IEEE Robotics & Automation Magazine - September 2018 - 36

ground torques and energy-injecting push-offs would be
delayed on soft ground or an unexpected drop and rushed
when landing on higher ground or stubbing its toe. This
change in timing prevented the controller from applying large
ground forces when they were not feasible.
Verification of Compliant Dynamics
We further sought validation that the designed passive com-
pliance was actually significant when exhibiting these loco-
motion capabilities. Specifically, we asked whether the
springs were deflecting enough, such that they had an
appreciable effect on the gait dynamics during typical loco-
motion. Figure  11 plots the passive spring deflection for
each leg's length (data collected during the same 1.6-m/s
walking experiment used to calculate the TCoT in the
"Energy Economy" section). The peak leg deflection during
walking was approximately 5 cm of the 85-cm leg length. In
terms of energetics, computing the energy stored in each of
the leg mechanisms' two component springs corresponded
to approximately 20-25 J peak per leg, which roughly equat-
ed to the kinetic energy of the 60-kg robot traveling at
0.81-0.91 m/s. Evidently, then, passive compliance is inte-
gral to ATRIAS's dynamics.

Set Point Actual

Demonstration at the DARPA Robotics Challenge
In the course of two days at the beginning of June 2015,
ATRIAS had seven successful shows in front of live audiences
in Pomona, California. Each show demonstrated walking on
rough terrain, running on flat ground, kicks, and dodgeball
impacts. Not once did ATRIAS crash or fall during these
demonstrations. We performed four shows beside our tent
within the Expo area and three in front of the Fairplex Grand-
stands, where the main event was taking place.
Lessons Learned
The ATRIAS biped pushes template matching to the extreme
in its aim to embody the SLIP model. It has carbon-fiber legs
so light they are fairly fragile and require mechanical overload
protection. Even at this end of the scale of passive dynamics,
there are enough discrepancies between the reduced-order
SLIP model and the robot to cause issues for model-based
controllers. In the end, SLIP-inspired controllers were mixed
with natural intuitions and tested in a multibody simulation
to achieve our results.

Left
Right

0.9

Leg Length (m)

This degree of deflection and energetic relevance is impor-
tant for distinguishing this passive compliance approach from
the more general class of series-elastic actuation. Series-elastic
actuation is often used for force measurement (enabling
impedance control techniques), for which comparatively stiff
springs are a satisfactory solution. However, as the springs
become very stiff, the compliance itself becomes less relevant to
the dynamics of the gait. When the time scales of spring com-
pression are orders of magnitude shorter than the time scales of
the gait cycle, the compliant dynamics can be decoupled from
the dynamics and control of a robot's overall motion. Comput-
ing the energy stored in the springs is a good indicator of
whether the compliance is significant to the gait dynamics,
because stored energy approaches zero with increasing stiffness.

0.8

0.7

Practical Control Development
0

Spring Energy
Stored (J)

0.6

0.4

0.8
Time (s)
(a)

Left Leg

1.2

1.6

Right Leg

20
10
0

0.6

0.8
(b)

1.0

1.2

Figure 11. A verification that passive compliance plays a
significant role in the dynamics of a walking gait. (a) A plot
of the set point of the leg length, the length as measured by
the actuator position compared with the actual measured leg
length, which includes spring deflection. The shaded regions
indicate the passive deflection of the leg when in contact with
the ground. (b) A plot of the energy stored in the springs, which
peaks between 20 and 25 J in each leg. This equates to the
kinetic energy of the 60-kg ATRIAS traveling at 0.81-0.91 m/s.
36

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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september 2018

Design Controllers Based on Reduced-Order Insights,
but Test with Multibody Simulators
During early development, we would select touchdown leg
angles for the full-order robot to try to affect a particular apex
height and forward velocity for a SLIP model. A lot of effort
was put into deadbeat controllers to move between apex
states. An equal amount of effort was put into ground-reac-
tion force controllers and virtual-pivot-point controllers. As
we found, these controllers were very sensitive to exact foot
placement (centimeter variations would cause trouble) or to
imprecise force vector control.
No robot will ever perfectly match a reduced-order model
(at least not while matter still has mass), but it is easy for a
robot to approximate simple spring-mass dynamics. The SLIP
model was used extensively to inspire our controller, but
that is where the relationship ends. We manually tuned our
controller in our multibody simulation environment, finding
natural frequency, stride-velocity proportionality, and other
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