Supplementary Materials for
A bipedal walking robot that can fly, slackline, and skateboard
Kyunam Kim
et al.
Corresponding author: Soon-Jo Chung, sjchung@caltech.edu
Sci. Robot.
6
, eabf8136 (2021)
DOI: 10.1126/scirobotics.abf8136
The PDF file includes:
Supplementary Text
Sections S1 to S7
Figs. S1 to S3
Tables S1 and S2
References (
74
–
79
)
Other Supplementary Material for this manuscript includes the following:
Movies S1 to S8
Supplementary
Text
Section
S1.
Experimental
data
for
walking
on
a
loosely-tensioned
rope
Figure
S1
presents
the
experimental
data
for
walking
on
a
loosely-tensioned
rope.
The
top
plot
shows
the
CoM
x
position
(horizontally
away
from
the
rope)
and
z
position
(upward),
each
plotted
against
the
y
position
(along
the
rope).
The
rope
is
deflected
downward
under
the
weight
of
the
robot,
which
makes
the
mean
z
position
increase
as
the
robot
moves
from
the
center
of
the
rope
toward
the
higher
attachment
point.
A
back-and-forth
movement
is
seen
in
the
y
direction
as
the
robot
takes
each
step,
shifting
its
CoM
from
one
foot
to
the
other
and
back,
as
described
in
the
trajectory
of
Fig.
5.
The
middle
plot
shows
the
evolution
in
time
of
the
tracking
error
in
the
sagittal
and
frontal
planes.
We
notice
periodic
disturbances
in
the
frontal
plane
caused
by
the
foot
advancing
to
a
point
on
the
pulled-down
rope,
which
is
at
a
higher
position
relative
to
where
the
robot
stands.
The
sagittal
plane
has
a
small
tracking
error
compared
to
the
frontal
plane
because
there
is
no
disturbance,
since
the
steps
are
made
in
the
frontal
plane.
The
bottom
plot
shows
the
commanded
propeller
thrust
signals
with
respect
to
time.
Section
S2.
Energy
consumption
and
Cost
of
Transportation
analysis
Although
energy
efficiency
is
not
the
focus
of
the
LEO
design,
the
Cost
of
Transportation
(CoT)
was
analyzed
to
present
the
current
limitations
of
such
a
hybrid
locomotion
system
and
to
inform
future
researchers
interested
in
this
direction
about
potential
challenges
that
have
to
be
addressed.
While
hovering,
LEO
consumes
an
average
of
992
W,
out
of
which
933
W
are
powering
the
propellers
and
59
W
are
powering
the
on-board
electronics
and
leg
actuators.
This
power
consumption
is
almost
cut
in
half
when
LEO
is
walking
on
the
ground,
drawing
an
average
of
544
W,
which
is
split
between
445
W
for
propellers
and
99
W
for
electronics
and
legs.
These
power
measurements
were
made
by
measuring
the
energy
required
to
recharge
LEO’s
battery after performing a walking or flying maneuver. Therefore, they include the overall power
consumption as well as the battery charge/discharge losses. With the relatively small batteries
used on LEO, the resulting flight endurance is about 100 seconds and the walking endurance
is about 3.5 minutes. The limiting factor is the 29 Wh capacity of the battery powering the
propellers.
In Fig. S2, the CoT for different animals, insects, and robotic systems as well as LEO during
its two main locomotion modes are plotted. When walking at a speed of 20 cm/s, the measured
CoT for LEO was
108
. When flying at 1 m/s, the CoT was
48
, and it decreased to
15
.
5
at
the flight speed of 3 m/s. The robots used for comparison have CoT values that are lower
than LEO’s, but they are lacking LEO’s multi-modal capabilities. The data used for the plot is
summarized in Table S2 and in (
74
).
Section S3. LEO’s nonlinear tracking controller: Exponential convergence
proof
The construction of the proof follows (
77
). The closed-loop dynamics is given by:
m
`
2
̇
!
e
+
k
!
e
+
k
I
Z
t
t
0
!
e
dt
0
=
⌧
ext
(6)
where
!
e
= ̇
↵