IEEE Robotics & Automation Magazine - March 2016 - 30

0.1
xSupport (°)

xSupport (°)

0.1
0.05
0

0.05
0

- 0.05
30 ms

40 ms

DECPL-On
aCOM (°)

6
4
2
0
−2

0 ms

40 ms

80 ms

90 ms

6
4
2
0
−2

0 ms

20 ms

40 ms

50 ms

0

1

2

3

4
5
Time t (s)
(a)

6

7

6
4
2
0
−2

1,000 Hz

DECPL-Off
aCOM (°)

20 ms

6
4
2
0
−2
6
4
2
0
−2

8

100 Hz

1,000 Hz
10 Hz

DECPL-On
aCOM (°)

0 ms

MC
aCOM (°)

DECPL-Off
aCOM (°)

6
4
2
0
−2

MC
aCOM (°)

-0.05

0

1,000 Hz

100 Hz

1

3

2

20 Hz

10 Hz

100 Hz
5 Hz

20 Hz

20 Hz

4
5
Time t (s)
(b)

10 Hz

6

7

8

Figure 7. The COM pitch angle trajectories for a translation disturbance in the support surface with (a) different high-level control
delays and (b) different sampling rates. The top row shows the commanded and measured translation for the support surface (black
and gray, respectively). The DEC without passive loop controller (DEC PL - off) is outperformed by the MC controller (Dt max = 30 ms
versus Dt max = 40 ms, respectively). Activation of a low-level passive loop in the joints (DEC PL - on) increases DEC with passive loop
controller performance (Dt max = 80 ms) above the MC controller performance. The same trend is observed for the different sampling
rates of high-level commands: the passive loop brings the DEC with passive loop controller performance (fsampling, min = 10 Hz) beyond
the MC controller performance (fsampling, min = 20 Hz).

significantly improved the performance. Joint failure was prevented and the system remained stable until 100 ms of time
delay, increasing robustness against high-level delay even
above the MC controller. The passive loop allowed the system
to react to the disturbance instantaneously, passive stiffness
and damping counteracting plantar ﬂexion. Therefore, the
impact of the impulse disturbance was reduced
before the high-level conHumans use feedback
troller became active to
stabilize the robot.
loops with different
A similar trend was
observed when considertime delays.
ing the high-level sampling rate, as shown in
Figure 6(b). Activating the passive loop in the DEC controller increased robustness against low sampling rates from 20
to 10 Hz, making it comparable to the MC controller. The
data obtained from these experiments conﬁrms that incorporating a low-level passive loop with the original high-level
controller can have a positive inﬂuence on the controller's
overall robustness.
30

*

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

march 2016

Acceleration Disturbance in the Support Surface
To conﬁrm the increase in robustness against high-level delays and sampling rate limitations by the passive loop, we
introduced a different perturbation. The system was placed
on a linear motion platform powered by a linear motor, as
shown in Figure  1(e). The platform was displaced 0.04 m
within 0.5 s, starting from rest, moving the robot backwards. The resulting COM pitch angle trajectories for the
MC controller and the two variants of the DEC controller
are provided in Figure 7(a) and (b), when different time delays and sampling rates are considered.
The DEC without the passive loop controller has a higher
robustness for this type of perturbation [Figure 7(a)], as it
became unstable at 15 ms of time delay for the tilting surface,
and now it is stable up to 30 ms of time delay (at 40 ms there
was an emergency shutdown due to instability). However, it
still performed worse than the MC controller, which was capable of reaching 40 ms of time delay (although it could
stand up to 70 ms of time delay with the tilting surface).
Again, an activation of the passive loop increased the performance of the DEC controller, rejecting a time delay of 80 ms,
which outperforms the MC controller. Note that the DEC
Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2016
