IEEE Robotics & Automation Magazine - September 2018 - 24

The ATRIAS biped [3] is a physical embodiment of this
mechanical intelligence approach [24], equipped with four
degrees of passive compliance in its legs and motor-free pin
joints for feet. While eschewing actuators and inserting
springs make control less formally tractable [4], we found
that thoughtfully applying insights from reduced-order
models [5] can yield a range of agile and stable locomotion
behaviors. In doing so, we aimed to demonstrate that three-dimen-
sional (3-D) bipedal walking and running are not only possi-
ble with a passive-dynamics-based approach, but that the
result is sufficiently robust to serve as a viable framework for
practical locomotion in unstructured environments.

Table 1. The specifications of the ATRIAS
bipedal robot.
ATRIAS at a Glance
Top speed

2.5 m/s

Maximum ground height variation

15 cm

Maximum kick impulse

60 kg·m/s

Surface incline

15°

Airborne time per step while running

30 ms

Mechanical cost of transport

1.0

Total cost of transport

1.3

Battery life

30 min

Leg length

1.0 m

Height

1.7 m

Weight

60 kg

Spring stiffness

3 kN·m/rad

Leg stiffness at 0.9-m rest length

20 kN/m

Control rate

1.0 kHz

Lines of controller code

880

Figure 1. The ATRIAS bipedal robot performing one of its seven
live dynamic demonstrations in front of a live audience at the
DARPA Robotics Challenge. For one component of the show, the
spring-legged robot walked over uneven surfaces without visual
sensing or external support.

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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september 2018

Zero moment point (ZMP) approaches have long been the
go-to methods for generating stable bipedal locomotion [6]. The
core strategy of maintaining full actuation through flat-footed
contact is at the heart of the field's most visible humanoids,
including ASIMO, HUBO, and the HRP-series humanoids [7],
[8], [22]. Given ZMP's track record of success, elaborations of
this basic concept [9] were ubiquitous at the high-stakes
DARPA Robotics Challenge [10], [20], [28], [40], [47], [48].
However, these approaches require planning with respect to the
environment to ensure ZMP criteria. As terrain becomes less
structured and locomotion becomes faster, it becomes more dif-
ficult to rely on planning for locomotion stability.
In contrast to a planning approach, researchers have also
studied locomotion as a potentially self-stable phenomenon
[39]. Using reduced-order spring-mass models [11], they
have developed locomotion strategies to mitigate [12] or
entirely reject disturbances without feedback [13]. These pas-
sively compliant models and corresponding simple control
strategies theoretically have been extended across walking
and running [30], [34]. These math models, while simple, are
sufficiently relevant to biological locomotion that they are
commonly used to analyze stabilization in animal locomotion
[26], [29], [32], [35]. As with animals, our robot will not pre-
cisely match these simple math models, but we may use the
insights from and general behaviors of spring-mass systems to
guide the control policies of our robot toward self-stability.
Likely the most famous examples of insight-driven biped
control were the Raibert hoppers [1] and their successors
[14], which were amazingly agile but required power through
an offboard pneumatic tether. Other examples include the
hyperefficient walkers [15] and [16], which also had control
designed to work effectively with their passive dynamics. Rec-
ognizing some merit to passive dynamics and compliance,
some engineers have begun to develop formal approaches to
the challenge of underactuation in robotics [41], [43]. Varia-
tions on methods such as hybrid zero dynamics [46] have
been successful in achieving planar walking, both with com-
pliance [17], [18], [31] and without [19], as well as running
[42] and preliminary walking implementation in 3-D [36].
Other methods have begun to show promise in simulation for
achieving robust bipedal running [21], [45].
Our specific goal at the DARPA Robotics Challenge was
to exhibit robust walking and running on unstructured ter-
rain with all components, including batteries, onboard the
machine. The purpose was to demonstrate the practical po-
tential of this compliant approach to bipedal locomotion.
With these soft spring-leg mechanisms, we were able both to
walk and smoothly accelerate up to running speeds (2.5 m/s).
The dynamic approach to stability allowed ATRIAS to recover
from large unmodeled impulses (i.e., kicks). Furthermore, we
demonstrated walking on uneven ground without any vision
or preparative planning, including 15-cm steps and nonrigid
terrain. The resulting locomotion was also energy efficient
compared to bipeds of similar scale, with a total cost of
transport (TCoT) of 1.3. (Cost of transport, either mechani-
cal or total, is a nondimensional metric of energy economy,
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