IEEE Robotics & Automation Magazine - September 2021 - 134

Position
-5
5
0246 8101214161820
t (s)
(a)
Velocity
-1
1
0246 8101214161820
t (s)
(b)
Acceleration
-5
5
0246 8101214161820
t (s)
(c)
Joint1
Joint2
Joint3
Joint4
Joint5
Joint6
Joint7
Figure 2. The (a) joint position, (b) velocity, and (c) acceleration zoom representation of the first 20 s of the third trajectory. The full
version of the trajectory is used as the identification data set.
10
20
-20
-10
2
4
4.4
Zoom
t (s)
5
5
10
t (s)
Figure 3. The low-pass filter effect on joint torque: an example for the second joint of the
third trajectory. A zoom-in plot in the time interval of 4.4-5 s is reported.
In practice, this means properly spanning the collected
data within the allowed range of joint positions, velocities,
and accelerations characterizing the robot under study. In
our cases, five different trajectories have been considered
and generated as in [4], each playing the role of identification
trajectory; the remaining ones play the role of validation
trajectories.
As an example, one exciting trajectory is shown in Figure 2.
The corresponding base regressor is characterized by a condition
number of approximately 50 with a minimal singular value of 34.
134 * IEEE ROBOTICS & AUTOMATION MAGAZINE * SEPTEMBER 2021
15
20
Real Torque
Filtered Torque
Data Filtering
Since the data are spoiled from noise,
it is necessary to carry out low-pass
filtering on these data. A Butterworth
second-order low-pass filter with a
cutoff frequency equal to 5 Hz has
been implemented. In the literature, a
similar choice of cutoff frequency is
adopted; for example, in [9], the
value of 1 Hz has been used in the
identification of the KUKA LWR IV.
In Figure 3, an example of the effect
of filtering on the torque data of joint
2 in one of trajectories is reported.
Results and Discussion
The CAD parameter values have been derived from the
official repository of the manufacturer [20], properly
referred to the adopted DH-compliant frames by resorting
to the Huygens-Steiner theorem. Moreover, the identification
algorithms described previously have been run. The
identified parameters are reported in Table 4, together
with the corresponding variance of the estimate (for
instance, the fourth trajectory is adopted to the scope of
identification, and the third trajectory is adopted for the
t2 (N. m)
q (rad/s2)
˙˙
t2 (N. m)
q (rad/s)˙
q (rad)

IEEE Robotics & Automation Magazine - September 2021

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