IEEE Robotics & Automation Magazine - March 2016 - 29

6
4
2
0
−2

aSupport (°)
15 ms

50 ms

100 ms

120 ms

0 ms

0

1

2

40 ms

3

4
5
Time t (s)
(a)

70 ms

6

6
4
2
0
−2
6
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2
0
−2

80 ms

7

1,000 Hz

DECPL-Off
aCOM (°)

6
4
2
0
−2

0 ms

10 ms

DECPL-On
aCOM (°)

DECPL-On
aCOM (°)

6
4
2
0
−2

0 ms

8

6
4
2
0
−2

aCOM (°)

DECPL-Off
aCOM (°)

6
4
2
0
−2

MC
aCOM (°)

aSupport (°)

6
4
2
0
-2

0

1

100 Hz

20 Hz

10 Hz

1,000 Hz
10 Hz

100 Hz
5 Hz

20 Hz

1,000 Hz
10 Hz

100 Hz
5 Hz

20 Hz

2

3

4
5
Time t (s)
(b)

6

7

8

Figure 6. The COM pitch angle trajectories for a tilt disturbance in the support surface with (a) different high-level control delays
and (b) different sampling rates. The top row shows the instant where the support of the surface is removed (black) and the
measured pitch angle of the feet (gray). The DEC without passive loop controller (DEC PL - off) is outperformed by the MC controller
(Dt max = 10 ms versus Dt max = 70 ms, respectively). Activation of a low-level passive loop in the joints (DEC with passive loop,
DEC PL - on) increases DEC performance (Dt max = 100 ms) above the performance of the MC controller. The same trend is observed
for different sampling rates of high-level commands: the low-level passive loop brings the DEC without passive loop controller
(fsampling, min = 20 Hz) almost on par with the MC controller (fsampling,min = 10 Hz) .

high-level commands of our controllers and asserting the respective robustnesses were, therefore, identiﬁed as an interesting aspect with regard to biomimetics. From a technical
perspective, the sampling rate for the execution of the highlevel controllers becomes an important factor, as it restricts
the complexity of the underlying computations. We, therefore, chose the high-level sampling rate as the second individual parameter to be varied.
We compared the behavior of the controllers when the
robot is subjected to a tilt disturbance on the support surface
[Figure 1(d)]. As the DEC controller features a passive loop,
which can be implemented directly within the joints' low-level controllers, we created two versions of the DEC controller,
namely, DEC without passive loop (DEC PL - off ) and DEC
with passive loop (DEC PL - on) . The delay and sampling rates
of the low-level commands were hereby not altered and remained at 0 ms and 1,000 Hz, respectively.
The system was placed on a wooden rocker board that
pivoted at its center around the normal to the sagittal plane
[Figure 1(d)]. The total pivoting angle was 4°. The board was
kept horizontal by using a support block, and the back of the
robot's heels was aligned with the pivoting axis. The system's

COM was located in front of the axis. The support block was
then removed manually, causing the board to tilt due to the
robot's weight, while the robot swayed forward. For both the
MC and DEC controllers, the time delay was increased from
0 ms, until the point
where the system became
The passive and SL
unstable. In a similar way,
the sampling rate was deloops form a servo
creased (in the absence of
delay) starting from 1,000
mechanism.
Hz, until the point where
the system became unstable. The obtained trajectories for the COM pitch angle with respect to the normal to
the sagittal plane passing through the robot's ankles are
shown in Figure 6(a) and (b).
The MC controller was able to reject much higher delays
than the DEC controller when the passive loop was inactive
(Figure 6). While the former remained stable until 70 ms of
time delay, the latter was unable to withstand 15 ms of delay,
as the ankle joints shut off due to active torque limit violation.
However, activating the passive loop in the DEC controller
march 2016

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2016
