IEEE Robotics & Automation Magazine - March 2016 - 31

controller with passive loop rejected up to 100 ms with the
tilting surface.
The consideration of different sampling rates, shown in
Figure 7(b), supported these findings. The MC and DEC
without passive loop controllers remained stable until
20 Hz of sampling rate. With the tilting surface, the DEC
without passive loop controller reached the same 20 Hz,
and the MC controller was more robust as it could reject
10 Hz. The DEC with passive loop reached down to
10 Hz, the same sampling rate it reached with this experiment as before.

9
aCOM (°)

aCOM (°)

Compliant Support Surface
This section investigates the ability of the MC and the
DEC controllers to reject an impulse disturbance while
balancing on a compliant support surface (with no time
delay for the control signals). The robot was placed with
both feet on one to three layers of gym mats, and afterward it was hit by a mass of 5 kg, as shown in Figure 1(f).
The robot received the impact at the hip, and it was intended to create a motion mainly in the sagittal plane.
One of the biggest challenges of balancing on a compliant
support surface is that the robot is not stable by default,

and needs to be actively stabilized by a controller. Since
the DEC approach only works in the sagittal plane, motions of the robot out of this plane are needed to be additionally stabilized. Two long ropes were stretched to the
left and to the right, preventing the robot from tipping
over to the side, while having a long enough lever arm to
avoid obstructions to the controller performance in the
sagittal plane. In contrast, the MC controller is capable of
stabilizing the robot in all directions of space. Instead of
using ropes, in this case, all the joints in the lower body
were activated, thus allowing the system to stabilize itself
in the frontal as well as in the sagittal plane.
The trajectories of the COM pitch angles and the foot
pitch angles (left and right) are provided in Figure 8. It can
be observed that for both controllers, the amplitude of
COM pitch angle sway is signiﬁcantly smaller than the amplitude of foot pitch sway. Thus, the ankle joints work very
hard toward reducing the overall COM movement, which
is smaller for the MC controller than for the DEC controller. For the latter, the difference between motion in the left
and the right foot is smaller than for the former, which
could suggest better adaptation to the underlying control
task. However, this could also be simply due to the fact that

6
3

aCOM,1
aCOM,2
aCOM,3

6
3

-3

-3
-6

-6

(b)

9
aFoot (°)

aFoot (°)

(a)

6
3

-3

-6

4
5
6
Time t (s)
(c)

aFoot,R,1
aFoot,L,1
aFoot,R,2
aFoot,L,2
aFoot,R,3
aFoot,L,3

-6

5
6
Time t (s)
(d)

Figure 8. (a)-(d) The impulse responses of the DEC controller with passive loop (a, c) and the MC controller (b, d) while balancing
on different compliant support surfaces. The top graph shows the COM pitch angle trajectories, while the bottom graph shows the
corresponding foot pitch angle trajectories. The index indicates the number of used mattresses. The amplitude of the foot angles is much
higher than the COM angles, highlighting the controllers' effort to stabilize the system. While the DEC with passive loop controller becomes
unstable when the robot receives an impulse standing on two layers of compliant support, the MC controller does so on three layers.

march 2016

IEEE ROBOTICS & AUTOMATION MAGAZINE

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