE ROBOT TO A CRITICAL
CONFIGURATION.
„
"
no external force acts on the machining
tool and
t = ,
faler 2 000 Hz is the lower
frequency that the system can reliably
detect without risking stalling and the
environmental noise covering the first
mode of the tool's frequency. The user is
thus alerted with the strong feedback of
the stiff virtual wall.
Even though the example system
uses the control architecture given in Figure
2, due to hardware limitations, the
three control blocks described previously
have different update rates: the
update rate of block A is about 500 Hz,
limited mainly by the sample time of the
sound signal acquisition; block B runs at
1,000 Hz, a commonly used refresh rate
for haptic devices; and block C is updated at 400 Hz, mainly
constrained by the computational time needed to solve
robot kinematics. Thus, the system runs the three loops in an
asynchronous execution.
EXPERIMENTAL VALIDATION
In this section, two sets of experiments are carried out to
evaluate the performance of the proposed method in the
example from the " An Example: Haptic Control of Machining
Tasks " section: a calibration test to map force to acquired
sound, and a demonstration of the system.
Virtual Wall
H
Acquired Frequency
FIGURE 7. The feedback force strategy for the machining application example.
64 IEEE ROBOTICS & AUTOMATION MAGAZINE SEPTEMBER 2023
MACHINING FORCE ESTIMATION TEST
To obtain the relationship between force and spindle frequency,
we repeat the experimental calibration process in the " An
Example: Haptic Control of Machining Tasks " section for
three scenarios: milling and grinding titanium and milling aluminum.
Each trial is repeated 25 times, with results in Figure 8
and Table 2. The curves in Figure 8(a) are generated by a simple
interpolation, but machine learning could be used for a
more accurate estimation. The three curves fit the average
radial force value, showing a similar near-linear behavior for
each configuration, validating our force estimation method
for different processes and materials. In Figure 8(b)-(d), the
error between the estimated (sound-based) and acquired (load
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