IEEE Robotics & Automation Magazine - March 2016 - 28

The estimation of the state of the COM was obtained using information coming from internal sensors, namely the onboard
IMU and the kinematic information of the robot. Since the DEC
controller is designed specifically for balancing in the sagittal
plane, the MC controller was artiﬁcially restricted to move only
in the same plane to provide a fair comparison beThe DEC concept successfully tween both concepts. For
the DEC concept, the control action x p, i of the pasreproduces human
sive loop would ideally be
implemented through a
balancing in simulations
local low-level joint controller working at a high
and in experiments using
sampling rate, separate
from the additional higha humanoid robot [17].
level full-state feedback
controller. Our implementation of this low-level passive loop uses the same real-time
system as the high-level controller. While low- and high-level
commands were generated by the high-level controller environment, the former maintained a 0-ms artiﬁcial delay and 1,000Hz sampling rate throughout all trials.
All experiments have been performed with the default set of
parameters listed in Tables 1 and 2, unless otherwise stated.
These parameters were tuned independently for the nominal
case (no time delay and fast controller sampling) on ﬂat ground.
Experimental Comparison
Transient Behavior
The ﬁrst experiment is focused on the transient behavior
generated by the two controllers to illustrate the conceptual
Table 1. The default parameterization
of the MC controller.

differences between both approaches. The robot was manually pushed down and to the front before being released, and
the trajectory of the COM in the sagittal plane was recorded.
This process was repeated 14 times for both the DEC-and
the MC controllers. To highlight the controller's intrinsic behavior, we reduced (for this experiment only) the stiffness
and the damping in the knees to 10 and 70% of their original
values (provided in Table 2), respectively, thus allowing a
larger deviation of the robot from the equilibrium
conﬁguration (especially along the vertical axis).
The recorded trajectories are displayed in Figure 5, where
a typical trajectory is also highlighted for a better understanding. The MC controller moves the COM along an almost linear trajectory connecting the perturbed position
with the equilibrium position and displays a moderate overshoot. In fact, as the MC controller is based on the system's
COM state feedback, it generates a virtual spring and damper
between the current and the desired COM location, thus
generating a trajectory almost along a straight line. In contrast, the DEC approach can be considered as a controller
based on a modular joint feedback. It generates an independent torque command for each joint module without intermodular communication. The trajectories in Figure 5 show a
mutual obstruction between modules, displaying a circular
overshoot. Here, the knee modules command an extension
of the knee pitch joints. As the upper body is also perturbed
to the front, an extension of the knees is counterproductive
for the ankle pitch joints, which try to move the COM back
into the equilibrium position. This effect can reduce the
overall performance of the DEC controller in certain
conﬁgurations, as the one examined in this experiment.
Tilt Disturbance in the Support Surface
One of the characteristics of the DEC algorithm is its robustness against controller delays, as these are inherent to nervous system control. Introducing artiﬁcial delays in the

Parameter Value
0.03

diag (0.25 Ns/m, 0.15 Ns/m, 0 Ns/m, f
15 Nms/rad, 17 Nms/rad, 10 Nms/rad)

diag (200 Nm, 100 Nm, 200 Nm)

DEC
Goal

−0.03

- 0.03

Table 2. The default parameterization
of the DEC controller.

Parameter

Ankle

Knee

Hip

K a, i

m 3 gh 3

m 2 gh 2

m 1 gh 1

D a, i

0.30 m 3 gh 3

0.20 m 2 gh 2

0.20 m 1 gh 1

K p, i

0.15 m 3 gh 3

0.15 m 2 gh 2

0.15 m 1 gh 1

D p, i

0.05 m 3 gh 3

0.05 m 2 gh 2

0.05 m 1 gh 1

IEEE ROBOTICS & AUTOMATION MAGAZINE

march 2016

Start
0

0.03
Dz (m)

diag (1, 500 N/m, 1, 500 N/m, 3, 000 N/m)
Dz (m)

0.03 0.06

Goal

−0.03

- 0.03

Start
0

0.03 0.06

Dx (m)

(a)

(b)

Figure 5. The COM trajectories for the MC and the DEC controller
after a perturbation from equilibrium in the sagittal plane. Two
consecutive dots correspond to positions obtained with a time
difference of 100 ms. The color of the highlighted trajectories
fades from red into blue over time. (a) The DEC controller's
discrete modules follow conflicting objectives, producing
trajectories with circular overshoot. (b) The MC controller's
whole state feedback-based algorithm produces almost linear
trajectories.

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